Mathematics Education in Sub-Saharan Africa: Status, Challenges, and Opportunities George Bethell June 2016 This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colours, denominations, and other information shown on any map in this work do not imply any judgement on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Rights and permissions The material in this work is subject to copyright. Because The World Bank encourages dissemination of its knowledge, this work may be reproduced, in whole or in part for noncommercial purposes as long as full attribution to this work is given. 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Contents Acknowledgements 9 Abbreviations and acronyms 10 Executive summary 13 Chapters 1 Introduction 25 1.1 Objective 25 1.2 Defining Sub-Saharan Africa 26 1.3 Variation and commonalities across the region 26 1.4 Research questions and methods 27 2 Context 31 2.1 Education, skills, and economic benefits 31 2.2 Mathematics in SSA – a suitable case for treatment 32 2.3 Science, technology, engineering and mathematics: their importance to growth 34 2.4 What type of mathematics is needed? 34 2.5 Summary 35 3 Current status: learning outcomes in mathematics in SSA 37 3.1 Context and sources of information 37 3.2 Mathematical achievement in the early years and across the primary phase of education 38 3.2.1 Trends in Mathematics and Science Study (TIMSS) at Grade 4 38 3.2.2 SACMEQ 39 3.2.3 PASEC 42 3.2.4 National assessments 44 3.2.5 Examinations 48 3.2.6 Early Grades Mathematics Assessment (EGMA) 50 3.2.7 Uwezo 51 3.3 Standards in the secondary phases of education 52 3.3.1 TIMSS at Grade 8 52 3.3.2 PISA 54 3.3.3 National assessments 55 3.4 The learning deficit and change over time 58 3.4.1 TIMSS 59 3.4.2 SACMEQ 59 3.4.3 Uwezo 60 3.4.4 National assessments 61 3.5 Summary 62 1 4 Factors affecting learning outcomes 65 4.1 Introduction 65 4.2 School quality 67 4.3 Interventions for improving outcomes 67 4.3.1 Expenditure on education 67 4.3.2 Pedagogical interventions 68 4.3.3 Strengthening accountability 69 4.4 Summary 69 5 Factors affecting learning outcomes in mathematics 71 5.1 Context 71 5.2 Culture and attitudes 72 5.3 Gender and mathematical achievement 75 5.4 Curricula 79 5.5 Teachers of mathematics 80 5.6 Textbooks 81 5.7 Assessment practices 83 5.8 Educational technologies 85 5.9 Summary 86 6 Teachers’ capacities and teaching conditions 89 6.1 Introduction 89 6.2 Evidence as to capacities 89 6.2.1 Mathematical capacity 90 6.3 Classroom conditions and pedagogical practices 93 6.3.1 Class size 94 6.3.2 Language of instruction 94 6.3.3 Availability of educational technologies 96 6.4 Pedagogical practices 97 6.5 Summary 99 7 Initial teacher education for those who will teach mathematics 101 in the basic phase of education 7.1 Introduction 101 7.2 Issues related to the quality of initial teacher education 102 7.3 Summary 105 2 8 Assessment practices 107 8.1 Introduction 107 8.2 Classroom assessments 107 8.3 Examinations 108 8.4 International and regional assessments 113 8.4.1 International large-scale assessments 113 8.4.2 Regional large-scale assessments 113 8.5 National large-scale assessments 115 8.6 Summary 119 9 Initiatives and innovations 121 9.1 Introduction 121 9.2 Early years and primary grades 121 9.3 Upper secondary grades and the secondary/tertiary interface 124 9.4 Teacher training and support 126 9.5 Using technology to enhance student learning in mathematics 129 9.6 Summary 133 10 Findings and recommendations 137 10.1 Summary of findings 137 10.2 Suggested interventions 138 10.3 Challenges associated with implementation in fragile states 145 10.4 Areas worthy of further research 146 Appendix A: Case studies for six countries 149 A.1 Overview 149 A.2 Case study: Cameroon 151 A.2.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 151 A.2.2 Secondary mathematics ‘lesson signature’ (Grade 9, 10 and 11) 152 A.2.3 Teacher characteristics and attitudes 153 A.2.4 Teacher Training Institutions 155 A.3 Case study: Democratic Republic of the Congo (DRC) 156 A.3.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 156 A.3.2 Secondary mathematics ‘lesson signature’ (Grade 9 and 11) 158 A.3.3 Teacher characteristics and attitudes 159 A.3.4 Teacher Training Institutions 161 3 A.4 Case study: Ethiopia 162 A.4.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 162 A.4.2 Secondary mathematics ‘lesson signature’ (Grade 9, 10 and 11) 164 A.4.3 Teacher characteristics and attitudes 164 A.4.4 Teacher Training Institutions 167 A.5 Case study: Nigeria 168 A.5.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 168 A.5.2 Secondary mathematics ‘lesson signature’ (Grade 9, 10 and 11) 169 A.5.3 Teacher characteristics and attitudes 170 A.5.4 Teacher Training Institutions 173 A.6 Case study: Rwanda 174 A.6.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 174 A.6.2 Secondary mathematics ‘lesson signature’ (Grade 9 and 11) 175 A.6.3 Teacher characteristics and attitudes 176 A.6.4 Teacher Training Institutions 179 A.7 Case study: Uganda 180 A.7.1 Primary mathematics ‘lesson signature’ (Grade 3 and 6) 180 A.7.2 Secondary mathematics ‘lesson signature’ (Grade 9 and 10) 181 A.7.3 Teacher characteristics and attitudes 182 A.7.4 Teacher Training Institutions 185 Appendix B: References 187 Figures Figure 3.1: Relationship between national mathematics scores at the early and late stages of 44 primary education (PASEC 2015, p.56) Figure 3.2: Examples of basic numeracy tasks used in Kenya for the Uwezo assessment of 2013 52 Figure 4.1: Correlation of national average scores on the TIMSS 2011 mathematics assessment 65 for population 1 (Grade 4) and the PIRLS 2011 assessment of reading literacy Relationships between national spending on educating a student from the age Figure 4.2:  68 X of 6 to 15 and national average PISA scores for mathematical literacy (Source: OECD 2013c, p.41) Figure 5.1: The student:textbook ratio for mathematics in primary grades 82 (Source: UNESCO, 2015) Figure 5.2: Key factors impacting on mathematical outcomes 86 Figure 6.1: Relation between teacher and pupil score in mathematics in SACMEQ III (r=0,69) 92 4 Figure 8.1: Chief Examiner’s report on the performance of candidates for the Mauritius 112 Certificate of Primary Education examination on a particular mathematics question Figure 8.2: Example of how information on student performance on a national assessment 114 item can be presented to mathematics teachers and other practitioners (Source NCES, 2011, p.30) Exemplar item map linking three levels of positive achievement (Basic, Figure 8.3:  116 Proficient and Advanced) with the IRT-based scaled scores and selected items from the NAEP assessment for Grade 4 Mathematics 2011 (Source NCES, 2011, p.29) Tables Table 1.1: The countries of Sub-Saharan Africa 26 Table 3.1: Overview of the major international and regional assessment programmes 37 conducted in SSA Table 3.2: TIMSS 2011: Average mathematics scores for population 1 (Grade 4) 38 for selected countries Table 3.3: SACMEQ levels and behavioural descriptors for mathematics 39 Table 3.4: National average scores for mathematics for countries participating in 40 SACMEQ III (2007) Table 3.5: SACMEQ III average mathematics scores by sub-group (Source: SACMEQ, 2010a) 41 Table 3.6: National assessment programmes conducted by countries within SSA 45 Table 3.7: Results of the 2014 Primary Leaving Examination in Uganda by subject 49 Table 3.8: TIMSS mathematics results for population 2 (Grade 8) for SSA participants 2003-2011 53 Table 3.9: Descriptions of the TIMSS international benchmarks for achievement in 53 mathematics (Grade 8) Table 3.10: Description of the PISA baseline level of competence (mathematical literacy) 54 Table 3.11: National assessment programmes conducted at the post-primary level by 55 countries within SSA Table 3.12: Summary statistics for the mathematics tests used in the Ethiopian national 56 assessment of 2010 Table 3.13: Ghana: TIMSS mathematics results over time for population 2 (Grade 8) 59 Table 3.14: Uwezo numeracy results over time (proportion of cohort ‘mastering’ basic numeracy 60 Table 3.15: Average scores for mathematics in South Africa’s annual national 60 assessment 2012-2014 Table 3.16: Average scores for mathematics in South Africa’s annual national assessment 61 2012-2014 Table 3.17: Average mathematics scores on the 2013 Ghana National Assessment with 62 equivalent averages for 2011 estimated through a procedure based on the use of common anchor items 5 Table 4.1: Comparisons of the proportion of a nation’s Grade 4 cohort reaching the ‘high’ 66 international benchmarks for TIMSS and PIRLS, 2011 Table 5.1: Gender differences by mean mathematics score for school systems participating 76 in SACMEQ III (after Saito, 2011) Table 5.2: Gender differences by mean mathematics score for participating countries 76 PASEC2014 (after PASEC, 2015) Table 5.3: Relationship between textbook ownership and mathematical achievement 82 (Source: Spaull, 2012) Table 6.1: Summary of the highest level of academic qualification held by primary 90 school teachers according to data collected in PASEC and SACMEQ surveys of learner achievement Table 6.2: Proportion (%) of teachers reaching the SACMEQ ‘competency’ level in mathematics 91 Table 6.3: Classification of language policies across SSA and their implications for medium 95 or media of instruction. (After Batibo 2013.) Table 8.1: Descriptors for the four levels of mathematical competence used for reporting 117 purposes in the Kenyan national assessment for Mathematics in Grade 3 Table 9.1: Findings of an evaluation of the impact of ECCD interventions in Ethiopia based 122 on test scores pre- and post-intervention (Source: Save the Children, 2014) Table A.1: Overview of the locations and educational language policies of the study’s 149 six focus countries Table A.2: Cameroon: Country key facts 150 Table A.3: Teacher responses to selected statements using a five-point Likert scale 154 Table A.4: Democratic Republic of the Congo: Country key facts 156 Table A.5: Teacher responses to selected statements using a five-point Likert scale 160 Table A.6: Ethiopia: Country key facts 162 Table A.7: Teacher responses to selected statements using a five-point Likert scale 166 Table A.8: Nigeria: Country key facts 168 Table A.9: Teacher responses to selected statements using a five-point Likert scale 172 Table A.10: Rwanda: Country key facts 174 Table A.11: Teacher responses to selected statements using a five-point Likert scale 178 Table A.12: Uganda: Country key facts 180 Table A.13: Teacher responses to selected statements using a five-point Likert scale 184 6 7 8 Mathematics Education in Sub-Saharan Africa: Acknowledgements The author would like to thank all those who organised the information presented in have contributed to the conduct of the study Appendix A of this report. and to the preparation of this report. Finally, our thanks go to the World Bank’s peer First and foremost, thanks are due to Sukhdeep reviewers Marguerite Clarke and Andrew Brar, former senior education specialist at the Ragatz. Their corrections and proposals for World Bank, who developed the concept and revision enhanced the quality of the final report secured support and funding for the study. which, we hope, will be of interest and value to Thereafter, Sukhdeep made major contributions its readers. to the collection of resources, report writing and peer review processes. Thanks are also due About the author to Ryoko Tomita, World Bank economist, who assumed responsibility for the study and saw it George Bethell is an independent consultant through to completion. specialising in educational assessment. His special interests include the use of assessment- The study was conducted by Cambridge related data to inform policy making and the Education where thanks are due to John impact of high-stake examinations on Martin, Jawaad Vohra and, in particular, classroom practices. Having started his career Elisabetta Naborri who co-ordinated all study teaching science and mathematics in the United activities including the surveys conducted in Kingdom, he subsequently served as a subject six focus countries. specialist at the University of Cambridge schools’ examination board where he was Special thanks are due to the international responsible for the preparation and scoring of experts Kwame Akyeampong and Ernest science examinations, and for standards setting. Ampadu who helped in the design of the study Having become involved in international and checked the accuracy of the report’s assessment whilst in Cambridge, George has, mathematical and pedagogical content. for more than 30 years, provided consultancy In addition, the author is most grateful to the services to international development agencies national experts who co-ordinated the and governments around the world. After classroom observations and the application of assisting in the localisation of examinations in teacher questionnaires in the study’s six focus Zambia in the mid-1980’s, he was involved in countries: Napthalin Achubang Atanga development projects in a number of African (Cameroon); Pierre Gambembo Gawiya (DRC); countries including Kenya, Lesotho, Namibia, Steve Dele Oluwaniyi (Nigeria); Emma Furaha Tanzania, and Uganda. In addition, he has a Rubagumya (Rwanda); Caroline Taliba wealth of experience gained in south and (Uganda); and, Candid Services PLC south-east Asia, and in a number of former (Ethiopia). Thanks are also due to Ayesha socialist republics. Khan who analysed the in-country data and 9 Mathematics Education in Sub-Saharan Africa: Abbreviations and acronyms AIMS African Institute for Mathematical Sciences AIMSSEC African Institute for Mathematical Sciences School Enrichment Centre CAI Computer Assisted Instruction CAR Central African Republic CCSS Common Core State Standards (USA) CCSSO Council of Chief State School Officers (USA) CEI Centre for Education Innovations CML Computer Managed Learning CONFEMEN La Conférence des Ministres de l’Education des pays ayant le français en partage CRFPE Centre Régionale de Formation de Personnels de l’Education de Dakar CSEE Certificate of Secondary Education Examination (Tanzania) DRC Democratic Republic of the Congo ECCD Early Childhood Care and Development ECCE Early Childhood Care and Education EFA Education For All EGMA Early Grade Mathematics Assessment ELM Emergent Literacy and Maths (programme) GBP (Great) British Pound GNP Gross National Product ICT Information and Communications Technology IEA International Association for the Evaluation of Educational Achievement ILSA International Large-Scale Assessments IMF International Monetary Fund IMO International Mathematical Olympiad IMU International Mathematical Union IRT Item Response Theory KCPE Kenya Certificate of Primary Education LAC Latin American and Caribbean LMIC Low- and Middle-Income Countries MED Microsoft Education Delivery (platform) MLA Monitoring of Learner Achievement NA National Assessment NAEP National Assessment of Educational Progress (USA) NAT National Assessment Test (The Gambia) NC Numbers Count (UK) NCLB No Child Left Behind (USA) NCERT National Council for Educational Research and Training (India) NCTM National Council of Teachers of Mathematics (USA) 10 NGA National Governors Association (Center for Best Practices) (USA) NGO Non-Government Organisation NLSA National Large-Scale Assessments NQT Newly Qualified Teacher OECD Organisation for Economic Co-operation and Development OER Open Educational Resources PASEC Programme for the Analysis of Education Systems PIRLS Progress in International Reading Literacy Study PISA Program for International Student Assessment PLE Primary Leaving Examination PRIMR Primary Maths and Reading Initiative RESAFAD Réseau Africain de Formation à Distance (Sénégal) RCT Randomised Control Trial RSA Republic of South Africa SABER Systems Approach for Better Education Results SACMEQ Southern African Consortium for Measurement of Educational Quality SC Save the Children SD Standard Deviation SE Standard Error (of a Mean) SES Socio-Economic Status SSA Sub-Saharan Africa STEM Science, Technology, Engineering and Mathematics TAC Teachers’ Advisory Centre (Kenya) TESSA Teacher Education in Sub-Saharan Africa TIMSS Trends in Mathematics and Science Study TLM Teaching and Learning Materials TTI Teacher Training Institution UIS UNESCO Institute for Statistics UK United Kingdom (of Great Britain and Northern Ireland) UN United Nations UNESCO United Nations Educational, Scientific and Cultural Organization USA United States of America USAID United States Agency for International Development USD US Dollar WAEC West African Examinations Council WASSCE West African Senior School Certificate Examination ZIMSEC Zimbabwe Schools Examinations Council 11 12 Mathematics Education in Sub-Saharan Africa: Executive summary The World Bank commissioned this study in along with a range of suggestions for the support of its efforts to improve mathematics consideration of national educational policy education in the countries of Sub-Saharan makers and the various stakeholders with roles Africa (SSA). It was commissioned in response to play in improving mathematical outcomes in to a growing recognition that countries in SSA schools and other educational institutions. will need to boost performance in the Science, These include inter alia, international Technology, Engineering and Mathematics development banks and aid agencies, non- (STEM) subjects if they are to realise their full governmental organisations (NGOs) and potential in a competitive global market philanthropic institutions working in the field of increasingly shaped by the use of new mathematics education, and the national and technologies. At present it is feared that the international assessment and research region’s economic development is being communities responsible for gathering, impeded by the limited availability of high- analysing and interpreting data. It is these quality education. In particular, poor stakeholders who will inform the decision performance in mathematics in primary and making process, formulate policies, and secondary schools is seen as a significant implement reforms to guide and support the barrier to improved economic and social practitioners – especially teachers of outcomes both at the level of the individual and mathematics – who, ultimately, will improve the of the nation. mathematics education of learners. Key objectives Report structure The study’s first key objective was to document Chapter 1 of this report lists the constituent the current state of mathematics education countries of SSA and describes the study’s across this vast and diverse region drawing research questions and methods. Chapter 2 primarily on research reports and evidence explores the economic and social arguments from international, regional and national for making the improvement of mathematics assessments of learner achievement in education in the region a priority. Chapter 3 mathematics. Evidence from the literature was presents evidence as to current levels of supplemented with data gathered in six numeracy and mathematical competence in the countries via classroom observations and the countries of SSA from a wide range of application of teacher questionnaires. The focus assessments. Chapter 4 looks at factors which countries were Cameroon, Democratic Republic have the potential to raise mathematical of the Congo (DRC), Ethiopia, Nigeria, Rwanda, achievement indirectly by improving the quality and Uganda. The second key objective was to of schooling in general. Chapter 5 considers the identify interventions which, evidence suggests, effectiveness of various interventions targeted have the potential to successfully improve specifically at improving mathematical mathematics education either directly or outcomes. Chapter 6 and Chapter 7 are indirectly through raising the general quality of dedicated to issues concerning the capacities education. The third key objective was to of serving teachers of mathematics and the extract the main findings and to present them pre-service training arrangements for those 13 preparing to teach mathematics in schools. physical structures; access to utilities and Chapter 8 describes assessment practices and services (e.g., potable water, electricity, and their potential roles in improving learning internet services); availability of teaching and outcomes. Chapter 9 gives an overview of a learning materials (TLMs) and educational range of more recent initiatives designed to technologies; effective school managers; and, improve mathematics education both in SSA above all else, well-trained and highly- and beyond. Chapter 10 summarises the study’s motivated teachers. Financial investment in main findings and sets out some suggestions schools serving disadvantaged communities is for overcoming barriers to progress. Finally, of particular importance when it comes to Appendix A sets out the findings of the in- improving educational outcomes and country surveys. In particular, it includes addressing issues of inequity. Spaull (2011) uses descriptions of ‘signature mathematics lessons’ SACMEQ data to show that the socio-economic for each country compiled from data gathered status (SES) of the school is a significantly during classroom observations. more important factor in determining outcomes than the SES of the student and their family. Main findings Notwithstanding the above, in SSA mathematics education requires special Investment in education yields significant attention for three reasons. First, it is a priority returns for individuals, communities, and because the economic strength of a nation nations. Returns are maximised when the depends on the capacity of its education education system promotes the acquisition of system to produce workers and consumers who critical cognitive skills - linguistic literacy, are mathematically literate. Secondly, the mathematical literacy, and problem solving learning deficit in mathematics for most skills. In an increasingly technological world, countries in SSA is huge and shows no signs of mathematical literacy (and its precursor, diminishing. Thirdly, widely held negative numeracy) is emerging as the most important attitudes towards mathematics together with of the cognitive skills. Unfortunately, a large an expectation of failure represent a significant body of evidence shows that mathematics barrier to progress. education in SSA is in a precarious state. The learning deficit between countries in the The factors that contribute to low levels of region and international norms is so large that, student achievement in mathematics in SSA are without extensive and sustained interventions numerous, varied, and interconnected in across all phases of education, the gap may complex ways. There is no magic bullet. Any never be narrowed let alone closed (Beatty solution will require simultaneous actions on and Pritchett, 2012). many fronts. Mounting a comprehensive and coherent campaign to raise the quality of Outcomes in mathematics are inextricably mathematics education will require careful linked to the general quality of schooling planning and significant investment. Even with offered to learners. Providing access to high a suitable plan in place the inertia associated quality schooling for all would inevitably raise with large education systems will be difficult to average achievement levels in mathematics. overcome: governments and other stakeholders The term ‘quality of schooling’ covers many will need to sustain their efforts over the factors: adequate financial resources; good long-term. There is no quick fix. 14 Whilst many problems will need to be Suggested interventions addressed, probably the most important group of interventions will be those concerned with Raising the status of education in 1.  equipping existing and future teachers of mathematics to that of a national priority mathematics with the knowledge and competences necessary to help learners Governments should explicitly classify the acquire deep understanding of mathematical raising of standards in mathematics (and other concepts. Enhancing in-service training STEM subjects) as a national priority. This opportunities and ensuring that teachers have priority should be made clear in all national access to high quality TLMs and educational strategic plans and be reflected in all ministerial technologies will bring some benefits. action plans. In practice, ambitious strategic However, in the longer-term steps must be objectives may be difficult to achieve but they taken to reform the initial teacher training will serve as a signpost indicating the desired programmes for teachers who will teach direction of travel and guiding the actions of, mathematics at the primary or secondary for example, ministries of education. levels. Without radical reform, inadequate initial teacher training will remain part of the Budgets for education in SSA tend to be problem and poorly prepared teachers will severely constrained but the evidence is that continue to serve as a brake on progress increased per student expenditure is towards better outcomes in mathematics. associated with better mathematical outcomes. Therefore, additional funding, over Increasingly, new technologies seem to hold and above that for general education, should possible solutions for many of the problems be allocated to interventions specifically associated with raising educational quality in targeted at improving mathematical outcomes general and mathematical standards in at the primary, secondary and tertiary levels as particular. However, as yet it is not clear which a matter of priority. approach will deliver the greatest returns in the context of SSA; cost effectiveness and long- International agencies that support term sustainability remain concerns. In governments in the implementation of particular, investing heavily in inflexible educational reforms (e.g. development banks, hardware configurations and/or committing to donors, NGOs, philanthropic organisations, etc.) single-source commercial software packages should reflect this shift in priorities in their would appear to be a risky strategy. On the policies and actions. For example, international other hand, harnessing the internet simply to development banks and aid agencies should deliver a wide range of resources to educational require those preparing any support institutions, teachers, students and their programme to state if/how proposed parents is relatively cheap and likely to bring interventions will address the issue of benefits with few attendant risks. promoting increased engagement with, and A number of interventions are suggested below. achievement in, STEM subjects. It should be noted that the order in which they appear is not intended to suggest a hierarchy of priorities. All, and others besides, will need to be included in any comprehensive action plan. 15 Changing attitudes towards mathematics 2.  Four key areas are in urgent need of reform: revising curricula of TTI; revising the way in Prevailing negative attitudes towards which those curricula are delivered; making mathematics should be challenged both within better use of new educational technologies; the education sector and in the wider public and, crucially, changing the profile of TTI tutors arena through a comprehensive and sustained – especially those who are preparing teachers public relations campaign. The three key for the primary phase of education. messages should be: (a) It pays to invest in the mathematical education of children because, The curricula of TTI should be reviewed and amongst other benefits, success in mathematics revised to ensure that they (a) help trainees to is linked to greater economic returns; (b) develop a far deeper understanding of the Everyone can be successful in mathematics - mathematical concepts they will teach even if you don’t need to be born with a special ability; this means sacrificing the breadth of the (c) Hard work in and out of school will bring content somewhat; (b) pay due attention to the better results in mathematics. development of pedagogical content knowledge, i.e. knowledge of the specialised Special attention should be paid to changing teaching and learning processes associated the view that mathematics is predominantly a with mathematics; and (c) provide trainees with subject for boys. Schools, institutions of further practical strategies for working with learners and higher education, and potential employers who approach mathematical problems through should reinforce the message that careers in various standard and non-standard routes. In STEM-related fields offer valuable opportunities short, the curricula of TTI and the way in which to all regardless of gender. Highlighting good they are delivered should reflect best practice female role models, using gender-appropriate in the classroom. learning materials, and adopting interactive teaching methods will help to improve the Revising curricula and teaching programmes confidence (i.e. self-efficacy) of girls in for TTI is important. However, it is not clear that mathematics and, hence, their achievement. the current managers and tutors of TTI are in a position to deliver a radically different approach Improving initial teacher training 3.  to preparing new teachers. One significant deficiency appears to be a lack of tutors having It is vital that new entrants to the teaching first-hand experience of teaching in primary profession are properly prepared. Unfortunately, school classrooms. Correcting this will be many TTI in SSA produce graduates who, as neither easy nor quick. Selected tutors from evidenced by the poor outcomes of their those currently in post should be trained students, are not effective teachers of through a suitable professional development mathematics. In addition, TTI which fail to programme (including a practicum) to become reflect the philosophy and methods of modern qualified specialists in mathematics education. mathematics curricula in their courses serve as Financial incentives should be offered to those a block against progress towards raising levels who successfully complete a certified course in, of mathematical competence in schools. These e.g. ‘the teaching of mathematics in primary must be transformed so that they become part schools’. In addition, recognised career paths of the solution. should be established, with incentives, to 16 encourage outstanding teachers and/or 4. Supporting practising teachers principals from the primary sector to become specialist tutors in TTI. Whilst the reform of initial teacher training is of paramount importance the needs of the There is an immediate opportunity to existing teaching force must not be neglected. strengthen teacher training through the use of Existing in-service teacher training programmes educational technologies but many TTI do not for teachers of mathematics should be seem well-placed to take advantage of this. strengthened and, where necessary, new Without intervention, there is a danger that TTI programmes should be developed. As a matter will fall further behind and will not be able to of principle, such training should form part of a prepare their trainees to make use of e-learning formal continuum of professional development and m-learning tools. Governments should which “starts with pre-service education; encourage partnerships between TTI and, for includes periods of school-based enquiry and example, NGOs to build capacity and practice teaching; continues into an induction/ incorporate new technologies within the mentoring period of introduction into full-time courses offered to prospective teachers. teaching; and is followed up with a continuous Fortunately, some examples of good practice program of career-long professional are emerging in SSA. For example, in some development, support and supervision” (USAID, countries TTI are already incorporating open 2011, p.6). educational resources (OER) made available by the Teacher Education in Sub-Saharan Africa All in-service training programmes should meet (TESSA) initiative in their taught programmes. the criteria set out by Walter and Briggs (2012) who suggest that “The professional The inertia of large organisations such as TTI development that makes the most difference to may make it difficult to make significant teachers: (1) is concrete and classroom-based; progress quickly. However, individual trainees (2) brings in expertise from outside the school; could respond far more quickly if they were (3) involves teachers in the choice of areas to encouraged to take greater responsibility for develop and activities to undertake; (4) enables their own professional development. Therefore, teachers to work collaboratively with peers; (5) TTI should formally and systematically provides opportunities for mentoring and advocate and facilitate self-development as an coaching; (6) is sustained over time; and (7) is adjunct to their taught courses. Most supported by effective school leadership” importantly, trainees should be given free (Walter and Briggs, 2012, p1.). access to a wide range of materials and resources relevant to effective mathematics Programmes designed to improve the teaching. These should include both traditional effectiveness of teachers of mathematics TLMs (e.g. textbooks, teachers’ guides, and should provide participants with the exemplar worksheets) and e-based learning pedagogical skills necessary to move from a materials for both teachers and students. The teacher-led, rules-focused approach to a more key to this is for TTI to allow trainees free and collaborative exploration of mathematical unlimited access to the internet so that they problems. However, given the generally poor can see, for example, video clips of model preparation of teachers in SSA, pedagogical lessons and download materials for their own content knowledge should not be ignored since education and for use in their practicum. this is required if teachers are to recognise the 17 various levels of understanding that their evidence that new textbooks in SSA are students may display (USAID, 2011). systematically evaluated as to their effectiveness as aids to learning i.e. that they In addition to formal training, peer support and are closely aligned with instructional objectives. collaboration between mathematics teachers appear to be of particular importance in Ministries of education should require all promoting better teaching and learning. An proposed textbooks to be subjected to a interesting development is the recent comprehensive evaluation by trained reviewers introduction, in South Africa, of a “1+4” teacher - including practising teachers of mathematics. development plan which ensures that This requirement may add to the initial costs mathematics teachers meet regularly to discuss of production, but this may be a small price effective teaching strategies. If this initiative is to pay for greater returns in terms of shown to yield significant improvements in educational outcomes. learner achievement, other countries should consider ways of promoting collaboration Whilst there is currently a great need for among subject teachers. physical textbooks in many countries of SSA, the internet offers a parallel route for allowing Providing more and better mathematics 5.  practising teachers, trainee teachers, students textbooks and parents free access to approved textbooks. For example, The National Council for In countries where the ratio of mathematics Educational Research and Training (NCERT) textbooks to students is significantly worse in India not only commissions physical books than 1:2 there is probably benefit to be gained but also provides e-copies for personal, i.e. in investing in the provision of more books non-commercial use, through its e-portal. (Fehrler, Michaelowa and Wechtler, 2007). In SSA, governments should, through their Fredriksen and Brar (2015) suggest practical agencies, establish ‘education portals’ allowing strategies for meeting the demand for free access to textbooks and supplementary textbooks in countries where financial learning materials. constraints are severe. However, research shows that simply supplying more textbooks will Supporting mathematics teachers 6.  not raise mathematical achievement through technology significantly - the textbooks have to be the right ones and teachers have to be trained in Many initiatives to turn the potential of digital using them effectively. technologies into improved teaching and learning have been launched in recent years. Determining whether a textbook is likely to be Unfortunately, it is not yet clear which, if any, of effective in the teaching of mathematics these will be most effective and/or sustainable requires rigorous evaluation in advance of in the long-term. However, technological tools publication. Currently pre-publication are emerging that individual teachers can, with evaluation of textbooks tends to focus on support, use to enhance their teaching of alignment with the content of the curriculum, mathematics. Typically these teaching tools and attractiveness to learners, physical quality and materials are not being created by government cost of production. However, there is little agencies: they are being generated by not-for- 18 profit organisations, academic institutions, and outweigh the costs. In the longer term, new commercial entities. The available pool of such initiatives such as PISA for Development and resources is constantly growing and changing TIMSS Numeracy may make the proposition so perhaps the best short-term strategy is not more attractive but, in the shorter term, more to be directive but simply to facilitate teachers’ promising alternatives include participation in access to ideas, models, materials and tools. regional assessments and the development of Ministries of education should establish national national assessments. education portals through which teachers may be guided towards potentially useful resources. The two regional assessments - SACMEQ and PASEC - have over recent years become In addition to an ‘official’ education portal, increasingly sophisticated and potentially more independent resource banks and online powerful. SACMEQ and PASEC should communities of mathematics teachers should strengthen their existing links through formal be established in order to facilitate the sharing agreements, the adoption of common of resources that have been shown to work in operational standards, and the use of a the classroom. A good example of this is the common reporting scale. This would move SSA resource-sharing website hosted by the Times towards a pan-African comparative assessment Educational Supplement in the UK. Teachers programme capable of measuring student from all phases of education and in all subjects achievement and monitoring trends over time. upload resources they have made and used Countries which do not yet take part in successfully. These can be accessed and used SACMEQ and PASEC studies should be by teachers from anywhere in the world. The encouraged to do so through, for example, informal, decentralised, and uncontrolled financial support and technical assistance from approach advocated here may not sit well with international agencies. more conservative policy makers. However, it A number of countries in SSA have, with the reflects the reality of a digital universe where encouragement of international agencies, teaching communities are not limited by implemented their own national assessment national borders and where the best teaching/ programmes over recent years. Unfortunately learning materials emerge through a process there is evidence that many of these are not akin to natural selection. That is TLMs which fulfilling their intended purposes. They do not, work well in the classroom are used and in general, yield the information that survive whilst poor TLMs ‘disappear’ through policymakers require and there is little evidence lack of interest. that they are providing schools and mathematics teachers with sound, practical Harnessing the power of assessment: 7.  advice that can be used to improve learning. regional and national assessments Therefore, all countries currently conducting national assessments should review these to Participating in international large-scale ensure that they are fit for purpose and are assessments such as PISA and TIMSS may bring providing value for the money invested in them. benefits but for countries in SSA where it is Where countries do not yet have the necessary known that achievement in mathematics technical expertise to enhance their national currently lies far, far below international norms assessment programmes they should be it is not clear that the potential benefits supported through technical assistance 19 provided through international agencies. offer examples of good practice. Of particular concern is the absence of In addition to the above, governments and feedback to mathematics teachers and other their ministries of education should instruct practitioners. The agencies responsible for national examination boards and other national assessments should take steps to assessment agencies to put in place ensure that their studies provide mathematics comprehensive feedback systems to supply teachers with concrete examples of student schools, teachers and other practitioners with performance at different achievement levels. both qualitative and quantitative information Examples of test items, descriptions of as to student performance in mathematics alternative solutions and popular (and all other subjects). misconceptions, and supporting statistical data are all necessary if national assessments are to Currently examination boards do not make have a positive impact on classroom practices. disaggregated data (e.g. student responses and Once again, external technical assistance may raw scores) available for external evaluation be necessary to put such a system in place. and/or analysis. This is a waste of potentially important information. Anonymised datasets Harnessing the backwash effect of high- 8.  should be made freely available to bona fide stake examinations researchers wishing to conduct secondary analysis since, as Fehrler, Michaelowa and In many countries of SSA, teaching and learning Wechtler (2009) conclude, “any kind of are dominated by the high-stake examinations measures to enhance transparency about… which act as gatekeepers at the transition learning outcomes appears to be valuable” points of the education system. The agencies (Fehrler, Michaelowa and Wechtler 2009, p.27). responsible for them are under great pressure to maintain the security of their systems and to Supporting student self-learning through 9.  ensure that individual students receive the technology correct result in a timely fashion. In focusing on this they neglect their role in enhancing When it comes to knowledge and education, education by providing materials and the internet has begun to undermine the information to teachers and students. hegemony of schools, teachers, ministry- approved textbooks, etc. Students who have Where they do not already do so, examining access to the internet can now easily agencies should be required to make materials supplement their formal education with which would help teachers and students information from elsewhere. This should not be prepare for examinations in mathematics (and seen as a threat but as an opportunity to raise in all other subjects) freely available via the levels of achievement without significant internet. Such materials should include additional investment from the state. This is examination programmes (syllabuses), reports particularly true in SSA where many students of examiners and, most importantly, past are currently being taught by teachers who lack papers (with their marking schemes). This confidence and/or competence in mathematics. could be implemented with little delay and at Three initial steps are recommended. First, little cost. The West African Examinations students, parents and local communities should Council’s e-learning portal and the website of be made aware of the possibilities for self- the Mauritius Examinations Syndicate already learning. They should be encouraged to access 20 suitable learning materials – possibly through a understanding of a concept through exploring user-friendly, national education portal. alternative routes towards solving non-standard Secondly, key players in education, both problems. Others investigate issues associated government agencies and NGOs, should be with adopting a constructivist approach in the encouraged to provide free access to existing teaching of mathematics. However, little open educational resources. Thirdly, NGOs and evidence has been gathered in the context of commercial partners should be encouraged to typical classrooms in SSA. Both of these issues collaborate with, for example, ministries of should be subject to action research. education in the generation of age-appropriate learning materials compatible with the content How effective are the textbooks currently and philosophy of national curricula for being used to teach basic mathematics in SSA? mathematics. Quantitative research repeatedly suggests that 10. Promoting further research the direct benefits of making mathematics textbooks available to all are, at best, small. One Some of the questions which during the hypothesis is that investing in textbooks is of preparation of this report have emerged as value only if the prescribed textbook is being worthy of further investigation and effective. There are, however, few rigorous research are described below. evaluations of textbook effectiveness. Another hypothesis is that teachers in SSA are not How can countries in SSA monitor trends in trained to use the textbook to maximum effect. mathematical achievement? Both indicate areas where further study would be of value. To date, national and regional assessments in SSA have not, in general, been able to provide How can national assessments of student sufficiently precise and reliable data on trends achievement in mathematics be improved so in student achievement. Key questions to be that they provide policy makers and teachers resolved are: ‘Can a country establish a quick with the information needed to improve and effective way of monitoring mathematical outcomes in mathematics? achievement over time?’ ‘What will be necessary to establish sufficiently precise Whilst a significant number of countries across baseline measurements and how can SSA carry out national assessments of learner subsequent measurements be systematically achievement in mathematics, there is little linked with those baselines?’ ‘How can existing evidence as to the technical quality of these. national assessments be modified so that they Few governments appear to be asking these can monitor trends over time?’ fundamental questions: Do our national assessments serve their intended purposes? Do How do learners understand mathematical they offer value for money? Have they had a concepts as demonstrated by their teachers? discernible impact on educational policy and/or How do they approach practice? Answering these questions will require mathematical problems? both qualitative and quantitative research. A number of research papers explore the various ways in which learners gain a deep 21 Where OER have been used as the basis of, Which of the e-learning and m-learning or to supplement, formal teacher education technologies in the classroom have the development programmes, have they greatest potential to raise levels of numeracy been effective? and mathematical competence? What are the challenges of introducing e- and m-learning Open Educational Resources produced by technologies - especially in fragile states? international development partners have been used in some TTI as the basis of new initial Over recent years, a significant number of teacher training programmes or to supplement initiatives to raise levels of numeracy and existing programmes. In other cases, OER have student achievement in basic mathematics been built into in-service professional through the use of digital technologies have development programmes for teachers. been piloted across SSA. Few of these have Independent evaluations of these initiatives are been subjected to fully independent scrutiny. required to determine whether they have There is a need to evaluate any such initiative contributed to the production of better before investing in implementing it at scale. graduates or not. If such programmes can be Evaluative studies should not only investigate shown to be effective and offer good value for the returns to learning but also the costs and money then the approach is more likely to be risks associated with adoption on a large-scale. adopted by other countries and other TTI. These are the key questions: Which technologies/approaches yield the greatest benefits in terms of improved outcomes? What are the costs associated with implementing a proposed technological solution at the regional and/or national level? Given the prevailing context, is the proposed technological solution viable and sustainable? 22 23 24 Mathematics Education in Sub-Saharan Africa: 1 Introduction 1.1 Objective In order to meet its key objective this study will document the state of mathematics education This study was commissioned by the World across the region and identify interventions that Bank in order to support the improvement of have the potential to successfully improve mathematics education in the countries of mathematics education in SSA. It is hoped that Sub-Saharan Africa (SSA). Here the term this overview of both the challenges and ‘mathematics education’ is interpreted in its opportunities will prove of value to the various broadest sense covering not only the practices groups with roles to play in improving of teaching and assessing mathematics in mathematical outcomes. These include inter schools and other learning institutions, but also alia: national educational policy makers; the socio-economic and cultural contexts in international development banks and aid which national policies related to the teaching agencies; non-governmental organisations and learning of mathematics are being (NGOs) and philanthropic institutions working developed, implemented and evaluated. in the field of mathematical education; and the national and international assessment and The study was commissioned in response to a research communities responsible for growing recognition that countries in SSA will gathering, analysing and interpreting data. It is need to boost performance in the Science, these stakeholders who will inform the decision Technology, Engineering and Mathematics making process, formulate policies, and (STEM) subjects if they are to realise their full implement reforms to guide and support the potential in a competitive global market practitioners – especially teachers of increasingly shaped by the use of new mathematics – who, ultimately, will improve the technologies. At present, it is feared that mathematics education of learners. economic development is being impeded by the limited reach of quality education. In particular, poor performance in mathematics at the school level is seen as a significant barrier to improved economic and social outcomes at the level of both the individual and the nation. 25 1.2 Defining Sub-Saharan Africa The World Bank classifies 48 countries as being located in SSA. These are listed in Table 1.1. Table 1.1: The Countries of Sub-Saharan Africa Sub-Saharan Africa Countries Angola Côte d’Ivoire Madagascar Seychelles Benin Equatorial Guinea Malawi Sierra Leone Botswana Eritrea Mali Somalia Burkina Faso Ethiopia Mauritania South Africa Burundi Gabon Mauritius South Sudan Cabo Verde Gambia, The Mozambique Sudan Cameroon Ghana Namibia Swaziland Central African Republic Guinea Niger Tanzania Chad Guinea-Bissau Nigeria Togo Comoros Kenya Rwanda Uganda Congo, Democratic Republic Lesotho São Tomé and Principe Zambia Congo, Republic Liberia Senegal Zimbabwe Variation and commonalities across 1.3  Botswana (GDP per capita ~USD 7,000). By way the region of contrast, many are extremely poor including the Central African Republic (GDP per capita The 48 countries of SSA exhibit huge variation in ~USD 360) and Malawi (GDP per capita ~USD terms of their geographical, cultural, historical, 255)1. Whilst some countries in the region have and economic characteristics. The region established relatively stable and robust political includes large, land-locked countries such as and economic systems, the majority can be Chad and Niger (both -1.3 million km2) and small, classified as ‘fragile states’. Of the 50 fragile island states such as Mauritius (-2000 km2) and states identified by the OECD (2015a) Seychelles (455 km ). It includes highly 2 worldwide, 28 are in SSA2 with seven (Central populated countries such as Nigeria (~177 African Republic, Chad, Democratic Republic of million) and Ethiopia (~97 million), and those the Congo, Côte d’Ivoire, Guinea, Sudan, and with fewer than one million citizens such as Swaziland) being judged as being under threat Equatorial Guinea and Comoros. Some countries in all five of the OECD’s ‘fragility clusters’ i.e. are relatively wealthy including oil-rich Gabon violence, justice, resilience, institutions, and (GDP per capita ~USD 11,000) and mineral-rich economic foundations. 1. Data extracted on 27 January 2016 from the World Bank’s World Data Bank at http://databank.worldbank.org/. All figures relate to 2014. 2. The countries in SSA classified by the OECD as being fragile states are: Burundi, Cameroon, Central African Republic, Chad, Comoros, Congo, Côte d’Ivoire, Democratic Republic of the Congo, Eritrea, Ethiopia, Guinea, Guinea-Bissau, Kenya, Liberia, Madagascar, Malawi, Mali, Mauritania, Niger, Nigeria, Rwanda, Sierra Leone, Somalia, South Sudan, Sudan, Togo, Uganda, and Zimbabwe (OECD, 2015). 26 Whilst variation in geo-economic contexts does 1.4 Research questions and methods contribute to differences in national levels of educational achievement, the differences, when The study addresses the following research judged against global norms, are relatively small. questions: Indeed, with few exceptions, the countries of 1. Why is mathematics education important in SSA appear to face remarkably similar problems general, and in SSA in particular? in raising the quality of their education systems. 2. What is the state of development of In particular, all the countries of SSA face the assessments in SSA? Which countries same challenge; that of raising achievement in measure learning outcomes in mathematics the critical area of mathematical literacy from at different levels of school education and disturbingly low levels. This echoes the findings how? What do large-scale assessments of an International Mathematical Union (IMU) reveal about mathematics learning in SSA? report on mathematics in Africa which 3. How do countries compare in mathematics concluded: “African countries… are broadly learning outcomes at pre-secondary level in similar in key issues that concern our advisers SSA? Can we identify groups that perform – institutional and national conditions that help better? How do countries compare in or hinder mathematical development. From their mathematics learning outcomes at reports, it seems clear that these conditions are secondary level in SSA? Can we identify virtually the same throughout the continent” groups that perform better? (IMU, 2009, p.1). Challenges typically observed 4. What are the main factors that affect include: low levels of investment; poor physical learning outcomes in general and, in conditions in schools and inadequate teaching particular, achievement in mathematics? and learning materials (TLMs); shortages of 5. Are teachers in SSA sufficiently well-qualified well-qualified and trained teachers of and competent to teach mathematics? Are mathematics – especially in rural areas and they adequately prepared by pre-service disadvantaged communities; examination and training courses to teach mathematical assessment systems which do not promote concepts effectively? What challenges do better achievement in mathematics and fail to teachers face when teaching mathematical provide mathematics educators with the concepts in the classrooms of SSA? information they need to improve student 6. Are the potential benefits of comprehensive achievement; inadequate pre-service training assessment practices being harnessed? Are programmes for teachers with teacher training there differences in the quality of summative institutions (TTI) ill-equipped to adopt new and formative assessments in SSA? approaches towards the effective teaching of 7. What interventions and/or innovations have mathematics; and, institutions and teachers been used in other countries that have ill-prepared to adopt new educational shown notable improvements in technologies as they become available. It is mathematical outcomes? To what extent can these commonalities which make it possible to potentially effective interventions from other construct a single narrative for the otherwise contexts be transferred to SSA? Can new diverse nations of SSA. technologies be used to improve mathematical outcomes in SSA? 27 8. What were the systemic factors that have Classroom observations will focus on the contributed to consistently high question: “What happens in classrooms where mathematics learning achievements in mathematics is being taught?” Researchers will select countries from other regions, in observe mathematics lessons for Primary particular East Asia? Grades 3 and 6 and one Secondary Grade (9, 10 9. What are the gaps in evidence and/or or 11) and will record their observations in a further areas of research that are required structured observation schedule. They will to (a) provide a comprehensive picture on gather data on the classroom environment and the status of mathematics education in SSA resources, on the teacher who delivers the (b) evaluate the effectiveness of lesson, and on what students are doing at interventions designed to raise standards? specific times during the lesson. Following each observed lesson the teacher will be invited to The study will achieve this through a complete a questionnaire. In addition to comprehensive literature review examining information about, for example, the teacher’s available information on the current status of experience and working conditions in the mathematics education in SSA including: school, the questionnaire will include a short student learning outcomes; teacher capacities; attitudinal survey. availability of textbooks and other resources; and initiatives being taken to improve Finally, in each focus country three institutions mathematics education in SSA. The literature providing pre-service training for teachers will review will also examine best practice in regions be selected according to their size, prestige/ that show strong results in mathematics reputation, and geographical location. The education and in countries that have registered institutions’ relevant curricula will be reviewed notable improvements in recent years. Best and a senior representative will be invited to practices from within Sub-Saharan Africa region complete an institutional questionnaire will also be identified. concerning the preparation of teachers who will deliver mathematics lessons at the primary or The literature review will serve as the secondary levels. predominant source of information. However, it will be supplemented by case studies in six In all cases, the samples will be small and countries chosen to represent a range of non-probabilistic and so quantitative indicators contexts in both Anglophone and Francophone will not necessarily be generalisable. However, systems3: Cameroon, Democratic Republic of the information gathered through classroom the Congo (DRC), Nigeria, Malawi, Rwanda, and observations and questionnaires will be cross- Uganda. In these countries, three mechanisms referenced to complementary data from other will be used to collect data: classroom sources. This will enable a more comprehensive observations; teacher questionnaires; and a picture of the state of mathematics education questionnaire for institutions providing initial in each of the focus countries to be prepared. (pre-service) teacher training. 3. Resource constraints meant that it was not possible to add a Lusophone country to the focus group. Information as to mathematical achievement is available for Mozambique through its participation in SACMEQ regional assessments (see Section 3). However, little information is readily available about mathematics education in the other highly populated Lusophone country of SSA – Angola (population ~24 million). 28 29 30 Mathematics Education in Sub-Saharan Africa: 2 Context 2.1 Education, skills, and economic benefits the methods used and the data available. However, recent estimates suggest that the Over the past decade, Sub-Saharan Africa has average private rate of return to a further year enjoyed strong economic growth with an of education in SSA is 12.4% (Montenegro and average regional GDP growth rate of 5.8%4. Patrinos, 2014, Table 3a). Returns vary across This growth is predicted to remain ‘solid’ even the phases of education with each additional in the face of uncertainties in the global year of primary schooling in SSA returning an economy and volatility in the price of average of 14.4% with a corresponding return of commodities (IMF, 2015, p.1). Notwithstanding 10.6% at the secondary level5. At the tertiary this positive picture, there is a belief that level, private returns to education are even countries within SSA are failing to realise their higher at 21.0% (Montenegro and Patrinos, full economic potential and that a key 2014, Table 3b). These high returns are impediment to this is the limited availability of indicative of the scarcity of human capital high quality education. relative to demand within the region’s employment sector. It is well established that education brings economic benefits to the individuals who are Traditionally, calculations of returns to educated and, indirectly, to those around them. education such as those cited above have In addition, investing in education brings many been based on the number of years spent in non-market returns including lower infant education. However, there is now a growing mortality (Boehmer and Williamson, 1995), awareness that whilst the duration of smaller families (Janowitz, 1976), better health education may be an important factor in in children (Currie and Moretti, 2003), and less determining economic returns, the quality of participation in crime (Machin, Marie and Vujić, that education must not be ignored. Indeed, 2010). Taking the private returns to education Hanushek and Wößmann (2007) conclude together with external, social benefits, it that, “educational quality – particularly in appears safe to conclude that investment in assessing policies related to developing developing human capital through education countries – is THE key issue” (ibid, p.1). In this offers returns which compare favourably with context, Hanushek and Wößmann (2007) investments in developing physical capital consider quality to be the extent to which (Colclough, Kingdon and Patrinos, 2009). education promotes the acquisition of cognitive skills deemed to be particularly Quantitative estimates of the economic relevant to employment, i.e. literacy and benefits which accrue to educated individuals numeracy/mathematical skills6. Research in terms of higher earnings vary according to undertaken in developed countries shows that 4. Data on percentage change in GDP (constant prices) for the period 2004-2014 from IMF World Economic Outlook Database, April 2015. 5. Returns to schooling depend not only on the levels of supply and demand in the employment market but also on the requirements of employers. As a result, the generalisation that returns to primary schooling in SSA currently exceed those to secondary level schooling may not hold for a particular country. For example, research in Ghana suggests that returns at the primary and junior secondary levels are now negligible and may even be negative (Palmer, 2007). 6. Green and Riddell (2012) include problem solving in their definition of cognitive skills in addition to literacy and numeracy / mathematical skills. In the OECD’s survey of adult skills, the cognitive skills considered are: literacy, numeracy and problem solving in technology-rich environments (OECD, 2013b). 31 the returns on these skills are significant. For significant effect. This leads them to a simple example, Green and Riddell (2012) show, using but powerful conclusion: “Once there is a Canadian data, that “(an) increase in literacy high-quality school system, it pays to keep and numeracy skills (of) half of a standard children longer in school – but it does not if the deviation is associated with an increase in school system does not produce skills” earnings equivalent to an additional year of (Hanushek and Wößmann, 2007, p.36). schooling” (Green and Riddell, 2012, p.3). Similarly, Crawford and Cribb (2013) find, using The implications for educational policy in SSA UK data, that “a one standard deviation are clear. After having invested, with great increase in Maths test scores at age 10 is success, in increasing enrolment rates at the associated with earning 13.0% more per week primary level8 and, more lately, at the secondary at age 30 … compared with 10.1% for a one level, the attention of governments must now standard deviation increase in reading test shift to raising the quality of education. In scores” (Crawford and Cribb, 2013, p.4). particular, national efforts should focus on Evidence as to the returns to cognitive skills developing schooling systems which promote in low-income countries in SSA is limited but the acquisition of key cognitive skills and several studies report positive estimates . 7 deliver significantly higher achievement levels Glewwe (1996), for example, shows that in literacy and mathematical skills. it is cognitive skills, rather than years of schooling, that determine earnings in Mathematics in SSA – a suitable case 2.2  Ghana’s private sector. for treatment Linking the quality of education at the micro Whilst policies are needed to promote better level to economic growth at the macro level is outcomes for all cognitive skills, mathematical far from straight-forward. However, using education in SSA is in particular and urgent mathematics and science test scores achieved need of attention. in the OECD’s Program for International Student Assessment (PISA) as indicators of First, there is mounting evidence that having quality, Hanushek and Wößmann (2007) find poor numeracy skills is a greater barrier to that “test scores that are larger by one standard economic and social well-being than having deviation … are associated with an average poor literacy skills. Parsons and Bynner (2006), annual growth rate in GDP per capita that is using UK data, found that “for women, while two percentage points higher” (Hanushek and the impact of low literacy and low numeracy Wößmann, 2007, p.32). Further analysis skills (on their life chances) is substantial, low comparing low- and high-income countries numeracy has the greater negative effect, even suggests that “the effect of quality is when it is combined with competent literacy” considerably larger in the low-income (Parsons and Bynner, 2006, p.7). For men, they countries” (Hanushek and Wößmann, 2007, conclude that “there is no real difference p.36). Interestingly, they also find that in low- between the effect (on life chances) of poor income countries, the duration of education literacy and poor numeracy together and poor when taken in conjunction with quality has a numeracy alone” (Parsons and Bynner, 2006, 7. For example, Boissiere, Knight, and Sabot (1985), Glewwe (1996), Jolliffe (1998), and Moll (1998) cited in Hanushek and Wößmann (2007, Table 3). 8. According to UNESCO (2015c), during the period 1999 to 2012 the enrolment of children in primary schools rose by 75% to 144 million. 32 p.7). Further evidence comes from the OECD’s Survey of Adult Skills conducted in 2011-2012 across 22 countries and from the secondary analysis of data conducted by Hanushek et al. Data from this survey suggests that an increase of one standard deviation in literacy proficiency is associated with an average increase of 8% in hourly wages whilst the corresponding increase for an increase of one standard deviation in numeracy proficiency is 17.8% (OECD, 2013b, p.224). Secondly, in recognition of the importance of mathematical skills in a competitive global economy, many high-income countries whose students perform at or around the international average are growing increasingly concerned about the gap between the mathematical achievement of their students and that of their peers in the high-flying economies of East Asia. However, the situation is far worse for nations in SSA where, as shown elsewhere in this report, standards in mathematics are currently extremely low in both relative and absolute terms. International data for countries in SSA is limited but that which is available makes for disturbing reading. For example, in TIMSS 2011, Grade 8 students from Korea, Singapore and Chinese Taipei scored, on average, more than 600 for mathematics – far above the TIMSS scale centre point of 500. All three participants9 from SSA scored at least one standard deviation below the international average (Botswana [397], Ghana [331], and South Africa [352]) (Mullis et al. 2012 pp. 42-43). For SSA, the achievement gap in mathematics is so large that Beatty and Pritchett (2012) predict that it would take of the order of 130 years for countries in SACMEQ to reach the current average levels of the OECD if business continues as usual (Beatty and Pritchett, 2012, Table 5). 9. Ghana met the sampling criteria for Grade 8 students but its average score of 331 placed it at the bottom of the international rank order. Both Botswana and South Africa tested Grade 9 students and so their scores are not directly comparable with those of Ghana or other TIMSS participants. 33 2.3 Science, technology, engineering and acknowledged (World Bank and Elsevier, 2014). mathematics: their importance to growth Steps have been taken in recent years to increase the number of students and Whilst this study focuses on the development researchers involved in STEM-related activities of mathematical skills across the ability range and to raise the quality of work in this field. and for a wide range of purposes, it is Some progress has been made in terms of the important to recognise the key role quantity and quality of research, but SSA mathematics plays as one of the STEM subjects started from a very low base and still has far to which are widely regarded as being critical to go. The region has also failed to close the gap national economic development in an on some of its potential competitors. The World increasingly technological world. In the world’s Bank (2014) suggests that the reasons for the major economies there is a consensus that the large and persistent gap between the demand industries that will, in the future, generate most for STEM skills and the supply include, “the low growth and offer the most rewarding quality of basic education in Science and Maths employment opportunities will be in sectors within SSA; (and) a higher education system related directly and indirectly to technology, skewed towards disciplines other than STEM engineering, science and similar disciplines. such as the Humanities and Social Sciences” Many western economies fear that they have (World Bank and Elsevier, 2014, p.4). already fallen behind the countries of East Asia where achievement in mathematics and science 2.4 What type of mathematics is needed? is far higher. As a result, investment in STEM subjects in schools and in institutions of higher ‘Classical’ mathematics curricula, many of which education is seen as a priority across the persist albeit in mildly modified forms in SSA, industrialised world. For example, in the USA were developed to meet the perceived needs of the President’s budget for 2016 alone allocates the late 19th and 20th centuries. However, it is more than three billion USD for enhancing becoming increasingly obvious that they are STEM education in and beyond high schools not well suited to a 21st century dominated by (United States, 2015). In the UK, the the rapid expansion of new technologies. government plan for growth in the period Borovik (2014) points out that such 2015-2021 pledges the equivalent of 8.9 billion technologies incorporate mathematical USD in the support of scientific excellence and algorithms and scientific principles that few are the development of technical skills and able, or need, to grasp. He suggests that “99% knowledge (United Kingdom, 2014). Similar of people have not even the vaguest idea about commitments to extremely high levels of the workings of 99% of technology in their investment in STEM can be found across the immediate surroundings - and this applies even world’s developed economies. more strongly to technological uses of mathematics, which are mostly invisible” In SSA, the importance of developing skills and (Borovik, 2014, p.3). In this new reality, knowledge in the STEM subjects to promote mathematics education need equip only a and sustain growth is now widely relatively small elite with the higher level skills 34 required by the productive STEM-based 2.5 Summary industries. The vast bulk of the population needs an education which focuses on the Investment in education yields significant development of ‘mathematical literacy’ and not, economic returns for individuals, for as in so many traditional curricula, on the communities, and for the nation. However, such mastery of procedures. For example, Borovik returns disappear when the quality of suggests that in a world where countries can education is poor. Maximum returns are enjoyed import, rather than design and manufacture, when education promotes the acquisition of high-tech components for their industries: “one the cognitive skills required by employers. Of can easily imagine a fully-functioning country these, evidence suggests that numeracy is the most important when it comes to generating where no-one has mastered, say, long division economic returns and spurring national growth. or factorisation of polynomials” (Borovik, 2014, Educational strategies for ensuring that all p.4). This clearly has significant implications for learners leave school as mathematically-literate curriculum design and delivery. citizens should be a priority. Mathematical literacy is defined in the PISA In an increasingly technological world, framework for mathematics as: “an individual’s education systems need to produce a sufficient capacity to formulate, employ, and interpret pool of young people educated in STEM mathematics in a variety of contexts. It includes subjects to meet the research, development reasoning mathematically and using and production needs of industry and mathematical concepts, procedures, facts and commerce. Some education will take place in tools to describe, explain and predict institutions of higher education and some will phenomena. It assists individuals to recognise be industry-based. However, for these to the role that mathematics plays in the world succeed, good foundations in mathematics and and to make the well-founded judgments and the other STEM subjects must be laid in schools decisions needed by constructive, engaged and – especially in the early years of education. reflective citizens” (OECD, 2013a, p.25). Ensuring that the vast majority of the The issues described above concern developed population become mathematically literate and developing countries alike. Some of the yields economic benefits at the micro and world’s wealthiest nations are already investing macro levels. First, more numerate workers heavily in order to catch up with the high-flying enjoy greater returns. Secondly, a workforce countries of East Asia. The scale of the enlisted from school graduates with higher challenge facing SSA, however, is dauntingly scores in tests of mathematical literacy typically large. Average student achievement is so low generates greater national growth. Thirdly, a that, at the current rate of progress, it will take workforce equipped, through education, with several generations for the region to approach better cognitive skills will adopt new the levels currently enjoyed by more developed technologies more rapidly than a less numerate economies – by which time the gap in workforce leading, potentially, to greater achievement may well have increased. Closing productivity (Riddell and Song, 2012). the achievement gap over a more acceptable timeframe will require truly radical reforms to the nature and organisation of mathematics education, and great innovation in the delivery of mathematics curricula. 35 36 Mathematics Education in Sub-Saharan Africa: 3 Current status: learning outcomes in mathematics in SSA 3.1 Context and sources of information The sources available fall into four main categories: international (global) large-scale Constructing a comprehensive picture of assessments; regional large-scale learning outcomes in mathematics across the assessments; national large-scale numerous and varied countries of SSA is assessments; and national examinations. Of problematic because the available data is these, international and regional assessments highly fragmented. The sources available to offer the best opportunities for drawing draw on are diverse in their purposes, their conclusions about relative and absolute levels methodologies, and in their measurement and of achievement in SSA. They have the added reporting scales. In short, there is no common advantage, especially over examinations, of metric and triangulation is difficult because bridges between data sets are, at best, collecting student, teacher and school tenuous. This problem would be more serious background data which can illuminate the key if the various surveys produced conflicting factors associated with better learning results but, as shown below, much of the outcomes in mathematics. Table 3.1 gives an available information points in the same overview of the major international and general direction – towards low average levels regional assessment programmes being of mathematical competence. conducted in SSA. Table 3.1: Overview of the major international and regional assessment programmes conducted in SSA Title Organisation Target population and typical Reporting scale Participation sample sizes Trends in Conducted under the auspices In-school students in Grade 4 and IRT-based scale: originally 59 countries/education systems are Mathematics and of IEA since 1995. Four-year in Grade 8. Typical sample is of the set with centre 500, participating in the 2015 cycle. The Science Study cycle focusing on mathematics order of 150 schools and 4,000 standard deviation (SD) 100 following SSA countries have taken part (TIMSS) and science. students. in TIMSS: Botswana, Ghana and South Africa. Program for Conducted under the auspices In-school students aged 15 years. IRT-based scale: centre 65 countries/economies participated International of OECD since 2000. Three-year Typical sample is of the order of 150 500, SD 100. in the 2012 cycle. Of all countries in Student cycle focusing on: reading schools and 4,500 students. SSA only the a-typical island state of Assessment literacy, scientific literacy and Mauritius has participated in PISA10. (PISA) mathematical literacy. Title Organisation Target population and typical Reporting scale Participation sample sizes Southern African Conducted since 1995 at five- In-school students in Grade 6 and In 2000 (SACMEQ II) The Consortium includes 16 Ministries of Consortium for or six-year intervals. Focus is teachers of Grade 6. an IRT-based scale was Education in Southern and Eastern Africa, Measurement on mathematics and reading The third SACMEQ cycle tested introduced having a centre Angola, Botswana, Kenya, Lesotho, of Educational achievement. about 60,000 pupils across 14 point of 500 and a standard Malawi, Mauritius, Mozambique, Namibia, Quality (SACMEQ) countries i.e. approximately 4,000 deviation of 100. Seychelles, South Africa, Swaziland, pupils per country. Tanzania (Mainland), Tanzania (Zanzibar), Uganda, Zambia, and Zimbabwe. Programme for PASEC has offered ‘diagnostic’ In-school students in Grades 2 Prior to 2013, results were Ten countries were evaluated in the Analysis of assessment services to and 6. reported as ‘percentage 2014: Benin, Burkina Faso, Burundi, CONFEMEN Francophone countries since Typical sample is of the order of 175 correct’ scores. The 2014 Cameroon, Ivory Coast, Congo, Niger, Education 1993. Since 2013, PASEC has schools and 2,500 students. survey used an IRT-based Senegal, Chad, and Togo. Systems adopted a new model to allow scale centred on 500 with a (PASEC) for international comparisons. standard deviation of 100. The focus is on mathematics and language (French or national language). Title Organisation Target population and typical Reporting scale Participation sample sizes Early Grade Conducted under the auspices Countries can identify the target Mixed scales including More than 40 countries worldwide have Mathematics of USAID. This is effectively an grade(s) but typically Grades 2 to 6. speed of response used EGMA and/or the complementary Assessment ‘on demand’ service rather than Typical sample size is of the order (‘automaticity’) and reading assessment EGRA. In SSA, (EGMA) a fixed-term survey. of 450 students at each target proportion correct. countries that have used EGMA grade11. instruments include Kenya, Malawi, Nigeria, Rwanda, Tanzania and Zambia. Uwezo12 Since 2009, Uwezo has School-aged children – including Criterion-referenced conducted annual surveys those who are out-of-school. assessment with results Three countries: Kenya, Tanzania and focusing on basic literary and Household surveys reporting on reported as ‘percentage Uganda. numeracy competencies. between 92,000 and 145,000 passing’. children per country. 10. Mauritius was one of ten countries/economies that took part in PISA+ which was a re-run of PISA 2009. 11. Note that 450 is the target sample size for each stratum of interest. For example, where a country wishes to report at the provincial level then -450 students are required in each province. 12. ‘Uwezo’ is Kiswahili for ‘capability’. The EFA Global Monitoring Report, 2015 classifies Uwezo as a national assessment. However, given that it was not specifically tailored to a particular nation’s requirements, here Uwezo is placed in a separate category along with EGMA. 37 3.2 Mathematical achievement in the early comprises about 150 schools and 4,000 years and across the primary phase of students for each target grade (Joncas and Foy, education 2011). Student scores are generated using item response theory (IRT) and reported on a scale Over the past twenty-five years, SSA has seen originally centred on 500 and having a standard much activity in the field of educational deviation of 100. The technical rigour of TIMSS assessment for the purposes of measuring means that average national performances can student learning, investigating the factors that be ranked and international comparisons made contribute to better outcomes, and identifying with a known degree of confidence. trends in levels of achievement. At least fifteen countries have designed and implemented their TIMSS assesses two populations – those own national assessment programmes 13 studying in Grade 4 and Grade 8. Of particular (UNESCO, 2015a, Table 1, p.305). A significant interest here is the younger population but, number participate in regional assessments unfortunately, only one country in SSA has such as SACMEQ and PASEC, but only a small participated at this level. In 2011, Botswana number have participated in international applied the TIMSS instruments, but to an studies. Much of this activity has focused on over-age population sampled from Grade 6. young learners and on the fundamental skills of The national average score for mathematics literacy (especially reading) and numeracy. was 419 – far below the scale centre point of Measuring and monitoring these skills has 500. Because Botswana’s sample did not match become increasingly important as primary that of other participants it was not placed in enrolment rates have expanded and concern the international rank order. However, some has grown over the quality of the education comparisons are of interest as shown in Table offered by state and private providers – 3.2. This shows that average mathematical especially to young learners. Objective achievement of Grade 6 students in Botswana evidence as to the quality of mathematics is much lower than that of Grade 4 students in education comes from a number of any of the other upper-middle-income assessments, each with its own philosophy, economies14 that participated in TIMSS 2011. methodology and objectives. Some of the key assessments and their headline findings are described here. Table 3.2: TIMSS 2011: Average mathematics scores for population 1 (Grade 4) for selected countries 3.2.1 Trends in Mathematics and Science Study (TIMSS) at Grade 4 Country Average scale Rank score (SE) (out of 50) The mathematical component of TIMSS is one Kazakhstan 501 (4.5) 27 of the most respected large-scale international TIMSS centre point 500 - assessments of student achievement in Romania 482 (5.8) 33 mathematics. TIMSS assessments are generally Turkey 469 (4.7) 35 considered to be ‘curriculum based’ (as Azerbaijan 463 (5.8) 36 opposed to PISA’s ‘literacy based’ approach) Thailand 458 (4.8) 38 with test instruments focusing on fundamental Iran, Islamic Republic of 431 (3.5) 43 mathematical concepts common to most Botswana (Grade 6) 419 (3.7) - national curricula. A typical national sample 13. Many more countries in SSA have conducted at least one national assessment over the period 1990-2015. However, the 15 cited here maintain on-going pro grammes of assessments and have completed at least one assessment since 2012 [UNESCO, 2015]. 14. World Bank classifications for the fiscal year 2016. Available at: http://data.worldbank.org/about/country-and-lending-groups#low-income. 38 3.2.2 SACMEQ The SACMEQ methodology has evolved over time. In particular, the method of calculating Established in 1995, SACMEQ is a consortium of student scores and reporting absolute levels of ministries of education across the southern and performance has become increasingly eastern Africa region. The constituent countries sophisticated. In SACMEQ II (2000), student are all, to a greater or lesser extent, scores were calculated using item response Anglophone15 except for Mozambique where theory to give scores on a scale centred on 500 the official language is Portuguese. Since its and with a standard deviation of 100. Moving to inception, SACMEQ has completed three cycles an IRT-based scale allowed SACMEQ to establish of student assessment and is currently a baseline against which changes over time completing the fourth - SACMEQ IV. The could be monitored. In SACMEQ III (2007), a assessments focus on the achievement of number of items from the previous survey were Grade 6 students in the areas of literacy included as ‘anchor items’ allowing results from (reading) and mathematics. National the two surveys to be placed on the same scale16. measurements are based on a probabilistic In addition to average scaled scores, SACMEQ sample drawn using methods comparable to reports the proportion of the target population those of TIMSS and PISA (SACMEQ, 2008). A reaching well-defined, absolute levels of nation’s sample size will depend on the number achievement. The levels descriptors for of strata identified as being of interest. mathematics are shown in Table 3.3. Combining However, the average number of schools the two reporting methods brings SACMEQ required is of the order of 185 giving a sample into line with the best practice established by of about 4,000 students. international studies such as TIMSS and PISA. Table 3.3: SACMEQ levels and behavioural descriptors for mathematics Level 1: Pre numeracy Applies single-step addition or subtraction operations. Recognises simple shapes. Matches numbers and pictures. Counts in whole numbers. Level 2: Emergent numeracy Applies a two-step addition or subtraction operation involving carrying, checking (through very basic estimation), or conversion of pictures to numbers. Estimates the length of familiar objects. Recognises common two-dimensional shapes. Level 3: Basic numeracy Translates verbal information presented in a sentence, simple graph or table using one arithmetic operation in several repeated steps. Translates graphical information into fractions. Interprets place value of whole numbers up to thousands. Interprets simple common everyday units of measurement. Level 4: Beginning numeracy Translates verbal or graphic information into simple arithmetic problems. Uses multiple different arithmetic operations (in the correct order) on whole numbers, fractions, and/or decimals. Level 5: Competent numeracy Translates verbal, graphic, or tabular information into an arithmetic form in order to solve a given problem. Solves multiple-operation problems (using the correct order of arithmetic operations) involving everyday units of measurement and/or whole and mixed numbers. Converts basic measurement units from one level of measurement to another (for example, metres to centimetres). Level 6: Mathematically skilled Solves multiple-operation problems (using the correct order of arithmetic operations) involving fractions, ratios, and decimals. Translates verbal and graphic representation information into symbolic, algebraic, and equation form in order to solve a given mathematical problem. Checks and estimates answers using external knowledge (not provided within the problem). Level 7: Concrete problem solving Extracts and converts (for example, with respect to measurement units) information from tables, charts, visual and symbolic presentations in order to identify, and then solve multi-step problems. Level 8: Abstract problem solving Identifies the nature of an unstated mathematical problem embedded within verbal or graphic information, and then translates this into symbolic, algebraic, or equation form in order to solve the problem. 15. Countries are permitted to translate SACMEQ instruments into major national languages. For example, Tanzania (mainland and Zanzibar) translates the tests into Kiswahili and Mozambique translates the tests into Portuguese. 16. The validity of SACMEQ scores for monitoring progress over time at the level of the individual country is explored further in Section 3.4 below. 39 The measured outcomes for the 15 countries is given. Students in this group are deemed to that took part in SACMEQ III (2007) are shown be “functionally innumerate (in that) they cannot in Table 3.4. The countries in this table have been translate graphical information into fractions or ordered by their average standardised score for interpret common everyday units of mathematics. In addition to the average score, measurement” (Spaull, 2011). Also included is the the proportion of students performing at or proportion of students at or below the ‘basic below the second level, i.e. ‘emergent numeracy’, numeracy’ level. Table 3.4: National average scores for mathematics for countries participating in SACMEQ III (2007) Country Average Standard Error Proportion (%) at or Proportion (%) at standardised score below Level 2 or below Level 3 Mauritius 623.3 5.83 11.2 26.7 Kenya 557.0 3.98 11.2 38.3 Tanzania 552.7 3.51 13.3 43.1 Seychelles 550.7 2.45 17.8 42.3 Swaziland 540.8 2.39 8.60 44.3 Botswana 520.5 3.51 22.4 56.4 Zimbabwe 519.8 4.98 26.6 57.3 SACMEQ III 509.7 1.16 31.4 63.0 South Africa 494.8 3.81 40.2 69.2 Zanzibar 489.9 2.35 32.4 73.4 Mozambique 483.8 2.29 32.8 74.2 Uganda 481.9 2.92 38.8 74.9 Lesotho 476.9 2.61 41.8 81.1 Namibia 471.0 2.51 47.7 81.7 Malawi 447.0 2.89 59.9 91.7 Zambia 435.2 2.45 67.3 91.8 The results show that Botswana’s Grade 6 On average, 31% of Grade 6 students are students perform significantly above the classified as innumerate with this proportion SACMEQ average. However, we know from the rising to more than 40% in South Africa, TIMSS 2011 results that Botswana’s Grade 6 Lesotho, Namibia, Malawi and Zambia. For 10 students perform far below their Grade 4 out of the 15 countries taking part, the majority counterparts in countries beyond SSA. This of students fall short of SACMEQ’s “beginning suggests that, with the possible exception numeracy” level. The situation is particularly of Mauritius, all other countries in the desperate in Lesotho, Namibia, Malawi and consortium are likely to perform extremely Zambia where at least four out of five children badly in global assessments. fail to reach this level. When we look at performance against the absolute levels of achievement of the SACMEQ framework, the picture is even less optimistic. 40 Underlying these aggregate results, SACMEQ’s in the lower and upper quartiles of the socio- rich dataset reveals significant variation economic status (SES) scale. Here, students in amongst groups as shown in Table 3.5. Overall, the upper quartile outperform their less the performance of boys is better than that of advantaged peers by a statistically significant girls but the difference is significant at the 95% margin in all countries except for Malawi. confidence level in just seven of the 15 Secondary analysis of South Africa’s data by participating education systems. Only in the Spaull (2011) reveals that whilst the socio- Seychelles did girls outperform boys by a economic status of individual students is a significant margin. Students studying in urban significant factor in predicting achievement, it is schools outperform their rural counterparts by far outweighed by the socio-economic status of a significant margin in 12 out of 15 education the school in which the student studies (Spaull, systems. The most consistent difference is 2011). This important finding is considered found when comparing the results of students further in Chapter 4. Table 3.5: SACMEQ III average mathematics scores by sub-group (SACMEQ, 2010a) Country Boys Girls Rural Urban Low SES High SES Botswana 517.5 (3.95) 523.6 (3.51) 501.1 (3.30) 538.8* (5.61) 479.0 (4.40) 553.1* (5.09) Kenya 567.6* (4.27) 546.0 (4.34) 544.5 (4.28) 580.0* (7.52) 540.9 (4.26) 595.8* (7.57) Lesotho 477.1 (3.02) 476.8 (2.80) 469.3 (3.03) 492.0* (4.43) 460.2 (3.31) 498.3* (3.87) Malawi 452.7 (3.30) 441.1 (3.11) 443.7 (3.44) 457.6* (4.66) 444.7 (6.23) 454.4 (3.39) Mauritius 616.1 (6.75) 630.7 (5.80) 613.2 (7.65) 634.1 (8.11) 554.2 (5.55) 719.2* (7.78) Mozambique 488.2* (2.36) 478.6 (3.22) 477.6 (4.39) 487.5 (2.59) 470.8 (4.17) 510.8* (3.31) Namibia 472.0 (2.76) 470.1 (2.62) 448.5 (2.18) 506.1* (4.66) 443.7 (2.74) 513.5* (4.88) Seychelles 535.2 (3.53) 566.7* (3.31) 550.2 (4.56) 550.9 (2.91) 498.7 (5.06) 593.6* (5.25) South Africa 491.2 (4.12) 498.4 (3.85) 456.7 (3.78) 533.1* (5.71) 446.2 (4.80) 578.6* (5.74) Swaziland 545.5* (2.59) 536.2 (2.61) 535.6 (2.80) 552.9* (4.08) 533.4 (3.27) 552.4* (2.95) Tanzania 568.5* (4.05) 537.5 (3.71) 542.1 (3.54) 575.7* (6.34) 540.4 (4.59) 579.4* (6.25) Uganda 486.7* (3.27) 477.2 (3.16) 470.8 (3.17) 511.5* (5.08) 465.4 (3.77) 504.2* (4.29) Zambia 440.8* (2.93) 429.2 (2.85) 428.6 (2.68) 447.2* (4.24) 424.5 (3.70) 463.1* (6.12) Zanzibar 489.3 (2.37) 483.9 (1.86) 477.8 (2.03) 500.5* (2.60) 471.1 (3.79) 510.0* (2.51) Zimbabwe 520.8 (5.80) 519.0 (5.25) 492.1 (4.10) 589.6* (6.57) 487.8 (5.86) 588.8* (6.99) SACMEQ III 511.9* (1.28) 507.6 (1.21) 493.9 (1.49) 533.2* (2.05) 488.7 (1.47) 541.7* (1.91) Note 1: Standard errors given in parentheses. Note 2: * indicates that the difference between the two associated sub-groups is statistically significant at the p<0.05 level. 41 3.2.3 PASEC competence as a benchmark. Michaelowa (2001) points out that “the choice of this Operating under the management of La particular cut-off point is subjective, but Conférence des Ministres de l’Education des motivated by the fact that the PASEC pays ayant le français en partage (CONFEMEN), questionnaires are to a large extent based on the Programme for the Analysis of CONFEMEN multiple choice questions which would lead to Education Systems (PASEC) provides almost 30% of correct answers even if answers assessment tools to affiliated Francophone were given at random” (Michaelowa, 2001, countries in Africa and Asia. Established in 1993, p.1703). Unfortunately, the average PASEC tools have, to date, been used in about performance of many PASEC countries fell far 20 African countries to assess student below even this most modest of expectations achievement in French and Mathematics17 with 7 of the 12 recording average scores below (EPDC, 2015). Prior to 2014, PASEC instruments the 40% threshold and disturbingly close to the were primarily used by individual countries for theoretical guessing level (CONFEMEN, 2010). diagnosis and research – the programme was not designed for making inter-country Since 2012, PASEC has been moving towards comparisons. For example, many countries the introduction of new instruments which will chose to test their Grade 2 and/or Grade 5 enable countries to make more robust students at the beginning and end of the international comparisons. In particular, PASEC academic year in order to monitor progress. procedures and assessment frameworks are Background data collected alongside the being brought into line with those of the student assessments allowed countries to SACMEQ IV project. The use of IRT to calibrate investigate the factors connected with items will allow PASEC and SACMEQ to link educational achievement including, for their IRT-based score scales through the use of example, repetition and double-shift schooling. common anchor items. In addition, PASEC’s National sample sizes vary but are typically adoption of the SACMEQ levels descriptors for around 175 schools and 2,500 students18. mathematics will allow Francophone and Anglophone countries across SSA to compare Evidence as to the relative and absolute levels the proportions of their students who reach, for of student achievement in mathematics from example, minimum standards of numeracy. The historic (i.e. pre-2014) PASEC assessments is technical challenges of, for example, ensuring limited and its interpretation problematic. appropriate sampling strategies and accurate Countries conducted their evaluations in translation will be daunting, but the different years and under different conditions. collaboration has great potential. Evidence of a In addition, student scores were reported as quantum leap in the quality and potential ‘percentage correct’ and, hence, were test power of a reformed regional, large-scale dependent. Notwithstanding these serious assessment can be found in the recently limitations, some attempts were made to published international report of the PASEC compare countries using, for example, PASEC’s survey of 2014 referred to as PASEC2014 historic ‘40% correct’ threshold of minimum (PASEC, 2015). 17. Countries which have used PASEC tools include: Burkina Faso, Benin, Burundi, Cameroon, Chad, Congo, Congo-Brazzaville, Comoros, Côte d’Ivoire, Djibouti, Gabon, Guinea, Madagascar, Mali, Mauritania, Mauritius, Niger, the Central African Republic, Senegal, and Togo (CONFEMEN, 2015). 18. For example, the 2008 evaluation in Burundi sampled 176 schools and 2,625 Grade 5 students and in 2007, Senegal sampled 158 schools and 2,189 students. 42 PASEC2014 covered ten countries: Benin, the ten participating countries20 more than half Burkina Faso, Burundi, Cameroon, Chad, Congo, the Grade 2 students (52%) fell below the Côte d’Ivoire, Niger, Senegal and Togo. In each ‘Sufficient’ threshold and nearly a fifth (18%) country, two populations were defined: ‘early could not even reach Level 1 (i.e. the minimum primary’ (Grade 2) and ‘late primary’ (Grade 6). level of competence measured by the test Typical national sample sizes for the Grade 6 instruments). The late primary population fared population were between 180 and 200 schools worse with 64% of students in nine reference and about 3000 students. The degree of countries (excluding Burundi) falling below the standardisation of both assessment instruments ‘Sufficient’ threshold and nearly a third (30%) and procedures was far greater than in earlier failing to reach Level 1. studies bringing it into line with international best practice for comparative studies. Most Secondly, the study confirms that national significantly, relative outcomes were reported mathematics scores at the early and late on IRT-calibrated scales and absolute outcomes primary stages are correlated to a moderately were related to well-defined, criteria-referenced strong21 degree (r=0.74 and rank order performance levels. The IRT-based reporting correlation ρ=0.62) as shown in Figure 3.2. This scale for 2014 was adjusted to give a group relationship suggests that countries which fail mean of 500 and a corresponding standard to equip their young learners with adequate deviation of 100. This gives a baseline against mathematical skills in the earliest years of which changes over time may be monitored education will fail to close the gap on their provided that future test instruments can be more successful neighbours by the end of firmly anchored to those used in 2014. In primary education. addition, PASEC2014 datasets are in the public domain19 making secondary analysis by independent researchers possible. Three key findings are particularly relevant here. First, across participating countries, absolute levels of achievement are low. PASEC2014 defines three positive levels of mathematical achievement for both the early primary and late primary populations. Each level has a detailed ‘Description of Competencies’ and the boundaries between levels are systematically linked to the IRT-score scale. The ‘Sufficient Competency Threshold’ lies between Levels 1 and 2. Students who fall below this threshold “risk encountering difficulties later in education due to insufficient mathematical competencies” (PASEC, 2015, p. 49). Unfortunately, in nine of 19. For example, data for the Grade 6 population is available at: https://drive.google.com/file/d/0By7A35n7_l4dTDFBMHB3UkFqXzQ/view?usp=sharing [Accessed 19 January 2016]. 20. Burundi is an exceptional case with 85% of Grade 2 students and 87% of Grade 6 students passing the ‘Sufficient’ threshold. 21. The product-moment correlation between national scaled scores is +0.74 and the Spearman rank order correlation is +0.62. 43 3.2.4 National assessments Figure 3.1: Relationship between national mathematics scores at the early and late stages of primary education (PASEC 2015, p.56) Over the past 25 years an increasing number of countries in SSA have carried out national 650 assessments. The main advantage of large- Average National Mathematics Score - Late Primary scale national assessments over regional and 600 Burundi international assessments is that they allow 550 countries to tailor the research questions to Senegal Burkino Faso address national priorities and issues of Togo 500 concern. In particular, tests can be better Benin Cameroon Côte d’ivoire Congo matched to national curricula and the general 450 ability levels within the student cohort. The 2015 EFA Global Monitoring Report lists 29 400 Niger countries in SSA that have conducted at least one national assessment since 1990 (UNESCO, 350 2015a). However, implementing a high-quality 350 400 450 500 550 600 650 national assessment is both expensive and Average National Mathematics Score - Early Primary technically challenging. As a result, many of the countries listed in the EFA report have not yet established a continuous and sustainable system of national assessments for monitoring Thirdly, the study reveals significant differences purposes. Table 3.6 shows 14 countries which amongst the 10 participating nations. have developed national capacity to carry out According to these results, the average assessments targeted at particular grades and performance in Burundi (for the late primary have repeated measurements on at least two population) is approximately one standard occasions over the past decade. With the deviation above the international average whilst exception of Mauritius, all other countries direct Niger languishes one standard deviation below. considerable effort towards measuring student To put this in perspective, 87% of Grade 6 performance in mathematics/numeracy and students in Burundi reach the ‘Sufficient’ language in the primary phase of education (i.e. threshold whilst the corresponding proportion from Grade 1 to Grade 6). for Niger is just 7.6%. Even when the extreme case of Burundi is removed, significant The national assessments used across SSA differences remain. For example, Senegal has differ in their methods of sampling, evaluation, 59% of students passing the ‘Sufficient’ analysis and reporting. There has been little threshold compared with just 19% in Chad. The external evaluation of the quality of these PASEC2014 report does not suggest reasons national assessments and several of the reports for the large variations detected but it provides reviewed as part of this study show serious valuable data for secondary analysis of inter- technical weaknesses - especially in the areas and intra-national differences. of probabilistic sampling, weighting of scores, and the calculation of standard errors and their 44 use in detecting statistically significant qualitative evidence as to the context in which differences. Notwithstanding these their students are learning or, as is more shortcomings, investment in national commonly the case, failing to learn. assessment does provide policymakers with Table 3.6: National assessment programmes conducted by countries within SSA Title Grade(s) Subjects Year(s) Burkina Faso Evaluation sur les Acquis 3 French, Mathematics Annually, 2001–2012 Scolaires 5 French, Mathematics, Annually, 2001–2012 Sciences Ethiopia National Learning Assessment 4 English, Mathematics, 2000, 2004, 2008, 2012 Environmental Sciences 8 English, Mathematics, 2000, 2004, 2008, 2012 Biology, Chemistry, Physics Ghana National Education 3, 6 English, Mathematics 2005, 2007, 2009, 2011, Assessment 2013 School Education Assessment 2, 4 English, Mathematics 2006, 2008, 2010 Lesotho National Assessment of 3, 6 English, Sesotho, 2003, 2004, 2006, 2008, Educational Progress Survey Mathematics 2010, 2012, 2014 Malawi Assessing Learner 5 Chichewa, English, 2005, 2008 Achievement Mathematics 3, 7 Chichewa, English, 2005, 2009 Mathematics, Life Skills Mauritius National Form III Assessment 9 English, French, Annually, 2010 to 2014 Mathematics, Computer Studies, Physics, Biology, Chemistry National Assessment 3 Mother Tongue, Portuguese, 2000, 2006, 2009 Mozambique Mathematics National Standardised 5, 7 English, Mathematics 2009, 2011 Namibia Achievement Test Nigeria National Assessment of 4, 5, 6 English, Mathematics, 2001, 2003, 2006, 2011 Universal Basic Education Sciences, Social Studies, Programme Life Skills South Africa Annual National Assessment 1 to 6, 9 Literacy, Numeracy Annually, 2011–2014 National Assessment Test 3 English, Mathematics, Annually, 2008–2014 The Gambia Integrated Studies Biennially from 2015 5 English, Mathematics, Annually, 2008–2014 Sciences, Social and Biennially from 2016 Environmental Studies 8 English, Mathematics, Annually from 2012 Science, Social and Environmental Studies Uganda National Assessment of 3, 6 English, Mathematics 1996, 1999, 2003, 2005, Progress in Education 2006, 2007, 2008, 2009, 2010 8 English, Mathematics, Annually, 2008–2013 Biology Zambia National Assessment 5 Literacy, English, 1999, 2001, 2003, 2006, Programme Mathematics, Life Skills 2008, 2012 Zimbabwe Early Learning Assessment 3 English, Mathematics 2012, 2013/14, 2015 (ZELA) 45 The findings of three well-developed national problems associated with sampling, potentially assessments with regards to the mathematical yields more information, and offers the achievement of students are described here for possibility of using data for both school illustrative purposes . 22 accountability and monitoring the progress of individual students. In Ghana, the national education assessment programme assesses student competency in Since 2011, South Africa has tested all students in mathematics and English in Grades 3 and 6. The the target Grades 1-6 and 9. The scale of the sample for the 2013 cycle covered all 10 regions exercise is vast with more than 25,000 schools of Ghana with a total, national sample size of participating in 2014 and a target population of 550 schools and approximately 37,000 students 7,376,334 students. The items used are (MES, Ghana, 2014). The sub-domains for predominantly of the constructed response type. mathematics were: numbers and numerals; basic Student scores are calculated as a percentage of operations; measurement, shaping space; correct answers with an ‘acceptable collecting and handling data. The tests were achievement’ threshold set at 50%. In addition, made up of multiple-choice items. Student above a minimum threshold of 30%, six scores were calculated as the percentage of qualitative levels are identified: elementary; correct answers. A threshold of 35% was set for moderate; adequate; substantial; meritorious; a ‘minimum competency’ level with 55% defined outstanding. In the 2014 study, 13.2% of Grade 3 as ‘proficient’. It should be noted that these are students failed to achieve the elementary level in arbitrary benchmarks and that the theoretical mathematics and only about two-thirds (64.4%) guessing level constitutes a significant reached the level deemed ‘adequate’. Of the proportion of these – particularly at the students in Grade 6, 28.9% failed to achieve the minimum competency threshold. In the 2013 elementary level and just over one-third (35.4%) study, 42.9% of Grade 3 students and 39.2% of reached the ‘adequate’ level (DBE, RSA, 2014). those studying in Grade 6 fell below the As in the case of Ghana, no information as to the minimum competency threshold. At the higher absolute levels of mathematical achievement competency level, 22.1% of Grade 3 students and associated with the designated levels is available 10.9% of Grade 6 students were deemed in the published reports. proficient. No information is available in the published reports as to the absolute levels of National assessment has a relatively long achievement, i.e. which mathematical tasks the history in The Gambia. In 2000 and 2002, students at each level could and could not do. students in Grades 3 and 5 were assessed using the UNICEF Monitoring of Learning Two countries in SSA – The Gambia and the Achievement (MLA) sample-based model. Republic of South Africa have adopted a census However, following the abolition of a high- approach to national assessment in which all stakes selection examination (Common students in the target populations are tested. Entrance Examination) traditionally held at the Using a census approach is far more expensive end of Grade 6, it was decided that all students than using a relatively small but representative in key grades should be assessed through a sample. However, it avoids many of the National Assessment Test (NAT). The main aims 22. These three examples were chosen because their reports were readily available. In other cases we could not find recent reports or other documentation. 46 were: to provide more information about the these are test-dependent it is difficult to quality of student learning during the basic extract any meaningful information. For phase of education; to provide information example, what can the reader make of the fact about the performance of individual schools; that the average score on the mathematics and to maintain the motivation of teachers and test for Grade 3 was 44.3% and that the students which was formerly boosted by the standard deviation was 19.8%? The report uses presence of the Common Entrance Examination these values to conclude without further (MBSE, The Gambia, 2015). Initially the NAT explanation that “Achievement in Mathematics targeted core curriculum subjects at Grades 3 continues to be a challenge” (MBSE, The and 5 with both populations and all subjects Gambia, 2015, p.57). assessed annually from 2008 to 2014. In 2012, the NAT was expanded to include all students The use of test-dependent percentage correct in Grade 8. In order to improve efficiency, a new scores in the NAT means that the results pattern of testing was introduced in 2015. The cannot be used to monitor trends. However, Grade 8 population is to be assessed every year the report for 2014 compares average scores but Grades 3 and 5 will be tested in alternate from 2012-2014 and uses these to imply that years (starting with Grade 3 in 2015). mathematical achievement has improved over time (ibid). It should be noted that an In 2014, approximately 32,000 Grade 3 alternative mechanism for monitoring changes students. 27,000 Grade 5 students and 22,000 over time has been proposed, and piloted, for Grade 8 students participated in the NAT. The the NAT. This involves incorporating a set of subjects tested were: English, Mathematics, common anchor items in tests used at four- or and Integrated Studies (Grade 3), English, five-yearly intervals with outcomes to be Mathematics, Science, Social and linked by IRT scaling. The intention is that this Environmental Studies (Grade 5) and English, method will be used, for example, to compare Mathematics, Science, Social and Grade 5 results from 2012 with those of 2016 Environmental Studies (Grade 8). The tests for and to compare Grade 3 results from 2012 with mathematics are composed of four-option those of 2017. After sharing the report for multiple-choice items and results are 2014, the government has taken on board calculated as percentage correct scores. Two feedback and has actively sought to address proficiency thresholds are set: ‘minimum these shortcomings in future NAT reports. competency’ at 40% of the maximum possible test score23 and ‘mastery’ at 80% of the maximum possible test score. In the 2014 report, these thresholds are not linked to behavioural descriptors and so no information is available as to what students at these levels can and cannot do in mathematics. The final report gives average scores and standard deviations (but not standard errors) for the tests applied at each target grade but since 23. The report of the 2014 NAT makes no mention of the 25% theoretical guessing factor which represents a significant proportion of, for example, the minimum competency threshold score. 47 The examples from the Gambian NAT highlight (junior) secondary phases, between the junior an important general issue with implications for and secondary phases, and at the interface of all countries trying to harness the potential of (senior) secondary and tertiary education. Such large-scale national assessments. The Gambia examinations, conducted by national or regional has followed international trends in assessment assessment agencies, are generally well- and has invested heavily in its national established and tend to have extremely high assessment system. It has put in place many of public profiles. As such, one would expect them the technical and administrative procedures to be a rich source of information as to the necessary for the conduct of a large-scale current state of mathematics education in SSA. assessment and it has successfully embedded Unfortunately, this is not the case. The high- the NAT in its education system. However, the stakes associated with the main examinations NAT is still some way from realising its full and the significant risks presented by potential and, is not offering the government malpractice mean that examining authorities, best value for money. To address this, two steps not unreasonably, give priority to maintaining are necessary. First, the scope and quality of secrecy and security throughout the the information yielded by the NAT should preparation, conduct, and result-processing continue to be reviewed by key stakeholders stages of the examination. As a result, relatively including policy makers and educational little attention appears to be paid to the practitioners with the support of assessment dissemination of quantitative and qualitative specialists. In short, the stakeholders should ask information about candidate performance at “Is the NAT providing answers to the most the subject level. pressing questions in our education system and, if not, how should it be transformed to The problem alluded to above has four main provide the information that we need in dimensions. First, many of the examinations forms we can understand and use?” Secondly, used to select students for opportunities at the technical limitations and shortcomings in the next level of education and/or to place students reporting of results should be rectified through in particular schools are ‘group certificates’. strengthening technical capacity and This means that students’ overall results are implementing rigorous quality control determined by aggregating their results from a procedures. This may require the sustained number of predetermined subjects – including, use of international technical assistance until without exception, mathematics. These sufficient local capacity and experience is aggregated results are of paramount interest in place. for students, their parents, schools, and the general public and so it is these that are issued 3.2.5 Examinations by examination boards and reported in the mass media. In many cases it is difficult, if not Formal examinations are a dominant feature of impossible, to find results by subject. Secondly, education systems across SSA. Their key where results for separate subjects are purposes are selection and/or certification of published, they are generally aggregated by learner achievement at critical transition points. ‘grade’ or ‘division’. However, the mechanisms Typically, these lie between the primary and by which grade thresholds (cut-scores) are 48 determined are not transparent. In the case of Two examples are given below for illustrative countries using examination procedures derived purposes. from earlier colonial models, it is likely that the grading process involves an uncertain mix of In Uganda, students sit the primary leaving norm-referencing and ‘expert judgement’. This examination (PLE) at the end of Grade 7. The makes interpreting pass rates and other examination comprises tests in: English performance indicators problematic. In short, it Language; Mathematics; Science; and Social is not possible to determine what the students Studies. Student scores on individual tests are receiving a particular examination grade know graded as distinction, credit, or pass. Subject and can do in mathematics. Thirdly, because results are then converted into points (1 to 9, each test administration uses entirely new with 1 being best). These are then added to give question papers without any systematic link to an aggregate point score which is then earlier tests, examination scores and pass rates converted into an overall grade for the PLE. cannot be used to monitor educational Higher ability students with between 4 and 12 progress in a meaningful way25. Fourthly, the points are classified as being in ‘Division 1’; national and/or regional authorities responsible those with between 13 and 23 points are in for high-stake examinations do not make ‘Division 2’; those with between 24 to 29 points primary data (e.g. student test scores and item are in ‘Division 3’; and, those with between 30 statistics) easily available to bona fide to 34 points pass in ‘Division 4’. It is this final researchers26. Even basic summative statistics classification which determines a student’s (e.g. average scores, standard deviations, etc.) place in the secondary education system and and overall test-score distributions are not so is the focus of attention for all stakeholders published as a matter of course. This means (Kavuma, 2010). The absolute performance of that the measurement characteristics of students in mathematics, or any other subject, subject-specific examinations cannot be is, to all intents and purposes, lost in the independently evaluated and the absolute grading and aggregation processes. Table 3.7 levels of mathematical achievement displayed shows the subject-specific grading of the PLE by test-takers cannot be determined. in 2014 (UNEB, 2014). Table 3.7: Results of the 2014 Primary Leaving Examination in Uganda by subject Subject Number of candidates Pass (or above) Credit (or above) Distinction Mathematics 585,906 85.8% 49.0% 5.8% Science 585,707 85.5% 63.5% 7.8% Social Studies 585,914 92.6% 75.5% 10.9% English 585,926 83.9% 57.0% 7.2% 25. In the absence of better measures, examination pass rates are often cited as indicators of educational quality and of changes in national levels of achievement. For example, in the Ugandan Certificate of Education, it was reported that “performance in Mathematics dropped significantly” because the proportion of candi dates gaining the highest division fell from 4.1% in 2013 to 1.8% in 2014 (Ahimbisbwe, P., 2015). However, other plausible explanations include an increase in the difficulty of the questions and/or the effect of unintentionally setting slightly higher standards. 26. For the purposes of this study, examination boards in six countries were asked by World Bank representatives to supply basic statistical information for their main examinations in Mathematics. Two boards in Nigeria provided aggregated data but not the subject score distributions and grade thresholds requested. All other examining agencies failed to respond. 49 In Kenya, students sit the Kenya Certificate of correspond closely to the mathematics Primary Education (KCPE) at the end of Grade curricula for primary grades of countries in SSA 8. Children are tested in Mathematics, English, and beyond. Results are reported separately for Kiswahili, Science, Social Studies and Religious each sub-domain. Number (and proportion) of Studies, primarily through multiple choice items tasks completed successfully are reported. In but with extended writing in English and addition, the numbers of addition and Kiswahili. “The marks in each subject are subtraction tasks completed successfully in one standardised” (KNEC, n.d.). Aggregated results minute are reported as a measure of are reported as a standardised score on a 27 ‘automaticity’. scale with a mean of 250. Students who score 200 or more are generally assured of a place Tests are conducted on a one-to-one basis with (“slot”) in a public secondary school. However, tasks being presented orally by a trained test pressure on such places is exceptionally high administrator. Students respond orally28. This with approximately 200,000 candidates for feature of EGMA allows tasks to be presented KCPE failing to gain automatic admission in in languages and dialects that the children 2014. No information as to the performance of understand rather than, as is often the case students on individual subjects appears to be with written tests, in a language in which the publicly available. child is not yet proficient. Test administrators use tablets and Tangerine® software to record The more general role of examinations in assessment and questionnaire responses. mathematics education is considered in The optimum sample size for a population of Chapter 8. interest (stratum) is of the order of 450, i.e. 40-50 schools with 10-12 students chosen 3.2.6 Early Grades Mathematics Assessment randomly within each. For example, in Rwanda (EGMA) in 2011, two grades were tested (P2 and P4) in 42 selected schools. In each school, 10 pupils The development of the EGMA Concept was were to be selected in each grade giving an co-ordinated by USAID under its EdData II intended sample size of 420 per grade (USAID, programme. At its core lies a framework for the 2012a). In Ghana in 2013, only one grade was acquisition of mathematical skills by young tested but the population was stratified first by learners based on extensive research (USAID, region (10) and then by language of instruction 2009). EGMA assessment instruments, (e.g. 6 in Greater Accra). 45 schools were methods and reporting procedures reflect the selected for each major stratum and fewer for, content of the framework. The EGMA for example, very small language groups. This measurement sub-domains for lower grades gave a total intended sample of 815 schools and (e.g. Grade 4) are: number identification; 8,150 students. The achieved sample was 805 quantity discrimination: missing numbers in schools and 7,923 students (USAID, 2014, p.7). patterns: addition and subtraction: word problems. For slightly older pupils (e.g. Grade In addition to student assessment, EGMA also 6), countries may choose to add, for example, collects background information from sampled multiplication and geometry. These, in general, students, teachers (one per sampled school) and school principals. This information is 27. Whilst the KCPE system is clearly norm-referenced, the implications do not appear to be fully understood by educational policy makers. For example, the 2014 results were announced by the Cabinet Secretary as being “relatively the same as last year (since)… 436.814 students got more than 251 marks, representing 49.61 percent of those who sat for the exam, compared to 49.71 percent last year” (Kenya Today, 2014). 28. For higher grades, some calculation questions may be presented in writing with students working out answers on paper. 50 primarily used to give a snapshot of the context 3.2.7 Uwezo in which mathematics is taught and learned. The methods used and the limited precision of “Uwezo is part of Twaweza, an independent the measurement procedure means that EGMA East African initiative that promotes access to data is not generally well suited to identifying information, citizen agency and improved relationships between background factors and service delivery outcomes across the region” achievement levels29. However, the clarity of the (Uwezo, 2014, p.2). It assesses what children EGMA structure and its criterion-referenced know and can do in relation to selected tasks lead to clear, comprehensible conclusions objectives of the national Grade 2 curriculum in and, in many cases, stark headline findings for reading and basic mathematics in Kenya, educational planners as exemplified below. Uganda and Tanzania. It is unlike any other “The majority of children scored zero across the major assessment of children’s learning in SSA sub-tasks, indicating that they have not in that it assesses children in their homes. As a acquired foundation skills in Mathematics.” result, it includes in its sample not only those EGMA in Bauchi and Sokota states, Nigeria, attending state and private schools, but also 2013 (USAID, 2013). those who are out of school. Its assessment instruments are short and clear with numeracy “Pupils were asked to compare single- and tasks assessing counting, number recognition; double-digit numbers, and to say which was the comparison of numbers and basic operations larger… . In Grade 2, 18% of pupils were unable (addition, subtraction, multiplication and to answer a single item, while in Grade 3, fewer division). Examples are given in Figure 3.2. than 12% could produce a correct response (to The approach is child-centred with assessors all items).” EGMA in Zambia, 2011 (USAID, not presenting the more difficult questions to 2012b). children who have ‘failed’ on simpler tasks. In each sub-domain, children are allowed to “… on the missing number, addition level 2 and choose which tasks they attempt. subtraction level 2 subtasks, there was a sharp drop-off in performance, with nearly 70% of the For example, in the multiplication task pupils unable to answer a single subtraction illustrated in Figure 3.2, the child can attempt level 2 item correctly - the easiest of these any three of the items. Mastery (success) in this being: 19 – 6 = .” EGMA in Ghana, 2013 task is defined as two or three correct. (Uwezo, (USAID, 2014). 2014). The criterion for ‘passing’ the numeracy test is success (at the defined mastery level) in “In P4, only 50% of the students were able to all of the numeracy sub-domains. Uwezo’s indicate the correct (geometrical) shape when assumption is that children older than the given its attributes. Of P4 students, 56% were target age for Grade 2 should be able to unable to name any of the shapes presented (in demonstrate mastery of the fundamental either English or Kinyarwanda). In P6, the mathematical concepts of the Grade 2 majority of students could indicate the correct curriculum. Unfortunately, the survey shape based on its attributes, but 38% could consistently shows that this is far from the case. name only one of the shapes.” EGMA in In Uganda for example, only 44% of those aged Rwanda, 2011 (USAID, 2012a). 29. Notwithstanding this cautionary note, in some countries data has been analysed to relate outcomes to, for example, socio-economic status. 51 10-16 passed the numeracy test (Uwezo, 2014, p.13). (The corresponding pass rate was 68% in both Tanzania and Kenya.) Figure 3.2: Examples of basic numeracy tasks used in Kenya for the Uwezo assessment of 2013 Count and Match Multiplication 7 9 2x4= 3x2= 5x3= 5 2 4 4x3= 5x2= 5x5= 8 6 1 3x4= 4x5= 3 Perhaps the greatest strength of Uwezo, like rapidly growing primary school enrolment rates. that of the original model established by ASER/ However, as yet, there has been much less Pratham in India, is its capacity to produce activity at the secondary level. The range of simple, clear and powerful messages. assessments is much narrower and, in particular, Statements, such as those shown below, can be there are few which yield information as to understood at all levels of the community and absolute levels of mathematical ability. As at are difficult for politicians to ignore. the primary phase, few countries in the region “Less than a third of children enrolled in Grade have participated in international large-scale 3 have basic Grade 2 level literacy and assessments, but at the secondary level there numeracy skills” (Uwezo, 2014, p.4). are no regional large-scale assessments “A significant number of children do not comparable to those of SACMEQ and PASEC. possess foundational Grade 2 level skills even as Some countries have started to develop their they approach the end of the primary school own national assessments for secondary cycle” (ibid, p4). education but these are less numerous and less well-developed than those for primary grades. 3.3 Standards in the secondary phases of The sources of information which do exist and education their key findings are described below. As can be seen from the above, the past 20 3.3.1 TIMSS at Grade 8 years have seen rapid development of assessment systems for measuring the Just three countries in SSA have participated in mathematical competences of students across TIMSS for Grade 8 students: Botswana; Ghana; the primary phase of education in many and, South Africa. Botswana and Ghana have countries of SSA. This has coincided with taken part in all three cycles since 2003. South 52 Africa participated in 2003 and 2011. All three Africa selected their samples from Grade 9. countries are participating in the current 2015 Whilst these cohorts fared better than their cycle. Table 3.8 shows that their performances predecessors, their average scores for have consistently fallen far below international mathematics still fell at least one standard norms and have been placed towards the bottom deviation below the international mean. Ghana, of the international rankings. In the 2011 cycle, in the only country to select from Grade 8, finished order to better match the TIMSS instruments with at the bottom of the international rankings for the the ability of their students, Botswana and South 42 participating countries/economies. Table 3.8: TIMSS mathematics results for population 2 (Grade 8) for SSA participants 2003-2011 Mean Maths Rank order/total Mean Maths Rank order/total Mean Maths Rank order/total score (SE) participants score (SE) participants score (SE) participants Botswana 366 (2.6) 42/45 364 (2.3) 43/49 397*(2.5) Ghana 276 (4.7) 44/45 309 (4.4) 47/49 331 (4.3) 42/42 South Africa 264 (5.5) 45/45 --- --- 352*(2.5) International 467 (0.5) 453 (0.7) 469 (0.6) The 2011 TIMSS report provides information as to on the TIMSS reporting scale and defined by the absolute performance of students by descriptive criteria. Four benchmarks are reporting the proportion of the cohort reaching defined as in Table 3.9. international benchmarks which are both fixed Table 3.9: Descriptions of the TIMSS international benchmarks for achievement in mathematics (Grade 8) International Scale score Descriptor Benchmark Advanced 650 Students can reason with information, draw conclusions, make generalisations, and solve linear equations. Students can solve a variety of fraction, proportion, and percent problems and justify their conclusions. Students can express generalisations algebraically and model situations. They can solve a variety of problems involving equations, formulae, and functions. Students can reason with geometric figures to solve problems. Students can reason with data from several sources or unfamiliar representations to solve multi-step problems. High 550 Students can apply their understanding and knowledge in a variety of relatively complex situations. Students can use information from several sources to solve problems involving different types of numbers and operations. Students can relate fractions, decimals, and per-cents to each other. Students at this level show basic procedural knowledge related to algebraic expressions. They can use properties of lines, angles, triangles, rectangles, and rectangular prisms to solve problems. They can analyse data in a variety of graphs. Intermediate 475 Students can apply basic mathematical knowledge in a variety of situations. Students can solve problems involving decimals, fractions, proportions, and percentages. They understand simple algebraic relationships. Students can relate a two-dimensional drawing to a three-dimensional object. They can read, interpret, and construct graphs and tables. They recognise basic notions of likelihood. Low 400 Students have some knowledge of whole numbers and decimals, operations, and basic graphs. 53 At the international median the proportions of 3.3.2 PISA the cohort reaching or exceeding each benchmark are: Low 75%; Intermediate 46%; It is widely recognised that the literacy-based High 17%; Advanced 3%. However, in Ghana, assessment frameworks of OECD’s PISA only 21% of students could reach the lowest programme reflect the demands of a modern, benchmark. By way of comparison, 36% of competitive, global market where new Moroccan students, 57% of Chilean students, technologies play an increasing role. In and 61% of Tunisian students reached this particular, PISA’s assessment of mathematical minimum level. At the other end of the literacy for 15-year-olds is seen as providing spectrum, 99% of Singaporean and Korean important information to national policymakers students surpassed the lowest benchmark. 50% trying to accelerate the development of human of Grade 9 students from Botswana reached resources appropriate for the 21st-century. the low benchmark but only 1 in 4 (24%) of the However, to date, the only PISA participant South African Grade 9 sample was capable of from SSA has been Mauritius. Mauritius took reaching this level. part in PISA+, the re-run of PISA 2009, and, in mathematics and science scored at a level The TIMSS 2011 Grade 8 assessment included commensurate with that of the two lowest the following item which typifies performance performing countries of the OECD, Chile and around the low international benchmark: 42.65 Mexico. Approximately 50% of students from + 5.748 = ? Internationally, 72% of students Mauritius reached the PISA baseline level of could solve this problem. However, only 36% of competence (Level 2) at which “they begin to Ghanaian students were successful. Clearly the demonstrate the kind of skills that enable them gap between the performance of students from to use mathematics in ways considered SSA and that of their international peers is fundamental for future development” (Walker, disturbingly large. 2010, p. xiii). This compares with the OECD average of about 78%. In considering this outcome it should be noted that Mauritius is not typical of the SSA region. It is a relatively wealthy, small island state which boasts a traditionally strong education system regularly outperforming other countries within SACMEQ by a significant margin. Table 3.10: Description of the PISA baseline level of competence (mathematical literacy) PISA level Scale score Behavioural Descriptor for the baseline level of competence 2 420 At Level 2 students can interpret and recognise situations in contexts that require no more than direct inference. They can extract relevant information from a single source and make use of a single representational mode. Students at this level can employ basic algorithms, formulae, procedures, or conventions. They are capable of direct reasoning and literal interpretations of the results. 54 Given the experience of Mauritius, it is highly consultations” (OECD, n.d.). In the medium likely that PISA would prove unsuitable for term, this is likely to be a more appropriate other countries in SSA with a significant monitoring tool for the region. To date, two mismatch between the demands of the African countries, Zambia and Senegal, have assessment instruments and the ability level of signed agreements to participate in the students. However, a new assessment package project’s development and piloting phase. It will - PISA for Development - is currently being be interesting to see their progress. prepared with the aim of increasing “developing countries’ use of PISA assessments for 3.3.3 National assessments monitoring progress towards nationally-set targets for improvement, for the analysis of Whilst nearly 30 countries in SSA have, on at factors associated with student learning least one occasion, conducted a national outcomes, particularly for poor and assessment in the primary phase of education, marginalised populations, for institutional only a handful have started to implement capacity-building and for tracking international national assessment at the secondary level. educational targets in the post-2015 framework Table 3.11 summarises the situation up to 2015. being developed within the UN’s thematic Table 3.11: National assessment programmes conducted at the post-primary level by countries within SSA Title Grade(s) Subjects Year(s) Ethiopia National Learning Assessment 10, 11 Mathematics, English, 2010, 2013 Biology, Chemistry, Integrated Studies Mauritius National Form III Assessment 9 English, French, Annually, 2010 to 2014 Mathematics, Computer Studies, Physics, Biology, Chemistry South Africa Annual National Assessment 9 Literacy, Numeracy Annually, 2011–2014 National Assessment Test 8 English, Mathematics, Annually from 2012 The Gambia Science, Social and Environmental Studies Uganda National Assessment of 8 English, Mathematics, Annually, 2008–2013 Progress in Education Biology 55 As at the primary level, these national Grade 12 students (NAE, Ethiopia, 2010). The assessments differ significantly in their Grade 10 sample comprised 140 schools and purposes and methods. There has been little approximately 5,600 students. The Grade 12 external evaluation of these assessment sample comprised 73 schools and programmes and there are some doubts as to approximately 2,800 students. Selected their technical rigour particularly when it comes students took tests in five subjects: English, to making comparisons amongst groups and/or Mathematics, Biology, Chemistry and Physics. monitoring changes over time. Key areas of Student performance at the subject level was concern are limitations in sampling procedures, reported as a percentage correct score. These reliance on ‘percentage correct’ reporting raw scores were then added to give an overall scales, non-standardisation of tests, and the score. An arbitrary minimum threshold of 50% treatment of weights and standard errors. In was set by the Education and Training Policy of general, the assessment agencies responsible Ethiopia (ibid). In addition, four levels of seem to require greater capacity in the field of achievement were defined on the basis of psychometric testing if they are to provide standardised scores (z-scores). For example, national assessment services which are fit for ‘Basic’ covered the z-score range 0 to +1. The purpose. The examples below illustrate some of proportion of students reaching each of these the key issues. four levels was reported without reference to the fact that they were norm-referenced30. Table In 2010, Ethiopia conducted its first sample- 3.12 summarises the results for mathematics. based national assessment for Grade 10 and Table 3.12: Summary statistics for the mathematics tests used in the Ethiopian national assessment of 2010 Grade 10 Grade 12 Number of cases 5525 2660 Mean (%) 34.7 54.3 SD (%) 14.18 16.4 Median (%) 31.7 53.3 Skewness 1.23 0.113 Proportion above 50% threshold 14.7% 57.7% Proportion ‘Below Basic Level’ 60.7% 50.4% 30. If the tests used in the Ethiopian national assessment had produced normal or near normal score distributions, the proportions falling at each level would have been known in advance. In the event they differed slightly because the tests produced positively skewed score distributions. This fact is not mentioned in the report which gives the impression that the percentage reaching each level is indicative of absolute levels of achievement. 56 Unfortunately, the use of a test-dependent, performed on specific test items. This, coupled proportion correct reporting scale, coupled with the fact that the tests used are placed in with an arbitrary minimum threshold and the public domain, is likely to have a positive norm-referenced ‘proficiency’ levels means that influence on future teaching/learning. the national assessment yields little useful information as to absolute levels of student In South Africa, assessment at Grade 9 is an achievement in mathematics. It does not help extension to the annual national assessment that the report does not include examples of programme used across Grades 1-6 described the multiple-choice items used in the above. All students in the target grade are mathematics tests nor does it provide tested (1,042,133 in 9,208 schools in 2014). appropriate item statistics. Scores are calculated as the percentage of correct answers. In addition, above a minimum The report also reveals the dangers of applying threshold of 30%, six qualitative levels are inappropriate statistical techniques to data identified: elementary; moderate; adequate; when drawing comparisons and investigating substantial; meritorious; outstanding. These contributory factors. For example, the national levels are not explicitly linked to specific sample used in Ethiopia is comparable in size to mathematical competences but relate to raw that used for large-scale international score thresholds. In order to reach the minimum assessments. However, when analysis is done in positive threshold (‘elementary’), a student order to compare regions, the sample sizes must score 30%. In the 2014 study, a staggering become dangerously small. For example, results 90% of Grade 9 students failed to achieve the are given for the region of Dire Dawa on the elementary level in mathematics (DBE, RSA, basis of just 107 students. These students are 2014, p.81). Indeed, the average score on the clustered in a small number of schools giving an test was just 11%. Clearly there is a catastrophic effective sample size much less than 100. This is mismatch between the demands of the test probably too small for valid comparisons to be items and the abilities of the students. The fact made but the report offers no caveat. that the test in mathematics failed to produce a reasonable distribution of scores, especially at The National Form III Assessment in Mauritius the lower end of the ability range, indicates a does not include many of the elements usually serious technical flaw in this element of the associated with large-scale national national assessment programme. Put simply, a assessments in that it does not collect test like this which is far too difficult for the information on background factors likely to average student will yield little reliable affect learning outcomes. Its main aim is to information as to what that student can do. If measure learning achievement and to provide we accept that the tests were prepared by diagnostic information so that schools and subject specialists on the basis of the teachers can improve the quality of learning curriculum’s content and objectives, the only (MES, Mauritius, 2015). The impression is of a conclusion we can draw is that the mock examination rather than a national overwhelming majority of students are failing to assessment targeted across the full ability master the essential elements of the prescribed range. That having been said, the report on mathematics curriculum. student performance does provide teachers with qualitative information as to how students 57 3.4 The learning deficit and change over time improving? Are there any signs that the learning deficit is getting smaller? Evidence gleaned from international, regional and even national assessments of achievement Monitoring trends in educational standards in mathematics suggests that the learning poses many technical challenges and is deficit between students who study in the problematic even for the most sophisticated of countries of SSA and their international peers is international large-scale assessments. The great. Results from TIMSS show that Botswana, fundamental cause of these difficulties is the Ghana and South Africa appear towards the fact that, under normal circumstances, the bottom of the international rank order even changes we can expect to see over relatively when they select over-aged students. short periods of time are small - especially in Botswana, the highest performing of the three, large systems. For example, Korea, a country fares significantly worse than, for example, which has been particularly successful in competitor nations from Latin America. For improving its educational outcomes, raised its example, in the 2011 TIMSS for Grade 8, TIMSS Grade 8 mathematics score by just 32 Botswana’s average score of 397 was points over the period 1995 – 2011 (Mullis et al., significantly lower than Chile’s score of 416 - 2012). This represents an improvement of less even though Botswana sampled Grade 9 than one-third of a standard deviation over 16 students. The situation was equally bad for the years. Therefore the challenge facing those who younger population where Chile’s Grade 4 wish to detect such changes in SSA is not only students outperformed Botswana’s Grade 6 to measure student achievement accurately students by more than 40 points. Unfortunately, and repeatedly, but also to estimate, with this suggests that the nine countries of SSA precision, the errors inherent in the that Botswana outperformed by a statistically measurements used to calculate differences. significant margin in SACMEQ III are even Without appropriate estimation of further behind. measurement errors there is a danger that false positives or negatives will be reported. This In PISA+, the performance of Mauritius was caveat is particularly important when comparable to that of Mexico, Chile, Bulgaria considering the findings of national and and Thailand showing that Mauritius is within regional assessments which do not fully meet touching distance of significant economic the technical requirements of, for example, competitors. However, it should be noted that in TIMSS and PISA. The main areas of concern SACMEQ III students from Mauritius when evaluating evidence from various sources outperformed all their regional peers by a as to changes in mathematical standards in SSA margin of almost three-quarters of a standard are: inadequate sampling and weighting deviation. While Mauritius may be approaching procedures; the use of different and/or the performance of the weakest countries in the uncalibrated tests for repeated measurements; OECD, the other countries of SSA lag far behind. the comparison of scores based on different metrics (e.g. test-dependent percentage Having established that mathematical correct scores); missing or inappropriate outcomes across SSA are poor in both relative estimation of errors of measurement. Such and absolute terms, the key questions are: Is shortcomings mean that many reports of rising there any evidence that things are getting and/or falling standards available in the better, i.e. that mathematical standards are assessment reports evaluated for the purposes 58 of this study must be disregarded or, at best, drawing a sample from Grade 9 in 2011 making treated with caution as is made clear in the comparisons with earlier results impossible. For regional and national examples below. Ghana, the average score appears to have risen significantly over time as shown in Table 3.13. 3.4.1 TIMSS However, it should be noted that the TIMSS report for 2011 excludes Ghana from its description of Only three countries in SSA have participated in trends over time. This is because the average an international large-scale assessment (TIMSS score estimates for Ghana are considered Grade 8) on more than one occasion. However, unreliable because more than 25% of students only Ghana has consistently sampled from the have achievement which is too low for accurate target grade allowing standards to be monitored estimation by the TIMSS assessment instruments. over time. Botswana and South Africa moved to Table 3.13: Ghana: TIMSS mathematics results over time for population 2 (Grade 8) Ghana: TIMSS grade 8 mathematics 2003 2007 2011 Average score 276 (4.7) 309 (4.4) 331 (4.3) Change from previous cycle - 33* 22* Change from 2003 base - 33* 55* 3.4.2 SACMEQ but statistically significant improvement. However, comparisons at the level of individual As mentioned previously, the method of countries reveal surprising volatility32 as shown in calculating student scores in SACMEQ surveys Table 3.14. For example, between the two surveys was changed in the second cycle (SACMEQ II) in the average mathematics score in five countries order to establish a test-independent baseline for rose by about a quarter of a standard deviation the 14 participating entities. Item difficulties and or more (Lesotho, Mauritius, Namibia, Swaziland student achievement scores were calibrated and Tanzania). Over the same period the average using IRT (Rasch) allowing them to be placed on score for Mozambique dropped by nearly half a a common scale. The initial calibration was standard deviation (0.46 SD). However, this adjusted to give a group average31 of 500 and a decline has been attributed to “rapid structural standard deviation of 100. In the following cycle, changes in the education system during this SACMEQ III, a number of items from the previous period that resulted in massive increases in Grade survey were included as ‘anchor items’ allowing 6 enrolments without corresponding increases in results from the second survey to be placed on human and material resources” (SACMEQ 2010b, the original scale. In theory, this allowed changes p.2). It will be interesting to see if the results of over time to be detected and compared. Indeed, the SACMEQ IV survey provide more robust the average mathematics score for the 14 evidence of trends in mathematical outcomes ministries participating in SACMEQ II rose from across the reference group of countries. 500.1 to 509.7 between the two surveys – a small 31. Each participating entity was given equal weighting in the calculation of the group average. 32. In international large-scale survey such as TIMSS and PISA the reference group of countries tends to be relatively stable and changes of the order reported for SACMEQ II-III would be viewed with some scepticism. One possible source of instability could be the difficulty of achieving comparable samples in the two cycles. For example, Ercikan et al (2008) observe that in SACMEQ II participating countries applied different exclusion rules (for example, Malawi excluded private schools and inaccessible state schools) and that 7 of the 14 countries failed to reach the effective sample size target of 400 students. 59 Table 3.14: Comparison of average mathematics scores in SACMEQ II and SACMEQ III by country Country SACMEQ II (2000) SACMEQ III (2007) Average Score SE Average Score SE Change (SD) Significant (Maths) (Maths) (p<0.05) Botswana 512.9 3.15 520.5 3.51 +0.08 Kenya 563.3 4.64 557.0 3.98 -0.06 Lesotho 447.2 3.24 476.9 2.61 +0.30 ** Malawi 432.9 2.25 447.0 2.89 +0.14 ** Mauritius 584.6 6.32 623.3 5.83 +0.39 ** Mozambique 530.0 2.08 483.8 2.29 -0.46 ** Namibia 430.9 2.94 471.0 2.51 +0.40 ** Seychelles 554.3 2.68 550.7 2.45 -0.04 South Africa 486.3 7.26 494.8 3.81 +0.09 Swaziland 516.5 3.41 540.8 2.39 +0.24 ** Tanzania 522.4 4.2 552.7 3.51 +0.30 ** Uganda 506.3 8.17 481.9 2.92 -0.24 ** Zambia 435.2 3.54 435.2 2.45 +0.00 Zanzibar 478.1 1.26 489.9 2.35 +0.12 ** SACMEQ Average 500.1 n/a 509.7 1.16 +0.10 Zimbabwe ----- ----- 519.8 4.98 3.4.3 Uwezo monitoring short-term changes, i.e. over periods of one or two years. Notwithstanding One of the strengths of Uwezo is that it these limitations, Uwezo does report explicitly assesses children in their homes using short, on trends over time. According to the 2013 criterion-referenced tests of key mathematical report, Uwezo ‘data show that there have been concepts. Results are reported as the no significant changes in outcomes at regional proportion of the cohort mastering or ‘passing’ aggregate level or in each country’ (Uwezo, the test. There is, as far as one can see, no 2014, p.19). However, at the country level some estimation of the errors inherent in the results. changes are quantified as summarised in As a consequence, Uwezo is not well suited to Table 3.15. Table 3.15: Average scores for mathematics in South Africa’s annual national assessment 2012-2014 Country 2009/2010 2010/2011 2011/2012 Kenya 67 69 68 Tanzania 46 63 68 Uganda 51 52 44 60 The key problem here is that some of the limitations which make it difficult to have reported changes are unfeasibly large. In large, complete confidence in the trends reported. stable systems we do not expect to see changes One of the main problems is that new tests are of this size from year to year. For example, is it developed for each cycle of the assessment plausible that Tanzania should see a five and, without IRT-based calibration, it is percentage point jump in the proportion of extremely difficult to compare scores. For students mastering basic numeracy in one year? example, the annual national assessment in Similarly, what could cause an eight percentage South Africa reports trends in average test point fall in the mastery rate in Uganda? scores as shown in Table 3.16. The figures are used to conclude that South Africa is, in 3.4.4 National assessments general, making progress in mathematics education across the primary grades. However, Well designed, national large-scale assessments the report explicitly recognises that ‘there is… no offer countries the opportunity to monitor control over the comparability of the tests and, progress in the achievement of their students. consequently, on the comparability of the results However, detecting relatively small changes and on a year-to-year basis’ (DBE, RSA, 2014, p.15). showing that they are statistically significant Without further evidence it is impossible to requires the use of sophisticated measurement decide whether the apparent improvement of and analytical techniques. Many of the national scores is due to better teaching and learning, assessments from SSA evaluated in the easier tests, greater familiarity with the test preparation of this study have technical format, or some other factor. Table 3.16:    Average scores for mathematics in South Africa’s annual national assessment 2012-2014 Mathematics: average score (percentage correct) by year Grade 2012 2013 2014 1 68 60 68 2 57 59 62 3 41 53 56 4 37 37 37 5 30 33 37 6 27 39 43 9 13 14 11 The problem of linking across different tests is are shown in Table 3.17. However, as recognised also recognised in the technical report of the in the report, significant changes were made to 2013 national education assessment in Ghana. the length of the mathematics tests between Here, a number of items from the 2011 2011 in 2013. This casts some doubt on the assessment were included as anchor items in all precision of the equivalent scores. variants of the 2013 test in order to link scores Notwithstanding this, the work done on test through an equi-percentile frequency estimation linking in 2013 has laid a more robust baseline method (MES, Ghana, 2014, p.22). The outcomes for future measurements of change. 61 Table 3.17:    Average mathematics scores on the 2013 Ghana National Assessment with equivalent averages for 2011 estimated through a procedure based on the use of common anchor items Grade 2011 (equivalent % correct score) 2013 (% correct score) Primary 3 38.6 41.1 Primary 6 39.5 38.2 Standard errors are not reported for the scores learning deficit is large and there is little and the technical report states that ‘pupils in evidence that the gap is starting to close. 2011 and 2013 performed similarly on their respective assessments. The 2013 mean Criterion-referenced assessments such as (percent correct) score was not dramatically Uwezo and EGMA show that in many SSA above or below the 2011 score equivalents’ countries the majority of students are failing to (ibid, p.26). master fundamental mathematical concepts in the earliest years of education. SACMEQ and In the examples of South Africa and Ghana PASEC results confirm that in many countries of cited above, we see that the teams responsible the region the problems of the early years for these national assessments are grappling persist and far too many students in Grade 6 with the technical challenges of constructing remain innumerate. It is critically important that tests having appropriate measurement firm foundations are laid in the primary grades characteristics and linking scores across the if higher mathematical standards are to be two administrations with sufficient precision. achieved at the secondary and tertiary levels. Progress is being made but, to date, national assessments offer little reliable data to prove At present few countries in SSA have conclusively that mathematical standards are comprehensive data on the mathematical rising, falling, or remaining static in the achievement of their students. In particular, countries of SSA. they have limited information as to what students know and can do in concrete terms. 3.5 Summary There is a need for countries to engage in high-quality assessment activities at the Evidence as to the state of mathematics regional and international levels. However, care education in SSA in terms of student should be taken to select assessments which achievement comes from a diverse and growing are aligned to the current low levels of student number of sources. The limited information achievement. For example, the new TIMSS available from international comparative Numeracy assessment and the forthcoming assessments suggests that all major countries PISA for Development are likely to be more in SSA would appear towards the bottom of the suitable than TIMSS and PISA. international rank order. The international 62 Over the past 20 years, many countries in SSA have started to implement national assessment programmes. In order for these to provide high-quality data for the purpose of strategic planning, stringent technical standards must be met. Therefore there is a need for countries to develop the necessary technical capacities and to implement rigorous quality assurance procedures in order to ensure that assessments are fit for purpose and that conclusions drawn on the basis of qualitative evidence are sound. Regional and national assessments conducted in the past were not well-designed for detecting, with precision, relatively small improvements in learning outcomes. As a result, there is little reliable evidence as to whether mathematical standards in SSA are improving, are stagnant, or are declining. Some assessments – most notably SACMEQ - are now establishing more secure baselines but others will need to adopt far more sophisticated psychometric techniques if they are to provide reliable information as to the direction of travel. 63 64 Mathematics Education in Sub-Saharan Africa: 4 Factors affecting learning outcomes 4.1 Introduction ocean: outcomes in mathematics are intimately linked with those in other subjects. For This study is specifically concerned with the example, Figure 4.1 shows that, at the national state of mathematics education in SSA and in level, average PIRLS reading scores and identifying strategies likely to raise standards average TIMSS Maths scores for the Grade 4 of achievement in this vital subject. However, population are highly correlated (R2 ~ 0.9). mathematics education is not an island in an Figure 4.1: Correlation of national average scores on the TIMSS 2011 mathematics assessment for population 1 (Grade 4) and the PIRLS 2011 assessment of reading literacy 650 600 SG 550 GB* NL US RU 500 PT TIMMS G4 Maths 2011 SI SK SE 450 MT NO RO ES PL NZ 400 AE 350 QASA R2 linear = 0.896 OM 350 400 450 500 550 600 PIRLS 2011 65 Whilst some of this relationship may be causal and subject-specific interventions. The pattern in that students with better reading skills tend of achievement across subjects in different to fare better on any mathematics question that countries is not uniform. In a few, students are makes higher reading demands (Martin and particularly strong in mathematics whilst in Mullis, 2013), the key factor is undoubtedly the many others performance in mathematics is quality of the national education system and, disproportionately weak. Table 4.1 shows therefore, the quality of a country’s schools. selected results33 of an analysis of the The implication is that raising the general proportion of students reaching the TIMSS/ quality of schooling will inevitably have the PIRLS ‘high’ international benchmarks in effect of raising achievement in mathematics. reading, science and mathematics (Martin and Conversely, failing to address issues of general Mullis, 2013). In some countries, most school quality will hamper specific attempts to noticeably Hong Kong, Singapore and Chinese raise mathematical standards. Fortunately, Taipei, performance in mathematics is there is a great deal of research available, much significantly higher than in reading and science. of it based on data gathered through However, in the majority of countries (20 out of international large-scale assessments, as to 33) a smaller proportion of students reach the what makes an effective education system and high benchmark in mathematics than in reading what makes a good school. Some of the key or science. Factors specifically affecting findings are summarised in this chapter. performance in mathematics are explored in However, this is not to suggest that Chapter 5. mathematics does not need special attention Table 4.1: Comparisons of the proportion of a nation’s Grade 4 cohort reaching the ‘high’ international benchmarks for TIMSS and PIRLS, 2011 Proportion of the Grade 4 cohort reaching the high international benchmark Country Mathematics Reading Science Hong Kong SAR 82% 67% 46% Singapore 78% 62% 68% Chinese Taipei 74% 55% 54% Finland 50% 63% 65% Hungary 37% 48% 46% Czech Republic 30% 50% 45% Italy 28% 46% 37% Austria 26% 39% 42% Sweden 25% 47% 44% Croatia 19% 54% 30% Poland 17% 39% 29% Spain 17% 30% 28% 33. The top three countries in this table are those for which the performance in mathematics was at least 10% higher than that in reading or science. The nine countries below the line show a performance in mathematics at least 10% lower than that in reading or science (Martin and Mullis, 2013). 66 4.2 School quality safe and pleasant environment (OECD, 2015b). For many parents in developing countries the A wealth of research shows that background key signifier of quality is the behaviour and factors such as parental education levels and effectiveness of their children’s teachers. They the socio-economic status (SES) of the family want the school’s teachers to be well qualified, correlate positively with student achievement. dedicated to teaching and, most importantly, However, recent research suggests that these present in school rather than absent (Morrow are, in fact, less important than the quality of and Wilson, 2014). In addition, they want schooling experienced by students. For teachers who ‘take care’ of their children both example, using a particularly rich Canadian data helping them to enjoy education and providing set, Green and Riddell (2012) find that parental discipline (ibid). It is these aspects which characteristics “have only modest effect on (the contribute far more to the perception of a acquisition of) cognitive skills, once we control school’s quality than, for example, its physical for the individual’s education” and that the structure and resources. This chimes with the impact of parental characteristics “arises finding of the McKinsey report on the world’s indirectly through their powerful influence on top school systems (McKinsey & Company, the child’s education” (Green and Riddell, 2012, 2007) that “the three things that matter most p.3). Similarly, using the dataset from SACMEQ (are): 1) getting the right people to become III for South Africa, Spaull (2011) finds that the teachers, 2) developing them into effective SES of the school is a far more important factor instructors and, 3) ensuring that the system is than the SES of the student. In Spaull’s words, able to deliver the best possible instruction for “This means that placing a poor child in a every child” (ibid, p.2). wealthy school is likely to more than compensate for any negative effects of a poor 4.3 Interventions for improving outcomes home background” (Spaull, 2011, p.16). It should be noted that here the SES of a school is likely This is not the right place to revisit the vast to incorporate aspects of ‘school quality’ that amount of research which over the years has promote student achievement including, tried to identify the most effective methods for amongst others, effective school management improving educational outcomes. However, and the employment of better qualified and some key findings, especially those of recent more motivated teachers. The lesson for literature reviews (McEwan 2012, Conn 2014, policymakers aiming to raise educational Evans and Popova 2015), are worth restating standards is that they should not be unduly here in order to provide more context for the distracted by home background factors which, mathematics-specific interventions discussed in in any case, they will find difficult to change, the chapter which follows. but should focus on providing high-quality, state-funded schools - especially for socially 4.3.1 Expenditure on education and economically disadvantaged communities. Parents from all parts of the socio-economic Evidence as to the effect of spending more on spectrum are prepared to invest in the the education of students is mixed and for education of their children particularly when more affluent countries it is not clear that they believe that the quality of schooling is high greater expenditure results in significantly and will lead to significant returns. When trying improved outcomes. However, as shown in to judge the quality of a school, parents tend to Figure 4.2, PISA data shows a significant place greatest emphasis on two key aspects – positive relationship between per capita academic achievement and the provision of a expenditure and student achievement for 67 countries that spend less than about USD wealthy countries in Western Europe and North 50,000 in educating each student from the age America (USD 7,943 for primary and USD 11,247 of 6 to 15 (OECD, 2013c). For this group, for secondary), but it is disturbing to see that it increasing per capita spending by USD 10,000 falls far below that of countries in Latin America is associated with an increase of approximately and the Caribbean (USD 1,187 for primary and 25 score points, or one quarter of a standard USD 1,017 for secondary). deviation, in mathematics achievement. Countries in SSA fall firmly in the category It is interesting to note that Vietnam bucks the where additional expenditure translates into underlying trend. It is one of the lowest spending better educational outcomes. Data34 suggests countries in this group and yet its average PISA that, in 2012, countries in SSA were spending an score for mathematics is significantly above the annual average of just USD 136 on each primary international average. This apparent anomaly is school student and USD 157 on each student in considered further in Chapter 5. secondary education. One expects the spending in SSA to be far below that of the Figure 4.2: Relationships between national spending on educating a student from the age of 6 to 15 and national average PISA scores for mathematical literacy (OECD 2013c, p.41) 650 Shanghai-China 600 Korea Mathematics Performance (Score Points) 550 Poland Japan Czech Republic Finland Estonia Netherlands Switzerland Vietnam Canada Germany Belgium Austria R2 =0.01 500 France Latvia Norway Portugal Luxembourg Malaysia Croatia Spain United Denmark Israel Italy Turkey New States 450 Lithuania Zealand Sweden Bulgaria Slovak Republic Iceland Australia Thailand Chile Hungary Ireland United Kingdom Slovenia Mexico 400 Jordan Brazil Montenegro Peru Tunisia Colombia 350 Uruguay R2 =0.37 300 0 20 40 60 80 100 120 140 160 180 200 Average spending per student Note: Only countries and economies with available data ar shown from the age of 6 to 15 (in thousand USD, PPPs) 4.3.2 Pedagogical interventions adapted to better match the needs and abilities of individual learners. Conn (2014) finds that There is strong evidence to suggest that the such interventions have a combined-effect size most effective interventions for raising the (~0.4 standard deviation) significantly greater achievement of learners are those designed to than those which focus on non-adaptive change the ways in which teachers teach. In teaching. Within this category, teacher-led particular, actions which promote adaptive methods, such as individualised instruction and teaching, i.e. where teaching methods are the effective use of diagnostic assessment, 34. Source: UIS database. Note that for less developed regions this includes EFA countries only. 68 have a positive effect. Indeed, where teachers 4.4 Summary consistently use assessment for learning techniques, significant gains in student The quality of mathematics education cannot achievement are reported although, as be considered in isolation from the overall discussed in the next chapter, effect sizes of quality of education. At the system level, between 0.5 to one standard deviation as success in mathematics correlates strongly with reported by Black and Wiliam (1998) are success in all other subjects. Therefore, probably optimistic. investing in improving the general quality of schooling offered to all learners is a necessary McEwan (2014) also finds that interventions condition for raising mathematical achievement involving the adoption of programmes of – but it may not be sufficient. Computer-Assisted Learning (CAL) programs show significant effect sizes (~0.15 standard Research shows that the quality of schooling deviation) independent of other overlapping offered to learners is the most powerful interventions. Evidence as to the specific determinant of outcomes. Spaull concludes that impact of technology-based interventions on “placing a poor child in a wealthy school is achievement in mathematics is explored further likely to more than compensate for any in the chapter which follows. negative effects of a poor home background” (Spaull, 2011, p.16). One of the most important Whilst the findings above give cause for indicators of school quality is the optimism, it is important to recognise that professionalism of teachers. Indeed, research interventions are most effective when they bring suggests that “students placed with high- significant, positive changes to the daily performing teachers will progress three times experience of learners (Evans and Popova, 2015). as fast as those placed with low-performing teachers” (McKinsey & Company, 2007, p.12). 4.3.3 Strengthening accountability The implication is clear: students – even those from disadvantaged homes and communities - Interventions related to teacher incentives and will perform well if they are taught in a well- accountability can have a positive effect on resourced school by a good teacher. learning outcomes but the effect sizes tend to be small and changes in teacher behaviour may Comprehensive reviews of interventions aimed not be as intended. For example, rewards for at raising learning outcomes suggest that those teachers linked to student results are likely to designed to improve the effectiveness of lead to teachers ‘teaching to the test’ as teachers have the greatest impact. In particular, reported in one Kenyan programme (Glewwe, activities and training focused on the use of Ilias and Kremer, 2010). Gains have also been adaptive teaching strategies and formative observed where contract teachers have been assessment methods appear to yield the employed to supplement permanent, civil greatest rewards. The challenge for countries in service teachers. McEwan (2014) reports effect SSA is to apply these findings to the specific sizes of the order of 0.1 standard deviation, but field of mathematics education. warns that some of this may be due to the smaller class sizes which often result from the appointment of contract teachers. 69 70 Mathematics Education in Sub-Saharan Africa: 5 Factors affecting learning outcomes in mathematics 5.1 Context Beyond the primary level there is more evidence to suggest that curricula are not well The central place of mathematics is fully aligned to the needs or abilities of the majority recognised in the school curricula of SSA. It is of learners. Here the delivered curriculum is a compulsory, core subject at primary and dominated by the requirements of high stake, junior secondary levels. In some countries, national examinations used to select students mathematics also features as a compulsory for further educational opportunities. In many subject in school leaving qualifications at the cases, the failure rates for mathematics are senior secondary level. The importance of extremely high suggesting that teaching mathematics is also reflected in the time strategies are ineffective and revealing great dedicated to its teaching which is comparable inefficiencies in education systems. For to that allocated in more developed systems, example, in Tanzania the Certificate of and, in some cases, exceeds international Secondary Education Examination (CSEE) norms (World Bank, 2008). Over the past 20 marks the end of four years of secondary years, the revision and modernisation of education (ordinary level). In 2012, of the curricula has been a feature of broader ~400,000 candidates who appeared for the educational reforms with emphasis being examination in Basic Mathematics only placed on moving towards outcomes-based ~45,000 were successful representing a pass and competency-based curricular models rate of just 12.1% (NECTA, 2013). In Zimbabwe, (Westbrook et al., 2013). In reality, however, the 2012 pass rate for Mathematics O-level mathematics curricula in SSA remain defined taken at the end of Grade 10 was just 13.9%. Of by content and delivered, more often than not, those who pass and go on to study by teacher-led methods. mathematics at the senior secondary or advanced level, success in the final exams is far At the primary level, the content of curricula from being a formality. For example, in Zambia corresponds to widely-accepted theories of more than 6% of ~103,000 candidates scored the developmental/acquisition of zero (sic) in each of the two papers of the mathematical concepts and appears to be 2012, Grade 12 examination in mathematics closely aligned to that found elsewhere. For (Lusaka Voice, 2013). These cases are typical example, there is a large degree of overlap of countries in SSA where examinations in between primary school curricula typically mathematics have remained essentially found across SSA and the curriculum/ academic in nature with the prime purpose of assessment frameworks that underpin EGMA selecting students for further study in and TIMSS (Grade 4). At this level at least, the mathematics or mathematically-based fundamental problem does not appear to be in subjects. Unfortunately, they do not appear to the content of the intended curriculum but in be providing those who are unsuccessful with its delivery. A wealth of evidence suggests that essential transferable skills for continuing their in classrooms across the region teachers are studies in other fields or entering the labour failing to help learners grasp the basic market. This has been recognised in South concepts of numeracy. This failure Africa where an examination in ‘mathematical undoubtedly has a knock-on effect on literacy’ was introduced in 2008 as an achievement in mathematics at higher levels. alternative to the traditional mathematics 71 exam for matriculation. This was a response to in learners. It should be noted that the two problems: prior to the change, 40% of effectiveness of any particular intervention will candidates were choosing not to take any be context dependent – what works in one mathematics as part of their matriculation situation may not necessarily work in another. studies and, of those that did, the success This is of particular importance when looking rates were very low. Under the current system, at mathematics education because the the pass rate for mathematics is about 55% prevailing ‘culture’ appears to be a key factor whilst that for mathematical literacy is closer in determining the effectiveness of teaching/ to 85% (SABC, 2015). While this suggests that learning behaviours. tailoring the curriculum and the examinations in this way has allowed more students to The factors considered in this chapter include: develop and demonstrate some mathematical attitudes towards mathematics and the ability, we should not forget that South Africa teaching of mathematics; curricula; teachers of still appears towards the bottom of mathematics, textbooks and teaching international rank orders for both mathematics resources; assessment; and the use of and science. educational technologies. When it comes to the delivery of the intended 5.2 Culture and attitudes maths curriculum, across much of SSA little appears to be working. This is in contrast to The great concentration of effective the situation in the highflying countries, mathematics teaching found in East Asia has particularly those of East Asia, which suggested to many that the culture in which consistently top international league tables of teaching and learning take place may be the performance in mathematics. These prove that critical factor in explaining why other systems, it is possible to teach mathematics effectively, notably those of Europe and North America raising a significant proportion of learners to lag behind. Three dimensions of this are: the very high levels of achievement. For example, value attached to education by the wider more than 30% of 15-year-olds in Shanghai society; general perceptions as to the difficulty China, Singapore, Chinese Taipei, Hong Kong of mathematics as a subject; and the prevailing China, and Korea reach the two highest levels view amongst teachers as to the nature of of the PISA achievement framework. By way of mathematics and how learners acquire true contrast, the OECD average shows less than understanding of mathematical concepts. 13% of students demonstrating this level of mathematical competence (OECD, 2014). The Much evidence, both anecdotal and research- question being asked by many countries, based, suggests that families in East Asia place developed and developing, is: what do we great value on education. Studies show that in need to do in our education systems, in our pursuit of educational success they are schools and in our classrooms to close the gulf prepared to invest much time, effort, and in mathematical achievement which is money in the education of their children (e.g. glaringly apparent in the results of international large-scale assessments? Marginson, 2014). Jerrim (2014) estimated the The research evidence available is extensive impact of these cultural factors by comparing and diverse. However, through recent meta- the results of Australian students with parents analyses a clearer picture is emerging of of Asian origin with those of their peers from approaches and methods which appear to an Australian background having more in promote the acquisition of mathematical skills common with the cultures of Western Europe 72 and North America. He finds that “Australian concepts. Lim (1999) suggests that one children with East Asian parents outperform consequence is that the first group comes to their native Australian peers by an average of see difficulty in mathematics as a challenge to more than 100 PISA test points (equivalent to be overcome through endeavour whereas the two and a half years of schooling)” (Jerrim, second group sees the difficulty as an 2014, p.6). However, he suggests that there is insurmountable obstacle. Findings from PISA no single, causal factor and that the climate in support this with, for example, 84% of which students in East Asia learn is shaped by Japanese students saying they wouldn’t be put a number of interrelated factors including the off by difficult problems whereas only half of “selection (by parents) of high quality schools, US students said the same (Schleicher, 2014). the high value placed upon education, The powerful statement below summarises the willingness to invest in out-of-school tuition, a situation in the UK but will resonate in many hard work ethic and holding high aspirations countries – including those of SSA. “It is for the future” (ibid, p.6). Replicating this culturally acceptable… to be negative about enabling environment through government Maths, in a way that we don’t talk about other action in countries where very different life skills. We hear ‘I can’t do Maths’ so often it attitudes prevail may not be socially desirable, doesn’t seem a strange thing to say (Kowsun, would certainly be extremely difficult to 2008). Maths is seen as the remit of ‘mad implement, and, if attempted, would probably scientists’, ‘nerdy’ boys, and the socially inept take several generations to achieve. Clearly, (Epstein et al., 2010). We talk about Maths as trying to bring about wholesale and radical though it is a genetic gift possessed only by a cultural changes is not the place to start when rare few, and inaccessible to the general deciding how to raise mathematical public” (National Numeracy, 2014, p.1). achievement in the short- to medium-term. In PISA 2012, first time participant Vietnam The achievement of a society’s learners performed beyond the expectation of many appears to be linked to the attitudes towards with an average mathematics score of 511, the learning of mathematics generally held by significantly above the OECD average of 494 that society’s non-specialists (rather than (OECD, 2014)35. With a GDP per capita of maths educators). For example, the hard work approximately USD 2,000 and a total spend ethic associated with East Asian cultures leads on education of just USD 7,000 per student to a belief that success in education (and in (ibid), Vietnam outperformed by a significant mathematics and the sciences in particular) margin many far richer countries including, for results mainly from application and example, the USA (PISA Maths score 481, GDP perseverance. In western cultures there per capita USD 55,000, expenditure per appears to be a general acceptance of the student USD 116,000). Cultural factors have view that success in mathematics stems been suggested as one possible factor behind primarily from natural, inherited ability. In other the country’s success including the ‘growth words, students in East Asia are told that mind-set’, shared by teachers, which holds that anyone can learn mathematics provided they “abilities can be developed through dedication are prepared to work hard enough whereas in and hard work-brains and talent are just the many western cultures the dominant message starting point” (Dweck, 2006 cited in tends to be that only those lucky enough to Philippines Basic Education, 2013). Other have natural ability can grasp mathematical possible factors include the large investments 35. Bodewig (2013) suggests that Vietnam’s result should be interpreted with some caution as “The net enrolment rate in upper secondary education stands at 60 percent, and only as few as a third of the students from the poorest 20 percent of the population are in upper secondary school. Since PISA assesses competencies of 15 year-olds in school, this suggests that it only captures those Vietnamese students that remain in upper secondary education – typically the better off, and likely better performing, students” (Bodewig, 2013, weblog). 73 that Vietnam has made in improving the Chinese mathematics teachers and found that, quality of its schools (Bodewig, 2013) and the in general, British teachers “reflect the professionalism of its teachers (Bodewig, 2013 pragmatic understanding of theory in and Rolleston, et al., 2013). Mathematics teaching, (whilst) Chinese teachers generally reflect the scientific When it comes to exploring attitudes towards understanding of theory” (Yu, 2008, p.121). learning mathematics there is a significant This means that whilst the British teachers body of literature. Zan (2013), for example, focus on the appropriate application of theory, shows that students who have a negative and/ Chinese teachers place more emphasis on the or distorted view of mathematics may reveal introduction of new concepts and methods, this in different ways. Some may demonstrate and the position and function of proofs” (ibid, a profound lack of self-belief and an p.132)37. In her influential book on the teaching 36 expectation of failure . Others may have a of elementary mathematics, Ma (1999) fixed, instrumental view of mathematics which suggests that the difference between Chinese limits their willingness to bring other skills to and US teachers is one of both approach and bear on solving mathematical problems. Both competence. It is true that Chinese teachers in constitute considerable barriers to learning but Ma’s sample did show more competence when require different remedial actions. The first it came to carrying out some computations requires the teacher to instil confidence and (Ma, 1999 cited in Howe, 1999), but the more reassure the student that success is possible. important finding was that they were prepared The second requires the teacher to change the to use a range of techniques to help their student’s perception of mathematics as a students investigate and develop highly regulated, procedurally-led activity and understanding of the concept of interest. US to encourage a less rigid more creative teachers, on the other hand, tended to focus approach (Zan, 2013). The suggestion that on helping their students to master associated teachers can address this problem encourages procedures. Ma’s suggestion is that in order to optimism. However, one should not teach elementary mathematics effectively, underestimate the degree of professionalism teachers need the confidence that comes that this requires. Teachers who lack through having a profound understanding of confidence in their own mathematical ability or fundamental mathematics (PUFM) (Ma, 1999). who have themselves been brought up to She points out that Chinese teachers start to believe that mathematics is all about develop PUFM through high-quality early procedures rather than relations will find it training and then develop this further through, extremely difficult to bring about the desired for example, regular collaborative work with attitudinal changes in their students. fellow teachers of mathematics. The conclusion is clear: effective teaching at the The views of teachers towards the nature of elementary level needs confident, well-trained mathematics and mathematics education teachers who possess both subject knowledge alluded to above is also an area where cultural (i.e. concepts and procedures) and differences are to be found – some of which pedagogical knowledge (how to teach may be associated with learner achievement. mathematics). The implications of this for SSA Yu (2008) compared the views of British and are explored further in Chapter 6. 36. Ashby (2009) shows that this lack of self-belief starts early in a child’s education. His study on Grade 3 children showed that “ low and middle achievers quickly resigned themselves to failure, without truly attempting all of the questions” and that “many of the children showed signs of anxiety whilst attempting the worksheets, shuffling awkwardly in their seats, glancing at their peers with worried expressions and making negative comments about the difficulty of the current task” (Ashby, 2009, p.9). 37. In an attempt to replicate the success of world leaders in mathematics education, the UK government’s Department for Education established an exchange programme with the Municipal Education Commission of Shanghai. To date, two groups of Chinese mathematics teachers have spent time in British primary schools “to share their world-class approach to Maths teaching and help further raise standards in the subject” (United Kingdom, 2015). Anecdotal reports suggest that the exercise has “ encouraged (British) teachers to change the way they approach lesson planning to develop a deep understanding and fluency in Mathematics” (ibid). but no systematic evaluation as to the impact on student learning has yet been carried out. 74 5.3 Gender and mathematical achievement they start from a point where gender disparities in, for example, mathematics The third Millennium Development Goal was to education are great and deeply entrenched. achieve gender equality and the empowerment of women. The first target International and regional studies of learner within this goal was to “eliminate gender achievement provide a wealth of information disparity in primary and secondary education, on the relative performance of males and preferably by 2005, and in all levels of females in mathematics. However, as shown by education no later than 2015”. Whilst Saito (2011) outcomes at the primary and significant progress has been made across the lower secondary levels are mixed making it developing world, much remains to be done. difficult to draw firm conclusions. For example, This is especially true in SSA where gender the TIMSS 2007 results show boys in Grade 4 parity in primary education has not yet been outperforming girls by a significant margin in achieved and where the enrolment rates of 16 countries (with girls surpassing the boys in females at the secondary and tertiary levels 8). However, in the Grade 8 population, the lag far behind those of their male peers (UN, situation appears to reverse with girls 2015a). Whilst achieving equal access to outperforming boys by a significant margin in general education for girls remains 16 countries (with boys surpassing the girls in challenging, the situation in mathematics and 10). A similar pattern was observed in TIMSS other STEM subjects is further complicated by 2011 with, overall, little difference between the subject-specific gender issues. There are two average achievements of boys and girls at main inter-related aspects: the Grade 4 and slightly higher differences – in underachievement of girls in mathematics favour of girls – at Grade 8. Interestingly, girls especially at higher levels of the education from Botswana outperformed their male peers system, and the under-representation of at both Grade 6 and 9 in this study (Mullis et females in STEM study programmes at higher al, 2012). Results from PISA 2012 show that in secondary and tertiary levels. It should be the mathematics literacy domain, boys aged 15 noted that these are of almost universal outperformed girls of the same age in 38 concern with some of the world’s most highly participating countries and economies and that developed nations trying hard to attract more across OECD countries the average difference females into STEM courses and, ultimately, was 11 score points to the advantage of boys STEM-based research, innovation and (OECD, 2015c). One conclusion that can be production. In such countries there is a drawn from the mixed pattern of results is that consensus that promoting gender equality in the data does not support the traditional view, STEM areas will bring multiple benefits. For still held by many, that boys are better than example, the European Commission’s Expert girls in mathematics due to hard-wired genetic Group on Structural Change (2012) suggests differences. For example, in Hong Kong, that attracting more women into science and Shanghai, Singapore and Chinese Taipei - technology will, inter alia, increase the jurisdictions which appear at the top of the competitiveness of the workforce, assist in the PISA 2012 results for mathematics – “girls development of new economic opportunities, perform on a par with their male classmates in improve the quality of research and innovation mathematics and attain higher scores than all to the benefit of society, and contribute to boys in most other countries and economies social wellbeing and progress (EC, 2012). around the world” (OECD, 2015c, p.15, emphasis Clearly the economies of SSA should make added). Even in SSA there is strong evidence best use of their female human capital, but that, given the right opportunities, girls can 75 outperform boys in mathematics. Most notably, little average difference between the genders in the Seychelles girls in Grade 6 outperform across all 15 participating school systems, boys the boys by a statistically significant margin38. outperform girls in 11 cases and in 7 of these the However, as shown by Saito (2011), SACMEQ III difference is large enough to be significantly results show this to be an exception rather than significant. the norm. Table 5.1 shows that whilst there is Table 5.1: Gender differences by mean mathematics score for school systems participating in SACMEQ III (after Saito, 2011) Mean Maths Score (Girls) Mean Maths Score (Boys) Difference (Girls - Boys) Statistically significant Seychelles 566.7 535.2 +31.5 ** Mauritius 630.7 616.1 +14.6 South Africa 498.4 491.2 +7.2 Botswana 523.6 517.5 +6.1 Lesotho 476.8 477.1 -0.3 Namibia 470.1 472.0 -1.9 Zimbabwe 519.0 520.8 -1.7 Zanzibar 483.9 489.3 -5.4 Swaziland 536.2 545.5 -9.3 ** Uganda 477.2 486.7 -9.5 ** Mozambique 478.6 488.2 -9.6 ** Zambia 429.2 440.8 -11.5 ** Malawi 441.1 452.7 -11.6 ** Kenya 550.9 576.3 -25.4 ** Tanzania (mainland) 537.5 568.5 -30.9 ** SACMEQ III 507.5 511.8 -4.3 The results of the PASEC2014 study revealed a both measurement points in the primary phase similar pattern with most participating of education (See Table 5.2). countries showing boys outperforming girls at Table 5.2: Gender differences by mean mathematics score for participating countries PASEC2014 (after PASEC, 2015) Difference in Maths Mean Score: Girls - Boys Early primary Late primary (Grade 6) Burundi +8.7 +33.1** Benin +5.3 +5.5 Congo -4.0 -15.1** Togo -8.0 -8.0 Burkina Faso -8.9 -13.3** Senegal -15.0 -18.8** Niger -17.5** -7.2 Cameroon -19.0** +2.2 Cote d’Ivoire -26.3** -13.8** Chad -47.3** -21.9** 38. It has been suggested that the large advantage shown by girls in Seychelles is a result, at least in part, of the rigorous streaming policies applied by the Ministry of Education (Leste et al, 2005 cited in Saito, 2011). 76 Saito (2011) analysed SACMEQ III mathematics education of boys, they tend to have a results by school location and by school disproportionately large impact on girls. socio-economic status in order to identify differences in gender gaps. Whilst he notes a A good summary of the practical causes of small number of exceptions in each case, the disadvantages for girls is given by GIZ (2014). overall picture is that the gender differences The main barriers to schooling cited include: that appear at the national level are there poverty coupled with high costs for fees, within the sub-populations. For example, in uniforms and learning materials; long distances systems where boys outperform girls at the from home to school and the lack of national level they are, in general, doing so in affordable, safe transport; and the need for schools of low and high SES. Similarly, in poor families to use children in the home and countries where girls outperform boys at the in the fields. A further disincentive is the fact national level (i.e. Botswana, South Africa, that schools are often unfriendly and unsafe Mauritius, and Seychelles) they are doing so in environments. Many schools in SSA lack both urban and rural schools. In other words, appropriate sanitary facilities especially for gender gaps appear to be related to the girls at puberty (Saito, 2014). Security characteristics of the national system rather measures and safeguarding are weak with girls than, for example, school location and/or at risk of violence and sexual harassment socio-economic status. whilst travelling to and from school. For many this risk is even present within school with the Whilst differences in average scores by gender harassment by teachers of students (both are revealing, further analysis of PISA data genders) being perceived as a serious problem indicates another potentially important issue. in, for example, Kenya, Malawi, Tanzania, Evidence shows that girls at the upper end of Uganda, Zambia and Zimbabwe (Saito, 2013). the ability range underperform by a bigger margin than girls of average ability. For Schools in SSA, as elsewhere, tend to reflect example, whilst the average PISA 2012 gender the cultural values of the societies they serve. gap was 11 points in favour of boys, this rose Unfortunately, this often means that the significantly to 20 points for students in the education of girls is seen as being less top 10% of the ability range (OECD, 2015c). important than that of boys. Parents tend to This is of concern because the girls in this have lower expectations of their daughters group are precisely those who would add than their sons. This is a view shared by greatest value if they could be attracted teachers who, in general, tend to have a better towards further study and careers in opinion of their male students and, mathematics and other STEM subjects. consequently, pay less attention39 to the girls in their classes (Stromquist, 2007 cited in GIZ, The key factors impacting adversely on the 2014). Such prejudice and the low performance of girls in SSA in mathematics fall expectations of society impact negatively on into three main categories: generic factors the self-confidence of girls. Unfortunately, the associated with access to a safe learning impact of this on the performance of girls in environment; cultural and personal factors mathematics is particularly large and related to the perception of mathematics as a damaging. An analysis of PISA 2012 results subject and as a career option; and, factors suggested that ‘self-efficacy in mathematics’ is related to the teaching of mathematics in strongly related to achievement. Here ‘self classrooms. Whilst many of these hinder the efficacy’ is the extent to which a student 39. It should be noted that in the classroom observations conducted for this study in six focus countries (see Annex A) our observers detected no gender bias in the attitudes or actions of teachers. 77 judges her/his confidence to perform a series gender equality and female empowerment of mathematical tasks or solve mathematical that they use, ‘participation in the labour problems. It was found that girls tend to have market of the mother’ is particularly lower levels of self-efficacy and that the significant. Whilst this of benefit to both boys gender gap is wider in mathematics than in and girls, the impact is higher for girls. One science. In other words, when presented with a suggestion is that “mothers participating in mathematical problem, many girls believe they the labour market are somehow breaking the can’t solve it whilst more boys, of the same traditional view of men working in the labour ability, believe they can! Interestingly, this force and women staying at home. Then, the phenomenon is context dependent. For mother transmits to her daughter this break example, “67% of boys but only 44% of girls with the traditional gender role attitudes reported feeling confident about calculating which make her feel that she is not inferior to the petrol-consumption rate of a car… boys and thus believe that she can compete However, no gender differences in confidence also in those subjects a priori better suited to were observed when students were asked boys. This ultimately leads to girls developing about doing tasks that are more abstract and better maths skills and hence reducing the gap clearly match classroom content, such as with boys in maths” (de San Román and de la solving a linear or a quadratic equation” Rica Goiricelaya, 2012, p.18). (OECD, 2015c, pp. 70-71). In addition to ‘self efficacy’ the PISA gender analysis also looked In addition to these cultural attitudes towards at ‘self concept’ which is a measure of a girls and mathematical education, there is student’s belief in her/his abilities – another evidence that some teaching methods factor strongly linked to mathematical promote higher levels of achievement to the achievement. Once again, girls displayed lower advantage of girls. These include: presenting levels of self confidence. For example, 63% of mathematical problems in gender-appropriate boys disagreed with the statement “I am just contexts; setting mathematical problems that not good at mathematics” whilst the promote deeper understanding; using corresponding proportion of girls was 52%. collaborative methods in the classroom; and, Similarly, 45% of boys reported that they using assessment methods which are not “understand even the most difficult work in time-stressed. Research suggests that girls mathematics classes” whilst only 30% of girls perform better on tasks set in context but, as agreed with the same statement (ibid). Clearly shown by PISA data, the ‘self efficacy’ of girls girls feel far less confident than boys when it is severely impeded when boy-friendly comes to mathematics even in education contexts are used (OECD, 2015c). Boaler (cited systems with competent teachers and well in Cech, 2012) presents evidence that boys resourced classrooms. typically outperform girls in schools where traditional methods based on memorisation of The inter-generational transmission of gender mathematical procedures and ‘closed’ roles and its impact on achievement is assessment tasks. However, when ‘open’ tasks explored by de San Román and de la Rica demanding deeper investigation are set and Goiricelaya (2012) using data from PISA 2009. students allowed to collaborate on exploring They conclude that in societies where there is them, then both boys and girls improve but greater gender equality, girls perform better girls more so thereby closing the attainment reducing their disadvantage in mathematics gap. The beneficial effect of less directive and simultaneously increasing their advantage teaching methods is also found in the PISA reading literacy. Of the multiple indicators of 2012 data where the ‘use of cognitive- 78 activation strategies’ by teachers is associated others’ (Slavin et al., 2009b, p.4). A similar with better performance for girls (OECD, conclusion was reached by Tarr et al. (2008) 2015c). Boaler (2014) also argues that the who, using US data, found that on two traditional emphasis on speed in the teaching separate measures, “curriculum type was not a and testing of mathematics is detrimental to significant predictor of student achievement” students regardless of gender because they (Tarr et al., 2008, p247). These findings “cause the early onset of math anxiety… and suggest that the content and organisation of are especially damaging for girls” (Boaler, the intended curriculum is not a significant 2014, p.1). factor in determining the achievement of learners. This is not entirely surprising given The foregoing suggests that in addition to the large body of evidence suggesting that the interventions designed to raise the general dominant factor is the quality of teaching. level of mathematical achievement, specific Good teachers can help their students to reach policies and actions should be put in place in high levels of competence even when the order not only to maximise the achievement of curriculum they are following is less than ideal. girls, but also to engage them in STEM The implication for strategic planning in SSA is subjects at the highest levels. that reform of mathematics curricula may ameliorate the situation but it will not 5.4 Curricula automatically lead to significantly better outcomes if there are fundamental problems in Over the past decade or two, efforts have the delivery system. For example, research been made to reform curricula in all countries suggests that in many cases the institutions of SSA. In mathematics, as in other subjects, responsible for the pre-service training of attempts have been made to reduce teachers in SSA have not adjusted their own curriculum overload and improve sequencing. curricula and teaching practices to match the In some countries, e.g. South Africa, the demands of the more modern curricula importance of setting clear targets was prescribed for schools. Indeed, Akyeampong incorporated in outcomes-based models. et al (2011) suggest that TTIs do not always Child-centred approaches have also been have access to, let alone use, essential promoted as the best way to deliver the materials including the curriculum documents, curriculum. There is, however, little local teacher guides and textbooks used in schools. evidence to suggest that such curriculum Notwithstanding the above, mathematics reforms are effective – especially in raising curricula in SSA will need to be revised mathematical standards. Slavin et al. (2009a) extensively if it is decided that, for example, looked at studies evaluating the outcomes of the compulsory curriculum for all should focus mathematics curricula for elementary and on basic ‘functional mathematics’ with an middle/high schools. These represented elective course in ‘true mathematics’ being different innovations and a range of followed by the more-able minority. As supporting textbooks including a traditional described above, the South African Matric textbook, a textbook advocating a step-by- model requires candidates to enter for either step approach to teaching/learning, and an ‘Mathematical Literacy’ or ‘Mathematics’. The innovative textbook focusing on problem- examination papers for the two subjects show solving. They found that ‘there was very little the marked difference in approach. For evidence that it mattered which curriculum example, a ‘Mathematical Literacy’ paper of was used. None of them showed any strong 2015 included questions based on: the gross evidence of effectiveness in comparison to the salary, pension contribution and tax position of 79 an employee; returns from a small enterprise the classroom but also rewarded in high-stake making and selling sweets; information about examinations. However, on their own new a road trip using a map; authentic statistics for standards are not sufficient – new approaches births and deaths in South Africa for a given to teaching/learning are also required. The historical period; etc. (DBE, 2015a). In contrast, NCTM provides advice and examples of good the corresponding paper for ‘Mathematics’ practice in Principles to Actions: Ensuring included questions on: quadratic equations; Mathematical Success for All (NCTM, 2014). arithmetic and geometrical series; One of the key messages is that teachers, mathematical functions; differential calculus; preferably working in collaboration, should etc. (DBE, 2015b). For many, the introduction select tasks with an appropriate degree of of this model from 2008 has been a great complexity allowing students to explore success but there are detractors who hold that problems which can be approached from more “Maths Literacy is not even a watered-down than one direction. Such tasks promote the version of Maths. It is a dramatically less development of competing arguments and, demanding subject which does not develop hence, ‘productive struggle in learning’. The conceptual thought or problem solving” NCTM argues that “Effective teaching of (Equal Education, 2016, p.1). However, it is far mathematics consistently provides students, from clear that the more formal mathematics individually and collectively, with opportunities syllabus achieves this as examination failure and supports to engage in productive struggle rates are high and average test scores are low. as they grapple with mathematical ideas and relationships” (NCTM, 2014, p.48). It should be Implementing curricula which focus on noted that the success of such an innovative equipping all learners with profound approach depends on the universal availability understanding of fundamental mathematics of well-qualified and highly professional requires not only new curricular content and teachers of mathematics – a condition which is standards, but also new approaches to far from being met in the vast majority of planning and delivering learning activities. countries in SSA. Current thinking on this issue can be found in the Common Core State Standards (CCSS) for 5.5 Teachers of mathematics the USA40 (NGA and CCSSO, 2010) and in the work of the US National Council of Teachers of There are few who would disagree with the Mathematics (NCTM) which links mathematical proposition that the most important factor, by practice to the content and philosophy of the far, in ensuring that learners achieve high Standards. The Standards place the emphasis standards in mathematics is the presence in on mathematical proficiencies including: the classroom of an effective teacher. making sense of problems and persevering in Unfortunately, countries across SSA face huge solving them; abstract reasoning; constructing challenges in attracting sufficient numbers of viable arguments and critiquing the arguments suitably qualified applicants to train as of others; mathematical modelling; looking for teachers. Those who are attracted to teaching and using mathematical patterns and structure as a career all too often receive inadequate (ibid). This is a radical departure from typical training and, as a consequence, enter service practice in SSA where, as noted throughout ill-equipped to meet the considerable this report, rote memorisation and repetition demands of the profession. Poor conditions of of familiar procedures are not only practised in service and inadequate in-service support lead 40. As of August 2015, 42 states across the USA have adopted the CCSS in mathematics. 80 to low motivation making the retention of teachers, high level of teacher absenteeism, good teachers a major challenge (Mulkeen, large class size, short effective school year, 2010). The problems of attracting and high illiteracy among parents, and the retaining teachers affect all subjects but they shortage of reading materials at home” (ibid, are particularly acute in mathematics. For p.10). The positive relationship between example, Mulkeen (2010) reports that in The textbooks and learning is considered by many Gambia 38% of teachers at the upper basic to be self-evident and is also supported by a level were qualified to teach social and significant body of research (e.g. Fehrler, environmental studies but only 17% were Michaelowa, and Wechtler, 2009). However, as qualified to teach mathematics – even though discussed below, more robust quantitative it is a compulsory, core subject in the studies of the relationship between access to curriculum. Similarly, in Lesotho in 2005-2006 textbooks and mathematical achievement only 8% of trainee secondary school teachers suggest that the situation is, in reality, far were studying mathematics as one of their two more complicated. specialist subjects. As if this were not enough, many observers suggest that the teachers who The ratio of students to mathematics are in the classrooms do not have the textbooks in the primary phase of education necessary mathematical knowledge and varies dramatically across the region as shown pedagogical skills to help their students by Figure 5.1. For the 20 countries of SSA for master the subject. The competence of which recent data is available, eight have mathematics teachers is considered in Chapter textbook ratios close to unity and in a further 6 and the initial training of mathematics six countries, up to two students share each teachers is explored in Chapter 7. textbook. In Central African Republic and Cameroon the shortages are far more severe 5.6 Textbooks with ratios of 8:1 and 13:1 respectively (UNESCO, 2015a). The general consensus is that the availability of textbooks is a key determinant of learning outcomes especially in developing countries (Fuller, 1987). UNESCO uses the student:textbook ratio as a key indicator of the quality of schooling (UNESCO, 2015a) and the World Bank holds that, apart from the provision of qualified and committed teachers, making textbooks available to all students is likely to be a more cost-effective way of raising learner achievement than any other input (Fredriksen and Brar, 2015). This is particularly relevant in the case of mathematics education in SSA because not only are textbook shortages significant in many countries, but the textbook remains the main, if not only, teaching tool for many teachers. It is suggested that the provision of textbooks compensates for “the weakness of other quality inputs such as poorly-trained 81 Figure 5.1: The student:textbook ratio for mathematics in primary grades (UNESCO, 2015) Cameroon 13.1 C. African Rep. 7.9 Togo 3.6 Uganda 3.2 Angola 3.0 Chad 2.6 Congo 2.1 Gambia 2.1 Côte d'Ivoire 2.0 DR Congo 1.9 Ethiopia 1.5 Mozambique 1.3 Mali 1.1 Guinea 1.1 Sao Tome/Principe 1.1 Mauritius 1.0 Cape Verde 1.0 Niger 1.0 Benin 1.0 Rwanda 0.8 0 2 4 6 8 10 12 14 Number of students per mathematics textbook Information as to the availability of share their textbook in lessons. Once again the mathematics textbooks for students in Grade 6 situation varies dramatically from, for example, is also available from SACMEQ studies. Table Swaziland where every child has her/his own 5.3 shows that, on average, 22% of students in textbook to Tanzania where this is true for only SACMEQ countries report having their own 3% of students (Spaull, 2012). mathematics textbook i.e. they do not have to Table 5.3: Relationship between textbook ownership and mathematical achievement (Spaull, 2012) % with own Maths textbook (rank) Scaled Maths score (rank) Swaziland 100 (1) 541 (3) Lesotho 56 (2) 477 (7) South Africa 36 (3) 495 (5) Namibia 32 (4) 471 (8) Malawi 24 (5) 447 (9) Kenya 15 (6) 557 (1) Uganda 14 (7) 482 (6) Zimbabwe 12 (8) 520 (4) Zambia 11 (9) 435 (10) Tanzania 3 (10) 553 (2) SACMEQ average 22 512 82 It is interesting to note that whilst Swaziland in classrooms where for most students this is (100% with a textbook) has a relatively high their third language. This clearly presents a average score for mathematics, so do Tanzania barrier to their effective use by teachers and and Kenya with far lower proportions of learners. Secondly, the textbooks are written to students with sole access to a textbook. The match an academic curriculum which is beyond fact that the rank order correlation for these all but the most able students in this cohort countries is close to zero (ρ = -0.04) is under the prevailing conditions. compatible with the findings of quantitative research which suggest that the mere The policy implications of the research cited availability of mathematics textbooks has little above are significant. First, if the aim is to raise impact on learner achievement as measured by learner achievement in mathematics then there test scores. is little point in investing in providing more textbooks unless those textbooks have been Glewwe, Kremer and Moulin (2009) find, using proven to be effective. Secondly, if the the results of a randomised trial conducted in mathematics curriculum is not well matched to Kenya, that owning or sharing a textbook has the capacities of the majority of learners then no significant impact on student achievement simply providing a textbook will not bridge – except for students who, according to pre- the gap. intervention test scores, are already at the upper end of the ability range. Frölich and 5.7 Assessment practices Michaelowa (2011) show, using African data, that whilst textbook ownership is not The Systems Approach for Better Education associated with significant learning gains, Results (SABER41) is a World Bank-led initiative textbook sharing does bring benefits - to support countries wishing to strengthen their presumably through peer interaction and education systems on the basis of common knowledge sharing. Subsequently, Kuecken and standards and comparative data. SABER offers Valfort (2013) analysed the SACMEQ II data for partner countries tools for the systematic 11 countries and arrived at conclusions evaluation of practices in a number of domains consistent with those of earlier studies: the – including that of student assessment. The availability of textbooks has no discernible SABER framework suggests that a impact on student test scores except for comprehensive student assessment system students in the top 30% of the distribution for should include four major components: SES. Moreover, the gains for this group are classroom assessment; examinations; national associated not with textbook ownership per se, large-scale assessments (NLSA); and, but with textbook sharing. These findings raise international large-scale assessments (ILSA). A a critical question: If, in general, textbooks aid country’s status in each of these is evaluated learning, why don’t current textbooks lead to against a scale having four, criteria-related better outcomes in mathematics? Little work categories: Latent; Emerging; Established; and seems to have been done on this specific Advanced. The underlying assumption is that all question but Glewwe, Kremer and Moulin four forms of assessment can, when used (2009) suggest two plausible explanations for properly, promote better outcomes in terms of their findings in Kenya. First, they report that higher levels of student achievement. Clarke official textbooks are written in English for use (2012) gives a good overview of the research 41. For further information on SABER and links to SABER documents and case studies see http://saber.worldbank.org/index.cfm. 83 which supports this assumption. (2012) cites the findings of Black and Wiliam At the macro level, information from (1998) which relate to “high-quality, formative international and national assessments can classroom assessment activities” with gains shape educational policies and, in some cases, equivalent to an effect size of between 0.5 and spur the implementation of targeted reforms one standard deviation (Clark, 2012, p.3). These such as the “No Child Left Behind (NCLB)” gains are comparable to those found by strategy in the USA, and the “Every Child Rodriguez (2004). It should be noted that Counts” programme in the UK. Where national subsequent scrutiny of Black and William’s tests assess all students rather than a work combined with later research has cast representative sample, they can be used to hold some doubt on the reported effect sizes (Dunn schools and, in some cases, teachers and Mulvenon, 2009). However, there is a accountable for outcomes. Clarke (2012) consensus that assessment for learning is reports that there is evidence of a “weak, but associated with improved student performance. positive link between the uses of data from Stiggins and Chappuis (2004) suggest that in these assessments to hold schools and order for classroom assessment practices to educators accountable (through, for example, “close achievement gaps” they should meet the league tables, monetary rewards, or staffing four criteria reproduced below (Stiggins and decisions) and better student learning Chappuis, 2004, pp. 5-6): outcomes” (Clark, 2012, p. 4). For example, Dee and Jacob (2010) in their evaluation of the • Condition #1: Assessment development must impact of the assessment-based NCLB always be driven by a clearly accountability system in the US detected a articulated purpose. positive effect on elementary student performance in mathematics and noted that • Condition #2: Assessments must arise from this was most evident for disadvantaged and accurately reflect clearly specified and populations and low achievers. Interestingly, appropriate achievement expectations. they could find no similar effect for reading literacy. Using mathematics scores from the • Condition # 3: Assessment methods used National Assessment of Educational Progress must be capable of accurately reflecting the (NAEP) for students in Grade 4, they found a intended targets and are used as teaching positive effect size of 0.23 standard deviations tools along the way to proficiency. (Dee and Jacob, 2010). • Condition #4: Communication systems must Of all the forms of student assessment, the deliver assessment results into the hands of strongest claims are made for classroom their intended users in a timely, assessments where information is used for understandable, and helpful manner. formative purposes, i.e. where the information is used by teachers and learners to identify It has to be recognised that the burden of strengths and weaknesses and to adapt implementing a high-quality classroom teaching/learning strategies accordingly. This is assessment system that meets these conditions commonly known as assessment for learning or ultimately falls upon teachers. Teachers may assessment as learning, to distinguish it from have many legitimate reasons for resisting summative assessments of learning. Clarke change and there are significant technical 84 barriers to introducing new assessment for mathematics achievement was raised through learning strategies. Following Lock and Munby the use of technology with a significant effect (2000), three major obstacles stand out: (a) size of +0.28 (Li and Ma, 2010 cited in Chueng overcoming/modifying traditional beliefs and and Slavin, 2011). practices to allow teachers to adopt new assessment practices; (b) developing teachers’ In their rigorous review of relevant studies, knowledge and understanding of student- Cheung and Slavin (2011) looked at different centred assessment methods; and, (c) types of intervention including: Computer overcoming/modifying any contextual factors Assisted Instruction (CAI) in which usual in the school environment that mitigate against teaching practices are supplemented by changes in classroom practice. Overcoming computer-based materials and tools; and, these obstacles will be particularly difficult in Computer Managed Learning (CML) where an SSA where teachers, particularly those in the integrated computer system assesses students, elementary phase, are, in general, poorly assigns appropriate learning materials, tests prepared, inadequately supported, and working and maps student progress. Of these two, CAI under great pressure. produced the larger beneficial effect (effect size = +0.18) with CML appearing to offer less 5.8 Educational technologies benefit (effect size = +0.08). This reinforces the general consensus that technology is most In a world in which the lives of those in effective when it accompanies high-quality developed and developing countries alike are teaching (Fouts, 2002). The implication is that increasingly dominated by evermore ineffective teachers cannot be replaced by sophisticated technologies, it is tempting to technology. Even competent teachers require believe that the solution to the problem of poor additional training if they are to implement student achievement in mathematics lies in the computer-assisted instruction in their use of educational technologies in the classrooms successfully (ibid). classroom. Indeed, there are numerous examples of evaluation reports making It should be noted that the greatest number of spectacular claims for the impact of adopting studies in this area, and those of the highest particular programmes and/or hardware in technical standards, have been conducted in schools. However, rigorous re-evaluation of the US and other highly developed countries. It reported findings suggests that whilst positive is possible that the picture would be benefits are consistently found, the effect sizes significantly different in, for example, the are generally moderate. classrooms of SSA. There are some regional studies, some of which are referred to in Meta-analyses of research by Slavin et al. (2008 Chapter 9, but these tend to be less rigorous and 2009a) which reviewed studies of the use and their findings should be treated of technology in US elementary and secondary with caution. schools found positive effects at both levels. Observed effect sizes were, at best, modest There is little recent evidence as to the cost (+0.10 for secondary schools and +0.19 for effectiveness of technology-based interventions elementary schools). More optimistically, Li and for raising mathematical achievement and that Ma (2010) found that in US Grades K-12, which is available tends to come from 85 developed countries with more complete his analysis. This may suggest that using datasets and, it should be said, completely technology to support assessment for learning different environments from those typically and to supplement usual teaching practice found in SSA. In one study based on US data, might bring significant returns. Yeh (2010) finds that CAI yields greater effect sizes and is considerably more cost-effective 5.9 Summary than some other interventions including, for example, reducing class sizes and lengthening The factors impacting on achievement in the school day. However, his main finding is that mathematics are numerous and interconnected using computer-based, ‘rapid assessment’ in complex ways. Therefore, addressing the applications to provide students with feedback acute problem of poor mathematical outcomes as to their progress is by far the more cost- in SSA will require simultaneous and sustained effective intervention of the 22 he included in actions on many fronts. Figure 5.2: Key factors impacting on mathematical outcomes ACCESS TO HIGH QUALITY SCHOOLS AND SCHOOLING A MATHEMATICS POSITIVE CULTURAL CURRICULUM MODEL ATTITUDE TOWARDS WHICH IS FIT FOR MATHEMATICS PURPOSE AVAILABILITY OF ADEQUATE SUPPLY APPROPRIATE ACHIEVEMENT IN OF COMPETENT, WELL EDUCATIONAL MATHEMATICS TRAINED TEACHERS TECHNOLOGIES OF MATHEMATICS CONTINUOUS AVAILABILITY OF HIGH PROFESSIONAL QUALITY TEXTBOOKS DEVELOPMENT AND AND OTHER TLM SUPPORT FOR SERVING AVAILABILITY OF HIGH TEACHERS QUALITY DATA FROM A FULL RANGE OF ASSESSMENTS 86 At the primary level it is unlikely that the It is tempting to believe that educational content and organisation of the intended technology is the ‘magic bullet’ which will solve curriculum is a major factor in the extremely all the problems associated with mathematics weak performance of students in mathematics. education in SSA. Research suggests that this is The most serious problem occurs in the delivery not the case and that computer-based learning of the curriculum. Ultimately, this resides in the and assessment programs are most effective inability of teachers to equip their students with when they supplement high-quality teaching. the basic skills in numeracy. At higher levels, in many countries in SSA, low take-up rates and/ or high failure rates in high-stake examinations are indicators of a mismatch between the curriculum (as reflected in examination syllabuses) and the achievement levels of candidates. Whilst poor delivery of the curriculum impedes the progress of learners regardless of gender, there are additional factors which disadvantage girls to a greater extent than boys. Some of these stem from unhelpful views on the potential of girls to master mathematics whilst others relate to the use of classroom teaching strategies that do not encourage girls to engage and make the best use of their potential in this critical subject area. Evidence suggests (Ma, 1999) that the most effective teachers of mathematics have not only great subject knowledge but also a profound understanding of fundamental mathematics. She suggests that in China, “to give a student a cup of knowledge, the teacher needs a bucketful of knowledge” (cited in Goldenberg, 2007). Is it possible for countries in SSA to move closer to this approach to the teaching and learning of mathematics? Evidence as to the impact of textbooks and other learning materials on mathematical achievement is mixed. However, there is strong evidence to suggest that if teachers can be persuaded to implement assessment for learning in their classrooms (and are supported in doing so) then outcomes will improve. 87 88 Mathematics Education in Sub-Saharan Africa: 6 Teachers’ capacities and teaching conditions 6.1 Introduction related to the perceived lowly status of primary school teachers and their poor The dominant factor in the acquisition of working conditions. However, the teachers in mathematical skills is the quality of schooling their studies do not appear to be poorly enjoyed by learners (Green and Riddell, 2012). motivated “through self-perceived The quality of schooling has a number of inadequacies in their capacities as teachers” dimensions including school financing and (ibid, ix). This echoes the results of teacher management, physical infrastructure, the questionnaires applied in six focus countries availability of teaching and learning materials for this study. The overwhelming majority of and, critically, the presence of a professional teachers (>90%) in all countries and at both and dedicated teaching force. Indeed there is a the primary and secondary levels reported strong consensus that the most effective being both confident and well-prepared to interventions in raising educational standards, teach the mathematics curriculum. (See especially in developing countries, are those Appendix A.) More objective observers that focus on developing the capacities of suggest that the capacities of teachers, teachers and providing those teachers with an particularly in the teaching of mathematics, enabling environment: “The Dakar Framework are inadequate both in terms of their subject recognised the pre-eminent role of teachers in knowledge and the pedagogical skills with providing basic education of good quality. It which they are equipped. This has been linked stressed that, to achieve EFA… governments with the recruitment of trainee teachers with need to enhance the status, morale and low levels of general education and inadequate professionalism of teachers and enable them pre-service training (Lauwerier and Akkari, to participate in actions affecting their 2015). In this chapter we review evidence as to professional lives and teaching environments” the capacities of teachers who teach (UNESCO, 2015a, p.196). mathematics and we explore the conditions in which they work. In Chapter 7, we review the The success of governments across SSA in effectiveness of the training programs used to responding to Millennium Development Goals prepare such teachers. by increasing primary enrolment rates has amplified significantly the problems associated 6.2 Evidence as to capacities with attracting and retaining sufficient numbers of trained teachers, especially for the When considering the capacities of teachers basic phase of education. Amongst teachers in charged with teaching mathematics to service, Bennell and Akyeampong (2007) learners from Grade 1 upwards, discussions report low levels of job satisfaction and tend to focus on two key elements: motivation leading to “far-reaching adverse mathematical competence and pedagogical impacts on the behaviour and overall competence. The first concerns the extent of performance of primary school teachers and the teacher’s knowledge and understanding of thus learning outcomes” (Bennell and mathematical concepts and the second Akyeampong, 2007, p.x). They suggest that concerns the skills and strategies that the low motivation stems from a number of factors teacher has for developing knowledge and 89 understanding in her/his students. One of the training. In many cases these unqualified challenges for those investigating in this area teachers have been appointed to contract is to distinguish between teachers’ perceived rather than established posts. Of the 34 and actual levels of competence. The countries in SSA with data for 2012, trained mismatch between the two is significant, but teachers constitute more than 90% of the the undeniable fact is that the levels of workforce in 12 countries42 but in a further mathematical competence achieved by nine43 fewer than two-thirds of primary students remain unacceptably low, indicating teachers are qualified (UNESCO, 2015a). that teaching in this area is generally Typically, untrained teachers contracted by ineffective. communities need no formal qualifications and may not themselves have gone beyond 6.2.1 Mathematical capacity primary education - with or without a qualification in mathematics. Table 6.1 shows Over the past two decades, many countries the highest level of qualification gained by across SSA have expanded teacher numbers teachers according to data gathered for the to meet greatly increased demand for primary PASEC and SACMEQ regional assessments. school places, but have done so by recruiting (For PASEC these are teachers of Grades 2 those without proper qualifications and/or and 5, and for SACMEQ of Grade 6.) Table 6.1: Summary of the highest level of academic qualification held by primary school teachers according to data collected in PASEC and SACMEQ surveys of learner achievement Less than primary With primary Upper secondary Upper secondary Tertiary level school leaving school leaving education but without with Baccalaureate certificate certificate Baccalaureate or or A-level A-level PASEC 7.2% 18.7% 42.9% 31.0% Not applicable (6 countries) SACMEQ 10.8% 16.6% 45.3% 27.3% 5.5% (14 countries) The figures in Table 6.1 suggest that at least Grade 6 teachers have only primary school one-quarter of those teaching the basics of education whilst, at the other end of the mathematics did not study the subject in spectrum, 26% have enjoyed education at the schools at the upper secondary level. These tertiary level (ibid). figures disguise significant variation amongst countries. For example, in Tanzania fewer than Given the large number of primary grade 5% of teachers in the survey had more than a teachers with relatively low levels of junior secondary qualification whilst in qualification prior to any pre-service training, Swaziland more than 80% had either A-level or the question arises: do they know enough tertiary level qualifications (Bonnet, 2007). mathematics to teach mathematics? One There is also wide variation within countries, major source of evidence comes from the e.g. between rural and urban areas. In South second and third cycles of SACMEQ in which Africa, the heritage of a racially segregated the mathematical knowledge of teachers was education system is evident in that 30% of measured using a slightly extended variant of 42. Côte d’Ivoire, Mauritius, Burkina Faso, Namibia, Niger , Burundi, Tanzania, Cabo Verde, Democratic Republic of Congo, Madagascar, Malawi and Rwanda (UNESCO, 2015). 43. Liberia, Guinea-Bissau, Mali, Ethiopia, Equatorial Guinea, Angola, Benin and Senegal (UNESCO, 2015). 90 the multiple-choice test used for their scale used to report student achievement. The students. The results were scaled to place results for SACMEQ II are shown in Table 6.2. teachers on the eight-level, criteria-related Table 6.2: Proportion (%) of teachers reaching the SACMEQ ‘competency’ level in mathematics Percentage of teachers reaching the mathematics ‘competency’ level (SACMEQ II) Competency level 1 2 3 4 5 6 7 8 Botswana 0.0 0.0 0.0 2.3 5.1 26.4 47.9 18.4 Kenya 0.0 0.0 0.0 0.0 0.0 0.0 4.3 95.6 Lesotho 0.0 0.0 1.3 0.4 8.6 27.5 51.5 10.6 Malawi 0.0 0.0 0.0 1.8 6.9 10.5 51.3 29.4 Mozambique 0.0 0.0 0.3 2.9 4.6 16.3 44.3 31.7 Namibia 0.0 0.0 1.9 3.8 14.2 29.1 31.1 19.9 Seychelles 0.0 0.0 0.0 0.0 0.0 0.0 24.1 75.9 Swaziland 0.0 0.0 0.5 0.0 1.7 11.6 39.7 46.5 Tanzania 0.0 0.0 0.0 1.5 2.7 13.2 38.8 43.9 Uganda 0.0 0.0 0.0 1.2 5.3 11.4 27.9 54.2 Zambia 0.0 0.0 0.6 3.7 4.2 22.7 40.5 28.3 Zanzibar 0.0 0.0 6.3 6.2 19.3 30.0 28.9 9.3 Teachers (all) 0.0 0.0 0.9 2.0 6.0 16.7 36.0 38.5 Students (all) 6.2 34.3 29.8 14.6 7.5 4.6 2.2 0.9 Source: After Bonnet, 2007, p.28. Note that teachers in South Africa and Mauritius were not tested in SACMEQ II and so do not appear in this table. Given that the teacher’s test was not than their own” (Bonnet, 2007, p.29). Once significantly harder than that applied to again, the suggestion that 97.6% of students in students, one would expect nearly all teachers the primary phase have a teacher whose to be performing at or near the highest level as maths test score is higher than their own is indeed is the case in Kenya and the Seychelles. potentially misleading since in an effective However, the table shows a great deal of education system one would expect teachers variation and, in some countries, a significant not just to score higher but to outperform all proportion of teachers functioning at relatively but the best students by a significant margin. low levels. Bonnet (2007) notes that, overall, “2.9% of students are taught by teachers who Results from the third cycle of SACMEQ, as are not competent in Maths”. On the face of it, shown in Figure 6.1, confirm that, at the this does not seem as bad as many observers national level, the average mathematics score have suggested. However, in categorising achieved by teachers is strongly correlated teachers as competent, Bonnet uses the (r = 0.69) with that of students (Altinok, 2013). ‘Competent Numeracy’ level of the SACMEQ Within countries the picture is far more scale which applies to students – a very low complicated. For the majority of SACMEQ threshold to apply to teachers. Similarly, countries, the correlation between teacher Bonnet reports that “2.4% (of students) have a achievement and student achievement is teacher whose score on the Maths test is lower either absent or not statistically significant. 91 Figure 6.1: Relation between teacher and pupil score in mathematics in SACMEQ III (r=0,69) Kenya 900 850 Malawi Uganda Tanzania Seychelles Teacher Score Swaziland 800 Botswana Namibia Malawi South Africa 750 Mozambique Zambia Lesotho 700 Zanzibar 400 450 500 550 Student Score Altinok (2013) does find five countries - score) to 991 (i.e. nearly four standard Botswana, Kenya, Tanzania, Zanzibar and South deviations above the student mean). In contrast Africa - where teacher knowledge is positively to Altinok’s findings, Spaull concludes that associated with student achievement in teacher knowledge – as measured by their mathematics. However, only in South Africa is test scores – is only a weak determinant of the relationship considered strong (r=0.42). student achievement44. He estimates that the Altinok’s conclusion is that in some, but far student mathematics gain from raising the from all, countries there would be a relatively weakest performing 10% of teachers to the level small, but nevertheless significant, benefit to be of the strongest performing 10% of teachers is accrued from raising the subject knowledge of only 18.3 points (Spaull, 2007, p.22). This means teachers. In others, particularly South Africa, he that the considerable effort required to teach suggests that one potentially beneficial policy the bulk of teachers more mathematics would intervention would be “to allocate (the) most probably result in only small gains which he able teachers (to) either rural areas or to low estimates are equivalent in size to those socio-economic level groups (or both when it is associated with simpler interventions such as possible)” (Altinok, 2013, p.21). The special case getting teachers to set and mark homework of South Africa is investigated by Spaull (2011) more frequently. Spaull suggests that “the who also uses the SACMEQ III data. He shows ability to teach students well… is not very that the country exhibits a very wide range of dependent on subject knowledge, but perhaps teachers’ mathematics scores from 612 (i.e. one more on the teacher’s ability to convey that standard deviation above the student mean subject knowledge” (ibid, p.23). 44. Filmer, Molina and Stacy (2015) used student and teacher scores on survey tests conducted in Uganda, Mozambique, Togo, Nigeria, and Kenya to estimate the effect of the mathematical knowledge of teachers on student achievement. They report that “a one standard deviation increase in teacher Mathematics knowledge increases student achievement by 0.105 standard deviations” (Filmer, Molina and Stacy, 2015, p.17). This relatively small effect size is not incompatible with Spaull’s conclusions reported above. 92 Perhaps the most serious limitation of this agreed with the statement “I am a confident approach to investigating the impact of a and competent teacher” and, at the same time, teacher’s subject knowledge on the subsequent 83% agreed with the statement “Most pupils achievement of her/his students, is that the need additional tutoring in mathematics.” (See measure of knowledge used is restricted to the Appendix A.) The role of teacher education in curriculum content that teachers are supposed perpetuating this over optimistic view is to teach and students are supposed to learn. explored further in Chapter 7. The SACMEQ test scores simply show that the vast majority of teachers have mastered the Classroom conditions and pedagogical 6.3  concepts and procedures required by the practices curriculum. They do not prove, however, that teachers have acquired what Ma (1999) calls Notwithstanding deficiencies in their subject the deep understanding of fundamental knowledge, most teachers face significant mathematics necessary to convey true challenges when they try to teach mathematics understanding to their students. Alternative in the classrooms of SSA. General problems measures (see, for example, Hill and Ball, 2004) identified by UNESCO include poor physical are necessary if we are to evaluate whether or facilities within schools, overly large classes and not teachers in SSA understand to a sufficient multi-grade teaching in the primary phase, and degree how their students learn mathematics. shortage of textbooks (UNESCO, 2012). There is, however, considerable variation across the Akyeampong et al. (2011) suggest that the region. Conditions range from those in problem is rooted in initial teacher education Mauritius where all primary schools have (ITE) because “the approach of many ITE electricity and potable water and where the curricula on learning to teach mathematics in pupil:textbook ratio is approximately 1:1 to Africa tends to be one-dimensional beginning those in, for example, Niger where 95% of with an emphasis on subject knowledge leading primary schools don’t have electricity, or to pedagogical content knowledge as the Cameroon where the pupil:textbook ratio for knowledge base” (Akyeampong et al., 2011, mathematics is 13:1. Such problems, where they p.38). This approach influences how teachers exist, impact on the quality of education and, perceive, or rather misperceive, their levels of inevitably, on student achievement in general. competence in both mathematics and the teaching of mathematics (Ball, 1990 and, Hill A second major factor is the way in which and Ball, 2004 cited in Akyeampong et al., mathematics is taught in classrooms across the 2011). For example, primary grade teachers region. Some data on typical teacher practice is interviewed for this study are firmly convinced available from regional assessment surveys and that they are competent teachers of targeted research. In order to supplement this, mathematics because they know what their classroom observations were conducted in six students are ultimately supposed to know. focus countries for this study. Key findings are However, they manage to ignore the fact that included in this chapter with more detailed most of their students reach, at best, only information given for each country in Appendix moderate levels of achievement. This cognitive A. In addition, a TIMSS video study of dissonance is reflected in the fact that of the mathematics lessons in seven developed 294 primary teachers interviewed for this study economies46 allows some comparisons to be across six countries, 91%45 agreed or strongly made with observed practice in SSA (Hiebert et 45. In five of the six countries studied, 88% or more of primary teachers expressed great confidence in their ability to teach mathematics (100% in Uganda and DRC). Only in Cameroon was there a significant difference with just two-thirds (68%) agreeing with the statement ‘I am a competent and confident teacher”. 46. Australia, the Czech Republic, Hong Kong, Japan, the Netherlands, Switzerland, and the United States. 93 al., 2003). However, it should be noted that the individualised diagnostic assessment with TIMSS video study looked at Grade 8 remedial interventions – both of which classrooms and so caution should be exercised contribute to higher levels of achievement. If when considering how mathematics is taught in this applies to well-prepared teachers, how primary grade classrooms. much truer will it be for poorly trained or even untrained teachers? Unfortunately, the financial 6.3.1 Class size costs of reducing class sizes and student:teacher ratios significantly in SSA are Research findings of the impact of class size on likely to prove prohibitive. For example, it has learner achievement is equivocal with many been estimated that reducing class sizes in line studies finding little or no evidence that smaller with EFA targets for quality teaching would classes lead to improved outcomes (e.g. require many countries in SSA to increase their Moshoeshoe, 2015, Altinok and Kingdon, 2009, expenditure on education by more than 4% of and Wößmann, 2006). However, in the context GNP (Benbow et al., 2007). Benbow et al. of SSA, large classes, particularly at the primary conclude “if we accept that large classes are level, are generally considered to present a currently irreversible, one must then develop considerable barrier to achieving quality in strategies that take into consideration financial and technical realities. Are there ways to cope education (UNESCO, 2015a). Of the 28 with large class sizes through less resource- countries in the region for which recent data 47 dependent means?” (Benbow et al., 2007, p8.) are available , 13 have average enrolments of The solutions they propose all depend on more than 50 students in Grade 2 and, of these, ensuring that teachers are well prepared in four (Malawi, CAR, DRC and Tanzania) report techniques of classroom management and in an average class size of more than 85. There is appropriate pedagogical techniques including also significant variation within countries. For small group work and peer-to-peer mentoring. example, in five of the six countries investigated This would have major implications for the for this study, the average observed class size reform of current teacher training practices as was approximately 40. However, the number of explored in Chapter 7. students present ranged from just 5 to 98. The other country in our survey, Uganda, had an 6.3.2 Language of instruction average of 66 students in observed classes. However, one class accommodated 120 Language policies are of particular importance students! The challenge of overly large classes in SSA where each country typically has a is exacerbated by multi-grade teaching which number of important indigenous languages remains a significant feature of many systems. and, as a result of colonial rule, a legacy For example, UNESCO reports that “in most European language (i.e. English, French, countries reporting data, at least 10% of pupils Portuguese, Spanish and, from the Dutch, are taught in such classes” with the number Afrikaans). At independence, different countries reaching nearly 50% in Chad (UNESCO, 2012). adopted radically different policies with regards to national/state languages. Batibo (2013) Overly large and multi-grade classes present identifies five approaches: Inclusive; Partially challenges to mathematics teachers especially Inclusive; Exclusive; Hierarchical; and, Adoption in poorly-resourced classrooms. In particular, it of the status quo ante. The nature of these and makes it difficult to arrange effective group their implications for the language or languages work with feedback, and to implement of instruction are summarised in Table 6.3. 47. World Bank databank available at: http://data.worldbank.org 94 Table 6.3: Classification of language policies across SSA and their implications for medium or media of instruction (After Batibo, 2013) Language Policy Type Characteristics Examples Inclusive Promotion, as far as possible, of all Namibia: English, the state language, indigenous languages to a national level and at least 16 local languages are – including use in education. used to a greater or lesser extent in education. Partially Inclusive A selected number of indigenous South Africa (11 languages out of languages are promoted for use, e.g., in 23); Zambia (7 languages out of 38); education. Other indigenous languages Mozambique (6 languages out of 33) are excluded. Exclusive A single indigenous language is selected Tanzania (Kiswahili); Botswana as the national language and used (Setswana); Malawi (Chichewa) exclusively in education. Hierarchical Different languages are used at different Zimbabwe adopted such a model but, administrative levels (e.g. national, in education at least, implementation provincial, district, etc.) was partial with Chishona and Sindebele dominant at all levels. Adoption of the status quo ante The language policies of the former Burundi and Chad (French); Angola colonial power are retained. Here the ex- (Portuguese); Equatorial Guinea colonial language remains the national (Spanish); Mozambique (Portuguese medium of instruction. - but moving to include 16 indigenous languages by 2017). Perhaps the most important aspect of such unfamiliar African language, “both teachers and language policies is that concerning the learners may often not be fluent enough to use language or languages to be used in instructing the language as a medium of instruction” young learners and those in the primary stage (Clegg and Afitska, 2010, p.iii). This presents of education. Policies vary from country to considerable challenges to teachers in all country48. In some, young learners entering subjects, but the problem is exacerbated in school are immediately immersed in a language mathematics where both teaching and learning which is not that of their home. In many others, depend on teachers and students it is expected that learners will be taught in understanding the special ‘linguistic register’ of their mother tongue in the early years but that, mathematics (Pimm, 1987, cited in Setati, before very long, there will be a transition to a 2002). This register extends beyond the preferred national language or an official specialised terminology of the subject to the ‘international’ language. Unfortunately, children correct use and understanding of, for example, who are taught and tested in languages that logical connectors in the main language. Setati they do not fully understand are placed at a (2002) suggests that “the Mathematics register significant disadvantage (UNESCO, 2014). is not well developed in most of the African Where teaching beyond the early years is languages” and that teachers (in South Africa) conducted in an international language or an would not invest the time or effort necessary to 48. National language policies in education change over time. A recent overview of the prevailing system can be found in Albaugh, 2012. 95 formalise spoken and written mathematics in be taught in basic (i.e. up to lower secondary the main language since “due to the dominance level) formal and non-formal education through of English, this work would generally be seen or the language they know best.” (McIlwraith, 2013, interpreted as a waste of time” (Setati, 2002, p.7.) Secondly, any strategy for developing an p.11). Without adequate preparation and appropriate register for teaching mathematics support in this specialised area, many teachers and/or using languages in the classroom should use code-switching to help their students but be should be systematically evaluated. Thirdly, the use of indigenous languages in this way is teachers require sufficient formal training in the often condemned by the authorities (Clegg and effective use of languages if they are to be Afitska, 2010). effective (Clegg and Afitska, 2010). This is particularly true for teachers of mathematics Kazima (2008) describes two approaches where specialised terminology and the need to towards meeting the challenge of dealing with explain unfamiliar abstract concepts present mathematical terminology when teaching in an significant challenges. African language. In Nigeria and Tanzania, efforts have been made to produce glossaries 6.3.3 Availability of educational technologies in local languages of the mathematical terms used at primary level (Kazima, 2008). For In a world where new technologies promise example, the term ‘percent’ is translated into solutions to problems in all aspects of our lives, Kiswahili as ‘sehenu za mia’ (literally ‘portion of it is tempting to believe that the use of hundred’). In Malawi, however, the national technology in the classrooms of SSA could language Chichewa was not conducive to bring about a quantum leap in the effectiveness expressing key mathematical terms and so a of mathematics teaching overcoming the many decision was made to borrow words from deficiencies described in this study. Indeed, English. For example, ‘percent’ is transcribed as there is some encouraging evidence and the ‘pelesenti’ and ‘rectangle’ rendered as potential of technological approaches to the ‘recitango’. Kazima (2008) concedes that teaching and learning of mathematics is neither of these strategies has been considered in Chapter 9 below. However, the systematically evaluated but suggests that current situation, as revealed by classroom “Malawi’s strategy has the advantage of observations conducted for this study, is not easiness” and that it is easier for learners when conducive to implementing radical they move to Standard 5 where English technological solutions, at scale, in the short- to becomes the language of instruction (Kazima, medium-term. 2008, p. 60). Data concerning the average number of Clearly, the issue of language in teaching computers in primary/basic schools was mathematics presents a significant barrier for collected in the third cycle of SACMEQ both teachers and learners. First, this should be conducted in 2007. At that time, the average recognised in establishing policies for the number of computers per school for all SACMEQ language, or languages, of instruction where countries was three49. However, this average is political/cultural factors tend to dominate highly skewed by the data for South Africa (Setati, 2002). A set of principles to guide the which reported an average of 13 computers per formulation of such policies is suggested in school. By way of contrast, Lesotho, Malawi, McIlwraith (ed. 2013) including: “Learners should Tanzania, and Uganda each had an average of 49. Spaull, N. 2012. SACMEQ at a glance series. Research on Socio-economic Policy (RESEP). Available at: http://resep.sun.ac.za/index.php/projects/ 96 zero. Kenya, Swaziland and Zambia reported 67% in Rwanda to 94% in DRC) classified having one computer per school but it is far themselves as being ‘non-users’ or mere from clear that this computer was available for beginners. As shown in Table 6.4, relatively few teaching. This picture is in line with the own or have the use of computers with internet classroom observations made for this study access, but a sizeable proportion of our cohort where in four countries (Cameroon, Ethiopia, do have a mobile phone with internet access. Rwanda and Uganda) no computers were seen For example, in Ethiopia none of the 70 in a total of 280 observed classrooms50. teachers interviewed had a computer but 57% reported having an internet-enabled mobile Even if modern technologies were available, it is device. This suggests that providing information far from certain that the majority of teachers and teaching tools through mobile devices may would be competent in their use. For example, offer the best opportunity for supporting of the teachers questioned about their teachers of mathematics - certainly in the computing skills, the majority (ranging from short- to medium-term. Table 6.4: Access to new technologies and self-reported computer competence of teachers interviewed for this study by country (See Appendix A) CMR DRC ETH NGA RWA UGA Proportion of teachers interviewed 71.0% 94.0% 82.4% 80.0% 67.1% 81.4% who consider themselves to be computer ‘non-users’ or ‘beginners’. Proportion of teachers interviewed 31.4% 5.7% 0.0% 21.4% 20.0% 12.9% who own (or have the use of) a computer with internet access. Proportion of teachers interviewed 48.6% 30.0% 56.5% 60.0% 61.4% 50.0% who own a mobile phone with internet access. 6.4 Pedagogical practices mathematics, two critical aspects have attracted much attention. The first concerns the Over the past decade or two, one of the main consequences of the fact that the majority of themes in the general field of curriculum reform teachers in SSA appear to hold the view that in SSA has been the promotion of student- mathematics is predominantly about rules and centred approaches and more active interaction procedures rather than, for example, the between teachers and learners. In particular, exploration of problems and proofs. The second teachers have been encouraged to use group concerns the nature of the interactions between work and formative assessment to engage and teachers and learners and those amongst support learners. However, there is a widely learners i.e. peer-to-peer. held view that practices in the classroom have not moved sufficiently far and that the delivery Where the rules and procedures of of the curriculum remains, to a great extent, mathematics are prioritised, teachers tend to teacher-led and passive. In the teaching of adopt an instrumentalist approach in the 50. In DRC, one of 70 classrooms had a computer and in Nigeria two computers were available in the 70 classes observed. 97 classroom. The emphasis is placed on telling or misconceptions are systematically exposed, showing learners what the rules are for solving challenged and discussed” (Swan, 2005 after a particular problem and, hence, what Askew and Wiliam, 1995). The dominance of the procedures are to be followed. The natural teacher-led, transmission method of instruction consequence is for the teacher to assume a was confirmed by the classroom observations dominant position and to hand the ‘correct’ conducted for this study. As described in procedure down to the learners. Students who Appendix A, by far the most frequently can remember and reproduce this method are observed teacher actions in all six countries given credit in examinations by examiners who, were ‘writing on the chalkboard’ and ‘explaining in turn, are looking for a particular solution. It is a concept orally i.e. lecturing’. argued that this procedural approach explains to a significant extent why students in the USA In traditional teacher-led approaches to are outperformed by their peers in, for example, classroom management, most interactions are Japan and China where teachers encourage initiated by the teacher. These usually take the students to develop alternative approaches to form of a question to which the class may problem solving (Stigler and Hiebert, 1999, and respond in chorus (Mayaba, 2009 cited in Ma, 1999). The question is do we see evidence Sepang, 2013) or which an individual student of a unidirectional instrumentalist approach in may be selected to answer. Such interactions the mathematics classrooms of SSA? are generally short and closed. If the offered answer is correct the teacher moves on. If the In a study of newly qualified teachers (NQT) in answer is incorrect the teacher may choose Ghana, it was found that whilst many were another student to respond or may immediately aware of the advantages of constructivist offer the right answer. In either case, the approaches, their practice in the classroom was interaction is unlikely to lead to a deeper “largely instrumental and without the kind of exploration of the root of the error or a wider learner-centred focus which has the potential discussion of alternative approaches to solving to allow pupils to construct their own the problem. Peer-to-peer interactions are understanding of the concepts” (Adu-Yeboah, encouraged where, for example, groups of 2011, p.57). Another manifestation of the students are allowed to collaborate on the teacher-led approach reported by Adu-Yeboah construction and evaluation of alternative (2011) was the frequent use by teachers of approaches to solving a mathematical problem. ‘demonstration’ to explain a mathematical In our classroom observations, direct concept. However, following the demonstration, questioning of students by the teacher was by “pupils were not observed working with these far the most common form of interaction - all teaching learning materials as part of a teachers asked direct questions throughout the problem-solving activity that (tested) their lesson with students responding either understanding of the concept” (ibid, p.58). This individually or, especially at the primary level, as directive approach does not allow students to a group. It was also common for individual explore alternative methods and, hence, students to be invited to solve problems on the develop deeper understanding. In addition, it chalkboard whilst their peers watched. It was does not allow students to make mistakes and relatively rare to see students working in reveal common misconceptions. This is groups or even in pairs. The ‘lesson signatures’ important because “teaching becomes more described in Appendix A for each of the six effective when common mistakes and countries surveyed reinforce the findings of 98 other observers that mathematics lessons in the reinforced by examination systems which classrooms of SSA remain strictly teacher-led reward those who can reproduce the ‘correct’ with little or no opportunity for individuals or answer as defined by the official marking small groups of learners to tackle non-routine scheme. As a result of this instrumentalist problems or explore alternative routes to approach, lessons are almost invariably teacher- a solution. led with few opportunities for students to engage in collaborative problem-solving and, 6.5 Summary hence, profound learning. The quality of teaching is a major factor in the The weaknesses of teachers described above quality of schooling and, as such, is a key are exacerbated by the poor conditions in determinant of learner achievement. High- which many find themselves teaching. Average quality teaching requires teachers who are well class sizes in nearly all countries of the region motivated, understand pedagogical theory, and are far larger than those of, for example, Europe have good classroom management skills. In or North America but even these disguise the addition, effective teachers of mathematics fact that many teachers in SSA are confronted need good subject knowledge and the special with huge classes of 60, 70, 80 or even more. In skills needed to develop deep understanding of addition, a significant number find themselves mathematical concepts in their students. In SSA trying to teach multi-grade classes – a the quality of mathematics teaching is poor as challenge even for a well-qualified teacher in a demonstrated by poor learning outcomes on a well-resourced school. range of relative and absolute measures. Language of instruction is a big challenge for all The root cause of the problem does not rest teachers especially where official policy is to with the teachers. They themselves are the teach young learners in a European language product of a poor general education system which is not the language of their home. and many, particularly those intending to teach However, it is a particular problem in the at the primary level, embark on their pre- mathematics classroom where specialist service training without having mastered terminology is required and where unfamiliar mathematics at school. Through their training abstract concepts must be explained. Teachers they improve their knowledge of the curriculum receive little formal training in this difficult area to the stage where most (but not all) are ahead and, in the absence of formal support, have to of their students as measured by student-level try to find their own solutions. tests, but they do not have sufficient depth of knowledge to be truly effective teachers Changing the culture of mathematics teaching of mathematics. and providing teachers with the knowledge, skills and resources they need is a monumental As a result of the environment in which they task. It needs to be tackled simultaneously on were originally educated and subsequently several fronts. However, reforming the systems trained, most teachers in SSA believe that by which primary school teachers and specialist mathematics is about learning the rules and teachers of mathematics are trained is a remembering correct procedures. They see condicio sine qua non. their role as transmitting these rules and procedures to their students and this view is 99 100 Mathematics Education in Sub-Saharan Africa: 7 Initial teacher education for those who will teach mathematics in the basic phase of education 7.1 Introduction chapter we focus on the quality of the initial training that prospective teachers receive in School teachers in the basic phase51 of relation to the teaching of mathematics. education clearly have a vital role to play in efforts to tackle the extremely low levels of In order to meet the great demand for numeracy and mathematical competence teachers, some countries have introduced found across SSA. However, the recruitment, relatively short ‘accelerated’ training training and retention of such teachers remain programmes for primary school teachers e.g. serious challenges for many countries. Liberia (9 months), Senegal (6 months) and UNESCO reports that nearly 7 in 10 countries Mali (45 days). However, most countries in SSA in the region currently face an acute shortage retain traditional, full-time college courses, of teachers and that the situation will be typically of two or three years’ duration, as the further exacerbated by a rising demand for main route of entry into teaching at the school places and high rates of attrition in the primary/junior secondary level. The curricula teaching force (UNESCO, 2015b). It is for the TTI typically cover three domains: estimated that “Sub-Saharan Africa … will need subject content knowledge; teaching methods; to create 2.2 million new teaching positions by and, ‘professional studies’ incorporating 2030, while filling about 3.9 million vacant elements such as theories of child positions due to attrition” (ibid, Section 3). In development and learning, and classroom response to this pressure, many countries have management skills. In addition to taught resorted to appointing contract teachers with courses, all trainees take part in a practicum no formal training or introducing alternative although the duration and nature of this varies entry routes involving minimal training from country to country. Assessment is requirements. For example, UIS data reports generally through formal examinations of both that 50% or less of newly appointed teachers subject content and pedagogical knowledge. have received training to national standards in The language of instruction in the TTI tends to Benin, in Mali (46%), in Malawi (46%), in be in the dominant European language (e.g. Angola (45%) and in Niger (37%) (ibid). When English or French) or in a state language such considered in conjunction with high as Kiswahili in Kenya - notwithstanding the student:teacher ratios an even more disturbing fact that early grades are usually taught in picture emerges. The 2015 EFA Global local languages. (See Akyeampong et al., 2011). Monitoring Report estimates that “ratios of The use of a European language of instruction pupils to trained teachers are above 100:1 in can also present barriers to trainees. For Central African Republic, Chad, Guinea-Bissau example, in Francophone West Africa initial and South Sudan, and above 40:1 in 38 other training is typically in French yet “the data countries in sub-Saharan Africa” (UNESCO, show that the mother tongue of over 98% of 2015a, p.198). Whilst the priority must be to trainee schoolteachers is not French” (World ensure that all teachers are trained, the quality Bank, 2005, p. 53 cited in Lauwerier and of that training is also of concern. In this Akkari, 2015). 51. Here the term basic education includes both primary and lower secondary grades. In SSA, many TTI prepare teachers for these levels only. A minority prepare specialist mathematics teachers for the upper secondary grades. In many countries an alternative route is offered by universities who prepare specialist teachers to degree level. 101 7.2 Issues related to the quality of initial level of education (Lewin and Stuart, 2002). In teacher education many countries, e.g. Uganda, Rwanda and Nigeria, the minimum requirement for new Entrants are not well qualified tutors is a Bachelor’s degree making it increasingly unlikely that primary school Entry requirements for those enrolling on teachers will progress through the ranks to pre-service programmes vary from country to become teacher trainers. Currently, most country. In some countries, e.g. Ghana, tutors within TTI have been secondary school entrants must have a school-leaving teachers at some point in their career qualification at the senior secondary level (i.e. (Akyeampong et al., 2011). The lack of personal senior school certificate, A-levels, or experience of teaching mathematical concepts Baccalaureate) and in Zambia entrants are from the basic school curriculum, especially in expected to have followed at least a short the poor conditions that prevail in many course at the tertiary level (UNESCO, 2015b). classrooms, surely presents a barrier to However, in many others, including Kenya, guiding new entrants to the profession. This is Uganda and Nigeria52 the minimum entry a situation which is exacerbated by the requirement is the successful completion of reported disconnect between the curricula of basic school (i.e. school certificate, O-levels or TTI and current approaches to delivering the the equivalent). According to the 18 TTIs mathematics curriculum in schools. surveyed for this study, the entry requirement implicitly includes the need for a ‘pass’ in The curricula of TTI are not well aligned with mathematics at the junior secondary level or school curricula above. However, it is not clear what this means, in absolute terms, for the levels of Akyeampong et al. (2011) argue convincingly mathematical competence that entrants can that the curricula of TTIs are not well aligned demonstrate. Indeed, most of the TTIs with the school curricula which their graduates responding to our survey (56%) agreed with will be required to teach. Reasons for this the statements “When they start their courses, include the separation of responsibility for most of our trainees have inadequate curriculum development in schools and TTIs, knowledge of the Mathematics curriculum” the lack of recent and relevant experience of and “Our tutors have to re-teach the TTI staff at the basic school level, and the Mathematics content that our trainees should startling revelation that “neither college tutors have learned in schools”. This is reflected in nor trainees are likely have access to the the way in which the content of the curricula materials, such as teacher guides and of TTIs is organised with much emphasis being textbooks used in schools” (ibid, p.18). One of placed on the teaching of mathematical topics the main consequences of this disconnect, rather than pedagogical skills. particularly with respect to the teaching of mathematics, is that recent reforms in Tutors have inadequate experience of approaches to the delivery of the curriculum in teaching in basic education classrooms are not reflected in TTIs. The general trend across SSA for some There is evidence that teacher trainers in TTI considerable time has been to promote active, rarely have experience of teaching at the basic child-centred teaching and learning in contrast 52. The UIS Fact Sheet of 2015 lists Uganda, Rwanda and Nigeria as having a qualification at the senior secondary level as the official minimum requirement for trainees. However, TTI in these countries reported to us that their current minimum requirement is, in fact, successful completion of junior secondary education. 102 to traditional passive, teacher-dominated numbers in the primary school”. This reinforces approaches. Traditional content-based the view that TTIs place the emphasis on programmes have tended to be reformulated raising the subject knowledge of their trainees as competency-based curricula and implicitly, to such an extent that strategies for teaching if not explicitly, constructivist approaches to key concepts to young learners are largely teaching/learning have been encouraged. neglected. Certainly the vast majority of the Whilst practice in the classrooms of SSA may teachers interviewed for this study had a not yet have shifted significantly in this positive view of this aspect of their training direction, this is the aspiration of those with more than 80% agreeing with the responsible at the national level for improving statement “My own mathematical skills the quality of education and raising improved a lot as a result of my training”. In achievement. However, TTIs tend not to reflect reconciling this with the fact that assessments new approaches in either the content of their have repeatedly shown that teaching of curricula or the way they model good teaching mathematics in primary grades is largely practice. This is particularly true in the ineffective we are led to conclude that TTIs do preparation of trainees who will teach not equip their trainees with the profound mathematics in the basic phase of education. understanding of fundamental mathematics that Ma (1999) suggests is essential for Many TTI programmes place a great deal of teachers. Perhaps part of the explanation for emphasis on developing the mathematical this rests in the way in which TTI tutors knowledge base of trainees who, in many present mathematical concepts and teaching cases, enter college with poor subject strategies to their trainees. knowledge and weak skills. A significant amount of time is dedicated to mathematics From the descriptions of observed teaching (at least 5 hours per week in the TTIs surveyed sessions given by Akyeampong et al. (2011) it for this study) with the content organised appears that tutors in TTIs tend to replicate according to mathematical topics drawn from their own ideas as to what primary school the basic curriculum. However, relatively little teaching looks like but that this, all too often, time is specifically dedicated to how those fails to mirror best practice. For example, topics should be taught. For example, in the whilst tutors stressed the importance of using programme for primary teachers in Rwanda, a teaching and learning materials (TLM), their ten-hour module on the critically important treatment of them was often superficial and/or concept of ‘number operations’ dedicates uncritical (ibid). This, perhaps, is unsurprising eight hours to teaching trainees about if the tutors have never taught in primary everything from “Writing numbers of up to 7 classrooms and have little practical experience digits in words and vice versa” to “Carrying of how young people respond, or fail to out operations in other bases (base five, base respond, to various TLMs. This inability to take eight)” and “Writing numbers in expanded into account where young learners start from, form with concepts of indices and bases”. the prior learning they have, and the However, the same module allocates a total of misconceptions they hold is indicative of just two hours to “Identifying instructional another deficiency – the failure of TTI tutors to materials to use in teaching operations on model some of the key characteristics of the numbers” and “Teaching operations on learner-centred, constructivist approaches 103 advocated in curricula and supported by more between UNESCO and the China Funds-in- modern TLM. Akyeampong et al. report that in Trust (CFIT) which aims to use Information and Ghana “classroom interaction was organised Communications Technology (ICT) to around tutors posing questions and waiting for strengthen pre-service and in-service teacher responses” and that in Tanzania “tutors tended training (UNESCO and CFIT, 2014). In the five to follow a standard approach to teaching: countries surveyed for the project in 201454, all demonstration, practice, teacher assessment reported problems with unstable power and home assignment” (ibid, p.39). These supplies and inadequate and/or unaffordable techniques are typical of the signature lessons internet services. In some countries, including we observed in six focus countries for this Tanzania and Nigeria, TTIs are expected to be study (see Appendix A) and “very far removed equipped with ICT resources – usually in the from the contextualised, problem-solving form of a dedicated computer laboratory. approaches of the competence-based and However, hardware and software are often thematic school curricula” (Akyeampong et al., outdated and trainee access to computer p. 40). rooms may be severely restricted (ibid). There is little evidence to suggest that the tutors Colleges are not well equipped to use new currently employed by TTIs have the technologies or train prospective teachers in knowledge, skills and experience necessary to their use deliver effective training in this area. As explored elsewhere in this report, This may not constitute a serious problem in educational technologies are increasingly seen the short term because most graduates will as having great potential for raising the quality start their teaching careers in schools where of education and, in particular, student educational technologies are not available. achievement. The relatively poor schools of However, in the not too distant future, SSA are not yet equipped to make this a technological solutions to the problems of universal reality but one might reasonably raising educational outcomes are likely to be expect TTIs to be leading the way in this field implemented in schools. TTIs will need to and at least demonstrating how such respond to this challenge. technologies might be used to advantage in the classroom. However, evidence gathered for Graduates of TTIs enter a non-supportive this study suggests that most TTIs are not well environment equipped in terms of hardware, software, or competent staff53. Even where colleges report Whilst not strictly a consequence of initial that they have resources, it was extremely rare teacher training programmes, it is worth to find that this was available for regular use noting that newly qualified teachers (NQT) by trainees. For example, no TTI reported that often find themselves teaching in schools trainees had access to video material for the where the environment is not conducive to teaching/learning of mathematics and none using a range of TLMs or more sophisticated had computer software specifically related to modes of engaging with learners. Pressure to mathematics instruction (see Appendix A). cover an over-loaded curriculum leading to a Similar deficiencies were found in a needs high-stake examination often leads NQT to assessment conducted for a joint project deliver lessons according to an inflexible 53. In four of our focus countries, Cameroon, DRC, Rwanda and Uganda TTIs reported that their technical resources are inadequate and that they do not use technology (i.e. video, broadcast material, computer software and applications, etc) ‘extensively’ in their training. In Nigeria and Ethiopia, some but not all TTIs reported that they had adequate technological resources and that they were using it ‘extensively’. 54. Congo, DRC, Liberia, Tanzania, and Uganda. 104 structure and to use TLMs in a superficial way secondary school teachers. Secondly, a – if at all. There is evidence that NQT are recognised career path is required for those sometimes discouraged by more experienced, who wish to progress from successful and more cynical, colleagues who doubt the careers in primary schools to posts benefits of using, for example, teacher-made within TTIs. TLMs (Akyeampong et al., 2011). • TTIs need to acquire the resources and 7.3 Summary personnel necessary to train their trainees in the effective use of the educational Many countries in SSA face an immediate need technologies both in the classroom and for to produce very large numbers of teachers to personal development. meet the growing demand for education. However, strategies for meeting numerical If TTIs fail to meet these challenges there is a targets for newly qualified teachers must significant risk that they will continue to ensure that the quality of their training is not impede progress towards raising levels of neglected. At present, there is evidence to mathematical competence in schools rather suggest that graduates from TTIs are not well than being part of the solution. prepared to teach basic mathematics to young learners – they do not leave college with the necessary “profound understanding of fundamental mathematics” (Ma, 1999) and they do not develop the pedagogical skills associated with delivering a mathematics curriculum which presumes a constructivist or, at least, a learner-centred approach. The problems facing TTIs are numerous and varied. Financial resources are limited, but there are three fundamental challenges which should be addressed without delay. • There is a need for TTIs to develop and implement radically reformed curricula which reflect both the content and philosophy of the required curricula for schools. • TTIs need to develop a cadre of tutors with the knowledge, skills and first-hand experience of classroom teaching necessary to deliver a reformed curriculum using active methods. First, tutors require training in how to teach prospective primary and 105 106 Mathematics Education in Sub-Saharan Africa: 8 Assessment practices 8.1 Introduction is much evidence to suggest that the reality of implementation by teachers has not matched As described in Chapter 5, the Systems the vision of policy makers. For example, in Approach for Better Education Results Sudan official guidelines have been published (SABER) evaluation framework for student for classroom assessment at both the primary assessment identifies four important forms of and basic levels but “classroom assessment assessment: Classroom Assessments; practices are generally considered to be weak, Examinations; National Large-Scale as they provide little useful feedback to Assessments (NLSA); and, International Large- students. Limited systematic mechanisms are Scale Assessments (ILSA). The implication is in place to monitor the quality of classroom that developing all four forms of assessment in assessment practices” (World Bank, 2013a, p.1). a systematic way is likely to lead to better Similarly in Ghana “National syllabi… include educational results at the national level. The guidelines for classroom assessment (and) structure of this chapter reflects the SABER there are some system-level mechanisms in framework and uses findings both from SABER place to ensure that teachers develop skills evaluations and beyond to describe current and expertise in classroom assessment; assessment practices in SSA with special however, there are limited resources (such as reference to mathematics. tools and materials) available to teachers for conducting classroom assessment activities. 8.2 Classroom assessments Classroom assessment practices are generally known to be weak, and there are limited The SABER student assessment framework formal mechanisms in place to monitor their defines classroom assessment as any form of quality” (ibid, p.1). This and other evidence assessment which “provides real time suggests that Paulo (2014) is right to conclude information to support ongoing teaching and that in SSA “the powerful engine of learning in individual classrooms. Classroom assessment for improving learning remain(s) assessments use a variety of formats including unharnessed” (Paulo, 2014, p.137). observation, questioning, and paper and pencil tests, to evaluate student learning, generally Kellaghan and Greaney (2004) suggest that on a daily basis” (World Bank, 2013a, p.2). barriers to the adoption of formative Such formative assessment practices, as assessment practices include: the tendency of argued in Chapter 5, offer an effective way of teachers to dominate all aspects of teaching raising student achievement. The potential and assessment leaving little room for student- benefits have been widely recognised in focused activities; poorly qualified teachers; educational reforms across SSA with many large classes; poor facilities and shortages of countries formally adopting policies for the teaching and learning materials (Kellaghan and implementation of classroom assessment and Greaney, 2004). Paulo (2014) notes the supporting schools through, for example, the negative influence of high-stake examinations publication of teacher guides and the which encourage teachers to focus on topics provision of in-service training. However, there likely to occur in examinations and to emulate 107 the format and nature of examination with them are extremely high. As a questions in their classroom assessments consequence, the backwash56 effects of leading to “misalignment between systemic examinations are widespread and profound. In assessment priorities and assessment for theory, such effects may be positive or learning reforms” (Paulo, 2014, p.144). Whilst it negative leading to what Braun and Kanjee seems safe to assume that teachers of (2006) refer to as the “paradox of ‘high-stakes’ mathematics in SSA face all these generic assessment as an instrument of change” (ibid, challenges, there is little evidence as to the p.2). For example, high-stake tests may subject-specific problems they may face. For motivate students to work harder and they example, Kanjee (2009) notes that teachers may encourage teachers to focus on the most are required to prepare their own classroom important concepts of the curriculum. On the materials but that it is unrealistic to expect other hand, high-stake tests encourage them to produce high quality assessment teachers to ‘teach only to the test’ and to instruments for formative purposes especially ignore other vital elements of a young person’s if they are inexperienced, have few resources education. Also, examinations (especially to hand and are under pressure of time. One those that set unrealistically high barriers) can approach to solving this problem is illustrated demotivate learners and promote cheating. by the development in South Africa of subject- specific Assessment Resource Banks (ARB). Bachman and Palmer (1996) point out that test Mathematics teachers can access sample effects can be seen at both the micro and assessment materials for a wide range of macro levels. Micro level effects are seen in the curriculum topics via the Thutong South behaviours of individual students and teachers. African Education Portal55. Kanjee (2009) Macro effects are seen at the level of the concludes that teachers value such materials education system and in the behaviour of and that their provision helps teachers to society as a whole. One of the most obvious improve their classroom assessment practices macro effects in SSA is the prevalence of (Kanjee, 2009). malpractice, whereby students, teachers, exam room invigilators, markers and/or others adopt 8.3 Examinations illegitimate means in order to gain unfair advantage (Greaney and Kellaghan, 1996). Throughout SSA, formal examinations tend to National and regional examining agencies be the most firmly established and most highly direct a great deal of effort towards preventing developed form of student assessment (e.g. malpractice but reports of widespread World Bank 2009, 2013a and 2013b). Their key cheating remain common throughout the purposes are selection and/or certification of region. For example, in South Africa, during learner achievement at critical transition the conduct of the 2014 Matric examinations, points. Typically, these lie between the primary “more than 2,800 Matric pupils and at least 34 and (junior) secondary phases, between the teachers and principals in KwaZulu-Natal and junior and senior secondary phases, and at the the Eastern Cape were allegedly involved in interface of (senior) secondary and tertiary mass cheating” (eNCA, 2015). In Kenya, at the education. Given that many examinations release of results for the 2015 Kenya Certificate serve as gatekeepers to limited and highly of Primary Education (KCPE), the Chief prized opportunities, the stakes associated Executive of the Kenya National Examinations 55. http://www.thutong.doe.gov.za/ (accessed 14 October 2015). 56. In educational assessment, the ‘backwash’ or ‘washback’ effect is the influence which a test or examination has on the teaching and learning which precedes it. 108 Council (KNEC) reported that “157 people have reflect, and hence promote, the underlying been prosecuted for engaging in examinations philosophy of the intended curriculum. irregularities” and that those charged included Kellaghan and Greaney (2004) report that “head teachers, their deputies, university “there are concerns about the extent to which students, parents, police officers and (examinations) are biased toward the testing candidates” (Wanzala, 2015). And in Ghana, of competencies needed by students in the the West African Examination Council (WAEC) next cycle of education” and go on to ask “Do cancelled the results of 453 students for the examinations adequately reflect the goals cheating in their West African Senior School of the curricula for those students (a majority Certificate Examination (WASSCE), in most countries) who will not proceed investigated 119 schools for engaging in mass further in the education system?” (ibid, p.9). cheating, and withheld the results of The World Bank (2008) highlights the view candidates from 185 schools where that examinations neglect many of the “examination irregularities” were suspected behavioural objectives and competencies (Citi fm, 2015). One of the consequences of explicitly required by modern curricula. the high public profile of examinations and “Modern curricula in SSA formally aim at the need to fight malpractice is that the learning outcomes like comprehension, examining authorities, not surprisingly, application of knowledge, methodological and prioritise the secrecy and security of social competencies, and problem solving. examinations at the expense of activities that Current assessment and examination practices could harness the power of examinations to are limited to the recapitulation of memorised promote better teaching and learning facts. Assessment documents in some SSA (Kellaghan and Greaney, 2004). Two major countries claim that a wide range of issues associated with examinations in assessment techniques are used to assess the general, and mathematics examinations in different knowledge, skills and attributes, particular, are considered below. however, the reality looks remarkably different” (ibid, p.57). This is particularly true Examinations do not, in general, reflect the of examinations in mathematics where, in the philosophy of the teaching/learning most selective of examinations, questions tend curriculum and, in some cases, are not well- to focus on abstract, academic concepts at the matched to student ability margins of the syllabus with students required to reproduce the preferred ‘correct’ procedure. A number of commentators have questioned In some examinations it is difficult to find a the validity of the high-stake examinations that single, straightforward question based on the tend to dominate the education systems of application of mathematical concepts to a SSA (Kellaghan and Greaney, 2004). Here the problem set in a real-world context. This is a term ‘validity’ goes beyond the narrow general characteristic of mathematics concept of ‘content validity’ on which agencies examinations at the lower and upper responsible for the conduct of high-stake secondary levels which, in many countries, are examination tend to focus. It includes multiple associated with high failure rates. For reasons aspects associated with an examination’s described previously, detailed test and item ‘fitness for purpose’ including the extent to statistics for mathematics examinations in SSA which assessment instruments and procedures are not widely available. However, the 109 Certificate of Secondary Education Is it a great surprise to find that of the 396,678 Examination (CSEE) Tanzania offers a candidates who took this examination 291,164 pertinent, if somewhat extreme example. (73.4%) scored zero on this task? This example According to National Examinations Council of raises three questions: Is the content and Tanzania (NECTA) (2014a) “The CSEE marks format of this question compatible with the the end of four years of secondary education. philosophy and objectives of the basic It is summative evaluation which among other mathematics curriculum? Does a question things measures the effectiveness of the which is completely impossible for three- education system in general and education quarters of the cohort add significantly to the delivery system in particular. Essentially, information function of the test? What impact candidates’ responses to the examination does this type of question have on the future questions is (sic) a strong indicator of what behaviours of teachers and on the motivation the education system was able or unable to of future learners? Unfortunately, the NECTA offer to the students in their four years of examiners’ report reveals that all 16 questions secondary education” (NECTA, 2014a, p.iii). on this examination had similar measurement With this in mind, it is disturbing to find that characteristics with approximately 90% of the the pass rate for the Basic Mathematics cohort scoring zero on each item. examination in 2013 was just 17.8% (NECTA, 2014b, p.1). To put it another way, of the Examiners’ reports also suggest that markers, 352,179 candidates who sat the examination when assessing student responses, are looking 289,613 (82.2%) failed to meet the minimum for a particular procedure and format for the acceptable standard. Reasons suggested by presentation of working. It is not clear whether NECTA for the high failure rate include alternative approaches would or would not “complete lack of knowledge”, “partial gain full credit. For example, a question told understanding on the topics in the syllabus” candidates that a shopkeeper selling an article and “failure… to show clearly the workings at shs. 22,500/= makes a loss of 10% and (and) formulas” (ibid, p.iv). However, evidence asked them to calculate the price which would from the reports of examiners suggests that yield a profit of 10%. The examiners’ report the question papers are not fit for purpose. stated that “(many candidates) did not realise For example, it is usually considered good that they were supposed to calculate first the practice to start an examination with an buying price (x) of the article… and thereafter accessible and relatively easy question to set calculate the selling price” (NECTA, 2013, p. candidates at their ease. However, the first 20). However, it is perfectly possible to solve question on the 2012 examination for Basic this question directly without going through Mathematics asked candidates to evaluate the the intermediate stage required by the expression below to three significant figures, marking scheme. This is relevant because it using mathematical tables. echoes general concerns with the directive, instrumentalist approaches modelled by tutors 2 in TTIs and exhibited by mathematics teachers 3 0.0072  81.3 across SSA. This is in contrast with a constructivist approach which allows for the 23140 possibility of different students choosing 110 different routes to mathematically average test scores and/or the mathematical valid solutions. competencies demonstrated by those who passed. At the secondary level, examination A telling comment on the relevance of the results were more readily available for mathematics tested in formal examinations to individual subjects including mathematics but the lives of students comes from a report on these were aggregated by reporting category the Uganda Certificate of Education (e.g. Grades A, B, C, etc. or divisions 1, 2, 3 examination of 2009: “This (question) was etc.). Without further information, e.g. cut-off testing knowledge on the laws of logarithms, scores and/or performance criteria, ability to manipulate the mantissa and interpretation of standards of performance in characteristic. It is unfortunate that these days mathematics is impossible. students are married to the calculator and do not see why teachers bother them by teaching Notwithstanding the above, a few examining logarithms” (UNEB, 2009, xi). agencies do produce reports for subject teachers. Typically these are written by Chief Information from examinations is not Examiners and are general in nature. disseminated to subject teachers and other Information about the level of difficulty of educational practitioners particular questions is also given in general terms without specific statistics. For example, Examinations generate a huge amount of data the Chief Examiner’s report for an O-level which, if properly analysed, can provide mathematics paper in Zimbabwe says of valuable quantitative information for performance on question 1: “(a) (i) Well done. educational policy makers and practitioners. In (ii) Fairly done. Wrong comma placement was particular, statistical evidence combined with common. Common wrong answers were 0,05 the subjective opinions of subject specialists and 0,0005. (b) Fairly done. 85 was a common can provide teachers with information about wrong answer seen.”(ZIMSEC, 2009, p. 1). It is the strengths and weaknesses demonstrated difficult to see how teachers can use such by examination candidates. Teachers can then general comments for diagnosis and effective use this information to improve their teaching remediation. In the few cases where specific and, hence, improve student performance. suggestions are made, these tend to be trivial. Unfortunately, the examining authorities of For example: “Qn. 6 was not popular. Problems SSA, with few exceptions, make little or no use noted: Candidates could not obtain the of the data they hold and do not have translation which moved the object to the systematic information feedback systems. In image position (and) did not extract the image fact, in preparing this study it was extremely co-ordinate from the location column vector. difficult to find any examination-related Suggestions: Teachers countrywide did not statistics beyond aggregated results tables57. teach vector transformations. It is therefore At the primary level, results are generally important that all schools be impressed upon aggregated across all subjects leading to an this topic” (UNEB, 2009, xiv). This is like the overall pass rate. Even when a separate pass coach of a soccer team instructing his or her rate for mathematics was reported no players to ‘score more goals’ – obvious conclusions could be drawn as to, for example, but unhelpful. 57. In the preparation of this study, examination boards across our six focus countries were asked to supply test-score distributions and other statistical information related to their mathematics examinations. Only in Nigeria did two boards respond positively - WAEC, Nigeria and the National Business and Technical Examinations Board - but even here raw score test distributions and grade cut-scores were not provided making any meaningful evaluation of mathematical standards impossible. 111 The West African Examinations Council has published regularly and in a timely manner. taken a considerable step forward by making This is in stark contrast with many other its traditional Chief Examiners’ reports for the national examining agencies where reports do West African Senior School Certificate not appear to have been published for several Examination (WASSCE) freely available years59. Secondly, separate reports are through its online e-Learning Toolkit58. The produced for each subject making them easier standard reporting format is clear and for subject teachers to use than the composite provides subject teachers and students with a reports published elsewhere. Thirdly, and most copy of the examination question followed by importantly, the information they contain is of model solutions and observations as to the a high quality and potentially more useful for typical performance of candidates. There is teachers - as illustrated in Figure 8.1 below scope for improvement in the presentation of, (MES, 2014). Note that in this example the for example, mathematical functions and author is making it clear to subject teachers diagrams, and the observations would be that there is no single correct solution to this strengthened by the inclusion of quantitative indicators of difficulty. However, the approach task and that the scoring process rewards any is fundamentally sound and could serve as a mathematically legitimate alternative. This is model for other national examination agencies. compatible with an approach to teaching which challenges students to explore The Mauritius Examinations Syndicate offers mathematical problems rather than instruction another notable example of good practice in which trains students to replicate the correct/ its Chief Examiner’s reports. First, these are preferred procedure. Figure 8.1: Chief Examiner’s report on the performance of candidates for the Mauritius Certificate of Primary Education examination on a particular mathematics question Question 46 Most candidates were able to identify the missing terms in the sequences given. Part (a)(i) was found to be the easiest sequence to work out. A few high performing candidates interpreted this sequence in a number of unexpected ways. Although their approaches were more complex, the responses which they gave were mathematically correct and they were rewarded accordingly. These candidates started bt determing the L.C.M. of the denominators before they could identify a familiar pattern. They consequently obtained the following answers: +2 +1 +0 1 2 3 6 8 9 9 , , , , , , 2 3 4 12 12 12 12 +2 +1 +2 6 8 9 11 OR , , , 12 12 12 12 1 1 1 + + + 6 12 18 1 2 3 29 OR , , , 2 3 4 36 58. WAEC e-learning toolkit available at http://waeconline.org.ng/e-learning/index.htm (accessed 3 February 2016). 59. For example, the most recent reports available from the websites of the Uganda National Examination Board and the Zimbabwe Schools Examinations Council as of October 2015 were for the examinations of 2009 112 8.4 International and regional assessments sophistication and the level of learning that (PISA) tests are directed at is likely to be 8.4.1 International large-scale assessments pitched far higher than anything that has been achieved in those education systems. It’s really As described in Chapter 3, few countries from not helping anybody improve their education SSA have participated in international large- system if the result is that none of the children scale assessments (ILSA) of student do well on the test” (ibid). In the same article, achievement in mathematics. Those that have van Leeuwen suggests that “(f)unding should taken part in TIMSS have, without exception, be targeted on the marginalised and not on fared badly falling far below international ranking countries with huge out-of-school norms even when national samples have been populations. Sampling can be used to inform drawn from over-aged populations. Only good policy, but assessment alone is no Mauritius has so far chosen to participate in replacement for a coherent, inclusive and PISA tests designed to measure the high-quality education system. The cure is not ‘mathematical literacy’ of 14-year-olds. more thermometers. Given the critical Although its results were below the shortage of teachers, it certainly is more international average, its students performed practitioners” (ibid). at levels comparable to those achieved by their peers in OECD member countries Chile Suggested advantages associated with and Mexico. However, one should not be participation in, for example, PISA include a misled by this outcome – SACMEQ studies positive influence of findings on policy show that mathematical standards in Mauritius reforms; capacity building in assessment and exceed those in other SACMEQ countries by a psychometrics which can be used to margin which is, in statistical terms, huge. strengthen national assessment systems; and Evidence strongly suggests that any other the possibility of accurate monitoring of country from the region electing to join an standards over time. Breakspear (2012) reports international large-scale assessment should that whilst PISA findings do help to shape expect to find itself towards the bottom of the policy decisions in some countries, those that measurement scale and, hence, international perform below the OECD average, e.g. Turkey rankings for mathematics. Therefore, the and Indonesia, are less likely to report a question to be addressed is ‘would significant impact (ibid). Bloem (2013) participation in TIMSS and/or PISA yield indicates that whilst participating in PISA information which would be likely to undoubtedly offers significant opportunities contribute significantly to raising national for building technical capacity, low- and achievement levels – especially in middle-income countries often lack the mathematics?’ At the same time policy makers capacity to take full advantage of these 60 should ask ‘would the costs involved in opportunities (Bloem, 2013). joining and conducting an ILSA yield benefits representing good value for money? Gillard, quoted in an interview (Exley, 2014), said “For 8.4.2 Regional large-scale assessments some countries it might well suit [them], but for other countries that are really still piecing The potential importance of SACMEQ should their education systems together, the be clear from earlier chapters. Not only have 60. The international fee for participating in PISA 2015 was €45,500 per year for four years giving a total of €182,000 (USD-200,000). In addition, participating countries are required to pay all national costs covering, inter alia, preparation of test booklets, test administration, coding of student responses, data entry, etc. 113 SACMEQ surveys provided participating of great significance. For example, the release countries with snapshots of the achievements of the full PASEC database will allow of their students, they have also yielded a researchers the opportunity to conduct high wealth of valuable data which has allowed quality secondary analysis for francophone researchers to investigate the complex systems and to systematically link PASEC data relationships that exist between learning with that of SACMEQ. If the considerable outcomes and background factors. More technical challenges associated with moving recent developments, most notably the to measurement and analytical standards adoption of IRT-based reporting scales, are comparable with those of TIMSS and PISA giving SACMEQ the potential to monitor can be overcome, then a SACMEQ/PASEC changes in relative and absolute standards consortium will be in a strong position over time with increased precision. Parallel to assume the role of a pan-African developments in PASEC assessments are also assessment agency. Figure 8.2: Coverage of the two major regional assessments of student learning: PASEC and SACMEQ Seychelles Regional Assessments in SSA SACMEQ III (2007) Mauritius PASEC 2014 Non participating countries in SACEMEQ or PASEC 114 8.5 National large-scale assessments resourced NLSA of SSA to replicate the technical standards of NAEP, there are lessons The role of NSLA in providing information that can be learnt and deficiencies which about the state of mathematics education in should be rectified. SSA was briefly described in Chapter 3. Here the focus is on the potential of such Mathematics educators cannot use results assessments to provide information which reported as ‘percentage correct scores’ practitioners – especially teachers of without access to the tests mathematics and the developers of TLMs for mathematics – can use to improve teaching In Uganda and Ethiopia, student achievement and learning. The reports of three, sample- in the NA was reported as the proportion (%) based national assessments are critically of correct responses on the mathematics test. reviewed: the Grade 3 NA of numeracy and In Kenya, raw scores (number correct) were literacy in Kenya (2010); the NA of normalised through a linear translation to give Mathematics, English Language, and Biology a score on a scale with a mean of 300 and a at the ‘Senior 2’ level in Uganda (2013); and, standard deviation of 100. In both cases, the the NA of Grade 10 and Grade 12 students in scores are test-dependent. This means that the Ethiopia in Mathematics, English, Biology, reported results, e.g. average scores, can only Chemistry and Physics (2010). be interpreted by reference to the particular tests used and the items therein. As far as we The potential of an NLSA to provide valuable can ascertain, in none of the cases we studied information to practitioners involved in were the tests used in the national mathematics education is perhaps best assessments made available to teachers and illustrated by reference to the National other practitioners. What then are Assessment of Educational Progress (NAEP) mathematics teachers to make of remarks of the USA. NAEP has been conducted such as “The mean score (for mathematics) regularly since 1969 and incorporates was 44.1% with a standard error (S.E.) of 0.37” extremely high standards of test construction, (UNEB, 2013, p.17) or worse still the baffling test administration, statistical analysis of comment “(at) the national level, the mean student responses, and reporting. NAEP score for Literacy and Numeracy was 297.58 provides policy makers, educational planners, and 295.6 respectively. Both are slightly below and researchers with a great deal of general the standardised mean scores of 300” (KNEC, data on the outcomes of the education system 2010, p.21)? Only in the Uganda report did we and background factors. However, it also find reference to student performance on provides detailed information on student individual items but even here interpretation performance in each of the target subjects. was difficult. For example, the report states For each round of NAEP, the information that “fewer than 20% of the students were available to mathematics educators includes: a able to compute the initial amount of money detailed description of the NAEP assessment deposited in a bank so as to earn an interest at framework (NCES, n.d.); a separate report on a given rate” (UNEB, 2013, p.20). Here a student performance on the mathematics mathematics teacher is likely to ask: ‘Why did tests; and examples of NAEP items in each this particular task prove so difficult? Was mathematical sub-domain and at each there something unfamiliar about the way in reporting level of achievement (both in the which the task was presented? What were the report and online). Whilst it is unrealistic to common mistakes made by students?’ Without expect the relatively new and less well- seeing the item, the teacher is left in the dark. 115 In the case of high-stake examinations where examples of test items should be included in new tests are set ab initio each year, question the report so that subject teachers can papers can be placed in the public domain interpret the findings intelligently. An example allowing teachers to scrutinise the assessment of good practice from the 2011 NAEP report tasks and adapt their teaching to better for students in Grade 4 is given in Figure 8.3. prepare future candidates. However, in national In addition to the limited number of examples and international assessments it is common included in the report, pools of ‘released items’ practice for test booklets to be collected after or practice tests should be provided so that testing and then kept secret so that some the national assessment system has maximum items can be reused. In this case, sufficient benefit in the classroom. Figure 8.3: Example of how information on student performance on a national assessment item can be presented to mathematics teachers and other practitioners (NCES, 2011, p.30) Mathematics Content Area: Number Properties and Operations Subtract: 6,090 A 1,147 B 1,247 C 2,257 D 2,853 - 4,843 This multiple-choice question from the 2011 mathematics assessment asks students to answer a subtraction problem involving two 4-digit numbers. The problem requires students to regroup twice to obtain the correct answer of 1,247 (Choice B). Students were not permitted to use a calculator to answer this question. Seventy-four percent of fourth-grade students answered this questio correctly. The most common incorrect answer (Choice D), selected by 13 percent of the students, resulted from not doing any regrouping and just subtracting the smaller number from the corresponding larger number at each place value. Choices A and C, while selected less frequently, represent different regrouping errors. Percentage of fourth-grade students in each response category: 2011 Choice A Choice B Choice C Choice D Omitted 7 74 5 13 1 The table below shows the percentage of fourth-grade students performing at each achievment level who answered this question correctly. For example, 73 percent of fourth-graders at the Basic level selected the correct answer choice. Overall Below Basic At Basic At Proficient At Advanced 74 40 73 90 97 116 Where the assessment purports to set also reports on the proportion of students absolute standards of performance, concrete reaching four so-called standards: ‘below examples are required for interpretation basic’, ‘basic’, ‘proficient’ and ‘advanced’. Students with a score lower than the In addition to percentage correct scores, all population mean are placed at the ‘below three national assessments reported on the basic’ level. Students with scores less than one proportion of students reaching certain levels standard deviation above the mean are of achievement. However, the definitions of deemed to be at the ‘basic’ level. The these levels were generally unclear. Where thresholds for the ‘proficient’ and ‘advanced’ criteria-related descriptors were offered, no levels are at two and three standard deviations details were given as to the standards-setting above the mean respectively. These are simply process by which the cut-scores between norm-referenced standards and tell us nothing levels were located. of what mathematical competencies the students at these levels can and In the case of Ethiopia, the national education cannot demonstrate. and training policy specifies the minimum (acceptable) achievement level as a test score The Grade 3 assessment in Kenya does of 50%. The report confirms that only 14.7% of describe four levels of mathematical the cohort achieved the minimum level on this achievement as shown in Table 8.1 (KNEC, test. This tells us little since if easier test items 2010, p.25). It then reports the proportion of had been selected then the proportion of the cohort at each level. Unfortunately the successful students in this population would report gives no details as to how student test have been higher and vice versa. In addition to scores were linked to the levels’ descriptors. this achievement threshold, the Ethiopia report Table 8.1: Descriptors for the four levels of mathematical competence used for reporting purposes in the Kenyan national assessment for mathematics in Grade 3 Level Description of Competency % of pupils Level 1 Applies single step addition or subtraction operations (e.g. add numbers without 4.6 carrying over, subtract without borrowing). Counts in whole numbers. Level 2 Applies a two-step addition or subtraction operation involving carrying over and 43.7 borrowing. Applies simple multiplication operations involving multiples of 10. Recognises simple fractions. Level 3 Translates information presented in a sentence into one arithmetic operation. Interprets 48.1 place value of whole numbers up to thousands. Interprets simple common everyday units of measurement such as days, weeks, litres, metres and shillings. Level 4 Translates information presented in sentences into simple arithmetic operations. Uses 3.6 multiple arithmetic operations (in the correct order) on whole numbers. 117 In Uganda, three proficiency levels are defined: This would be a first step towards providing ‘basic’, ‘adequate’ and ‘advanced’ described in teachers with a more comprehensive ‘item map’ terms of what students can and cannot do. linking mathematical tasks with student ability. However, as in the Kenyan case, there is no Examples of such item maps can be found in description of the process by which test score the mathematics reports of TIMSS and PISA. thresholds are set for these levels. In both cases Figure 8.4 shows the item map for Grade 4 the assessment reports fail to provide mathematics constructed using data from the mathematics teachers with items which 2011 NAEP in the USA. exemplify what students at each level can do. Figure 8.4: Exemplar item map linking three levels of positive achievement (Basic, Proficient and Advanced) with the IRT-based scaled scores and selected items from the NAEP assessment for Grade 4 Mathematics 2011 (NCES, 2011, p.29) Grade 4 NAEP Mathematics Item Map Scale Score Content Area Question Description 500 // 330 Number properties and operations Compose numbers using value to determine winners of a game ADVANCED 317 Geometry Divide a square into variuos shapes 293 Measurement Solve a story problem involving time (calculator available) (shown on pages 32 & 33) 291 Algebra Identify the growth relationship from a table (calculator available) 290 Data analysis, statistics and probability Compare two sets of data using graphs 282 279 Algebra Recognise and extend a growing pattern 278 Number properties and operations Order fractions with unlike denominatiors 276 Measurement Draw a line segment of a given length PROFICIENT 275 Number properties and operations Use place value to determine the total amount 269 Geometry Compare simple figures to identify a common property (shown on page 31) 261 Number properties and operations Identify and use factors to solve a problem in context (calculator available) 259 Number properties and operations Use place value to find a sum 254 Data analysis, statistics and probability Creata a pictograph of a set of data (calculator available) 250 Measurement Find areas of a scale drawing on a grid 249 243 Algebra Label sections on a grid from a list of coordinates 240 Number properties and operations Determine the sum of numbers represented on a number line (calculator available) 239 Number properties and operations Explain a property of divisibility 232 Number properties and operations Compute the difference of two 4-digit numbers (shown on page 30) BASIC 230 Number properties and operations Solve a story problem involving division (calculator available) 226 Data analysis, statistics and probability Identify the most likely outcome from a given spinner (calculator available) 221 Geometry Describe a real-world object in terms of a geometric solid 216 Measurement Identify measurements needed to determine area 214 214 211 Number properties and operations Compute the difference of fractions with like denominators 195 Algebra Determine numerical value of an unkown quantity in a whole number sentence 180 Geometry Identify a figure that is not symmetric (calculator available) 175 Measurement Identify the appropriate measuring device for a given attribute // 0 118 8.6 Summary mathematics teachers, can use to understand what students across the ability range can and Good assessment has a positive effect on cannot do. Providing statistical data is not teaching and learning. However, in SSA the enough since without concrete examples, potential benefits of assessment are not being teachers cannot interpret the numbers exploited. Moreover, some aspects of the intelligently and, hence, improve their teaching high-stake examinations used in the region strategies. Teachers need access to the national serve as a significant barrier to progress. High- assessment tests or, if this is not possible, a stake examinations need to be reformed so sizeable pool of exemplar items. that, over time, their content better reflects the curriculum’s central learning objectives and its From a strategic point of view, improving underlying philosophy. There is also an urgent assessment practices appears to offer a cost- need to ensure that the demands of the effective way of raising outcomes in examinations are more closely aligned with the mathematics. Some of the changes advocated ability levels of candidates. In the short-term, above with regards to examinations and the agencies responsible for examinations in national assessments can be implemented in mathematics should make assessment-related the short-term without incurring major costs. data and other information freely available for However, the vitally important task of subject teachers and other practitioners. introducing diagnostic and formative assessment practices in classrooms is likely to Effective assessment in the classroom is an prove a major challenge and will require greater effective way of raising levels of achievement. effort sustained over the long-term. However, changing teachers’ attitudes towards formative assessment and, hence, reforming assessment practices in the classrooms of SSA, is likely to prove difficult. Teachers of mathematics will need effective training and a lot of support – especially through the provision of high-quality, user-friendly assessment materials. Participation in international assessments such as TIMSS and PISA can provide a country with high-quality information about the status of mathematics education both in absolute and relative terms. However, for countries which are relatively poor and where student performance is known to be very low it is not clear that the potential benefits outweigh the costs. National assessments of numeracy and mathematics have the potential to provide information which practitioners, especially 119 120 Mathematics Education in Sub-Saharan Africa: 9 Initiatives and innovations 9.1 Introduction highly developed countries are concerned that if they do not improve their own levels of The scale and scope of the challenges facing achievement in mathematics and the other mathematics educators in SSA described in STEM subjects, then they will fall further this study are generally well recognised, as is behind the dynamic economies of East Asia. the urgent need to address them. Throughout As a result, they have launched major the region there are many examples of initiatives to address two problems that they initiatives designed to improve the quality of share with countries in SSA: levels of teaching and learning in mathematics. Partners mathematical achievement across the in these include governments, international aid education system that lag behind those of agencies, NGOs and philanthropic groups, and their international competitors, and a general even some commercial enterprises. A number lack of interest amongst students (especially of recent government-led initiatives are being girls) in pursuing further studies in STEM implemented at the national level. However, subjects at higher levels. Here we include many more potentially interesting innovations several examples of initiatives in mathematics are being tried on a small scale. Of these, some education from developed countries. These, report large, positive effect sizes but these however, should be interpreted with regard to should be treated with some caution. the context of SSA. Initiatives that appear to Evaluations are not always fully independent yield positive outcomes in highly-developed of the implementing agency and analytical/ countries may depend on the pre-existence of statistical techniques may not meet good resources and, most importantly, a recognised technical standards. More well-educated, well-trained and relatively importantly, innovations that are effective on a well-paid teaching force – conditions which are small scale may not be feasible at full scale or not generally met in SSA. sustainable in the long-term once external funding sources have been removed. 9.2 Early years and primary grades Notwithstanding this caveat, examples of current and/or recent initiatives are given in Pre-primary education this chapter simply to illustrate some of the approaches currently being explored. The Early Childhood Care and Education (ECCE) inclusion of a particular example here should was the first Education For All goal and its not be taken as an endorsement of that fundamental importance is confirmed by the approach. Indeed, most of these initiatives UN’s 2030 Agenda for Sustainable have not yet been rigorously evaluated as to Development (UN, 2015b) where the their impact on student learning, their cost- commitment is made to “ensure that (by effectiveness, or their long-term sustainability. 2030) all girls and boys have access to quality early childhood development, care and pre- The challenges that mathematics educators in primary education so that they are ready for SSA face are not confined to the region or just primary education” (UN, 2015b, p.17). There is to developing countries in general. Many a wealth of evidence showing that children 121 who have attended pre-school demonstrate Children (SC) in Bangladesh, Ethiopia and higher levels of achievement throughout their Rwanda62. The programme “raises awareness time in school. Bailey (2014) reiterates that of (emergent literacy and maths) skills and measures of early mathematics skills are “the how they develop through play and joyful strongest early predictors of children’s Maths learning, trains early childhood care and achievement years later” (Bailey, 2014). Results development (ECCD) teachers on how best to from OECD PISA confirm that the advantages support them and mobilises communities to enjoyed by students who have attended a promote these skills at school and at home in pre-school are still61 statistically significant order to ensure school readiness” (SC, 2012, when their mathematical skills are measured at p.1). The evaluation report for Bangladesh the age of 15 (OECD, 2014). suggests that the programme’s multi-faceted approach (including health and nutrition) Pre-primary enrolment in SSA has increased produced significant gains in the general over the past 15 years but still remains readiness of children to attend school. In relatively low, e.g. 19.5% in SSA compared with particular, by exposing children to early 74% in Latin America and the Caribbean mathematics concepts such as shapes and (Shaeffer, 2015). Ghana represents a notable numbers, their readiness to start mathematics exception having effectively introduced in schools was significantly enhanced (SC, universal pre-primary education by extending 2012). compulsory basic education to include kindergarten classes. Details as to how this In Ethiopia, the programme focused on the use was achieved and of the resulting challenges of an ELM ‘toolkit’ with facilitators of early are to be found in Shaeffer (2015). childhood care and development (ECCD) centres being trained on the use of programme Save the Children, Emergent Literacy and materials and play-based techniques. Early Maths (ELM) programme mathematics concepts included: number and quality identification; counting; concepts of One initiative which includes specific measures time, direction, space and shapes. Skills related to early years’ numeracy skills is the included: sorting; looking for patterns; and, Emergent Literacy and Maths (ELM) problem solving. Children63 were tested before programme being implemented by Save the and after the intervention using a 68-item test. Table 9.1: Findings of an evaluation of the impact of ECCD interventions in Ethiopia based on test scores pre- and post-intervention (Save the Children, 2014) Group Test score (%) before Test score (%) after Gain Control (no exposure to ECCD) 20.5% 22.4% 1.9% Group 1 (exposure to ECCD but 29.3% 43.2% 13.9% without use of ELM materials, etc.) Group 2 (exposure to ECCD with 27.8% 76.9% 49.1% use of ELM materials, etc.) 61. Bailey (2014) points out that the positive effect on mathematical achievement associated with having attended pre-school diminishes over time and that other factors may be larger than pre-school attendance in causing improved achievement in mathematics. 62. Save the Children has plans to roll out its ELM toolkits in Nepal, Indonesia, Afghanistan, Bangladesh, Pakistan, China (Borisova, n.d.). 63. Exact sample sizes are not given but the evaluation report suggests that the target was 120 in the control group and about 180 in each of the treatment groups. 122 The results are shown in Table 9.1 (SC, 2014). EGRA tests, was positive and highly significant Save the Children reports that it is to support with an effect size for reading fluency of 0.73 the use of its ELM materials in other countries (USAID/Kenya, 2014). According to the whilst also piloting a new “parent outreach authors of the evaluation report “this equates component to the toolkit focused on building to more than 1 year of gain for pupils in control parental capacity to support ELM skills at schools” (ibid, p.xii). However, the impact on home” (SC, 2014, p.2). the children’s numeracy skills, as measured by EGMA tests, was far less impressive. A Primary education moderate gain was detected for number identification and missing number tasks but In order for a country to enjoy high standards there was no discernible impact on, for in mathematics at the secondary and tertiary example, the more difficult topic of quantity levels, firm foundations must be laid in the discrimination. Students in the treatment early years of education. As a result, many group did, however, demonstrate significantly initiatives for improving outcomes focus on greater fluency (i.e. number correct per the primary phase of education. Some are minute) in addition and subtraction tasks. The specifically targeted at young learners in PRIMR evaluation report offers no clear developing countries but others have been explanation as to why numeracy skills were designed to address the concerns of advanced apparently less susceptible to improvement economies where there is a perceived learning than reading skills. deficit. Here we include one example from SSA and one from the UK. Some of the key lessons identified by the evaluation team are given below (USAID/ Primary Maths and Reading (PRIMR) Kenya, 2014, pp.73-74): Initiative, Kenya • “(Teachers’ Advisory Centre) Tutors’ visits to schools were critical for supporting teachers The Primary Maths and Reading (PRIMR) and improving pupil’s outcomes. Proper Initiative 2011-2014 was led by the Kenyan training of TAC Tutors is essential so that Ministry of Education, Science and Technology they can effectively support teachers. The and was funded by USAID/Kenya. It was results also indicated that schools visited implemented by RTI, International. The frequently were likely to have stronger programme partners developed new TLM pupil performance.” based on the school curriculum and developed the professional capacities of school principals • “Training of teachers is a complex task that and teachers. In particular, teachers were must assume teachers are adult learners trained in the use of interactive teaching who learn best by doing and interacting methods and, thereafter, supported through with other professionals. This implies that the periodic visits of ‘instructional coaches’ teacher training should be organised around trained under the programme. modelling and practice, and that having brief training sessions with follow-up The PRIMR evaluation found that the impact refresher meetings is more effective than on children’s reading skills, as measured by longer training courses.” 123 • “Evidence suggested that most of the assessment, and planning effective lessons and teachers supported by PRIMR had not activities. Thereafter, NC teachers were given attended professional development courses on-going support through a professional or in-service courses for several years since development programme and a quality leaving college or becoming teachers. The assurance system (ibid). The main aim of NC PRIMR Initiative’s regular professional specialist teachers was to “use shape, space development through training and other and measures, and handling data as contexts activities filled a demand for increased for the development and application of instructional practice and support.” children’s number skills” in order “to give children confidence in number and an • “Changes in instructional approaches: Old understanding of patterns and relationships so habits take time to change, and the shift that they (could) extend learning to other from traditional teaching to more active, aspects of Mathematics in their class lessons” sequenced, pupil-focused approaches was (ibid, p.3). The NC programme was piloted in the central focus of PRIMR. Some teachers 65 schools across the country and subjected continued to use two approaches to a comprehensive, independent evaluation concurrently at the beginning of PRIMR, in based on a randomised controlled trial. The part because of concern about whether the evaluation found that students in the group lessons properly covered the material that subjected to the NC programme did gain would appear in the national end-of-year significantly higher test scores than those in examinations. Advocacy was needed to the control group with an effect size of 0.33. change the mind-set of some teachers.” According to Torgerson et al. (2011) this is equivalent to seven additional weeks of Numbers Count, UK learning (resulting from a 12-week intervention). However, the costs involved in One of the main aims of the UK government’s implementing the programme were great. The Every Child Counts initiative of 2007 was to reported cost for each child in the programme develop an early intervention programme for was GBP 1,353 (equivalent to ~USD 2030) and learners in the first two years of schooling who the cost for each week of numeracy learning fail to master the basics of numeracy gained was £193 (~USD 290) per child (ibid, (Torgerson et al., 2011). The programme which p.78). This led the evaluation team to conclude emerged was known as Numbers Count (NC). that “the costs of the delivering the NC was a 12-week programme in which programme… are relatively high compared to children in the target population (i.e. low other Mathematics interventions” and that “the achievers in the bottom 10% of the ability relative cost may preclude it as a realistic range) spent 30 minutes of each day with a option for many schools” (ibid, p.112). trained NC teacher in addition to the normal mathematics lessons of their school’s 9.3 Upper secondary grades and the curriculum. These sessions were given on a secondary/tertiary interface one-to-one basis. Before starting work, NC teachers were given training on the teaching Borovik (2014) argues that modern, methods to be used, on identifying specific technology-based economies lead to an learning difficulties through diagnostic hourglass-shaped demand for mathematics 124 education with the vast majority only needing students of mathematics at the secondary the skills associated with mathematical literacy level but could find none. This reflects the and a smaller group requiring a deep conclusions of the IMU which also suggests understanding of mathematics at a far higher that there are “few or no career development level. The consequences of this are recognised opportunities for these students” (ibid, p.6). and explored in the International Mathematical Humble (2015), based on research carried out Union’s 2014 report on the state of in Tanzania, suggests that teachers are not Mathematics education in Africa (IMU, 2014a). good at identifying gifted pupils because they Much of the report focuses on the challenges use criteria based on, for example, facing mathematics educators in universities. performance in class, performance in However, it also points out that secondary examinations, and even helpful behaviour. They schools play a vital role in preparing students do not look for, or recognise, one of the key for further studies and that across SSA this characteristics of the truly gifted child – part of the education system is not working creativity. Humble concludes that “talented well. It suggests that most countries do not creative children can be found living in the have enough specialist mathematics teachers slums of sub-Saharan Africa. This research qualified at the graduate and post-graduate implies that there is a waste of human capital levels to properly prepare potential university in Africa as typically governments and candidates. It also suggests that the pressure education officials believe that such children, generated by rapid expansion at the primary who are first generation learners with illiterate level and now reaching the secondary level is parents, are not capable of greatness. Also too exacerbating this problem and that, in some few development experts believe that part of cases, the shortage of mathematics teachers the solution to poverty can come from the has been “eliminated artificially by a process of poor themselves. Yet in Dar Es Salaam we ‘inferior substitution’: that is, surplus teachers found ‘Slum Super Stars’ waiting to be (in other subjects) and temporary teachers are discovered, their contribution to economic assigned to teach Mathematics, even though growth of their country wasted as no one they are not qualified to do so” (IMU, 2014a, believes they exist. All they need is a chance p.3). Initiatives related to the training of – opportunity” (Humble, 2015, p.1). teachers are discussed in the section which follows. Notwithstanding the above, there is evidence as to the positive impact of competitive The IMU report also identifies the lack of Olympiads on student attitudes towards systems for identifying and tracking mathematics at the highest levels. mathematically gifted students as a problem. It acknowledges that implementing such Mathematical Olympiads in the Latin America systems would not solve the deep rooted and Caribbean region problems of mathematics education in SSA but it might “make a small but concrete The IMU (2014b) suggests that Mathematical contribution to mathematical development of Olympiads have proved effective in both African countries” (ibid, p.3). In preparing this identifying highly-talented students and study we looked for evidence of significant promoting the status of mathematics as a initiatives designed to find gifted and talented subject. At the highest level, several countries 125 in the Latin American and Caribbean (LAC) initiatives in terms of raising the mathematical region have competed for many years in the achievement of students is available. They are International Mathematical Olympiad (IMO). included in this study to serve as examples of These include: Cuba (since 1971); Colombia what is being tried. (since 1981); Mexico (since 1987); Uruguay (since 1997); and Venezuela (since 1997). The 1+4 Teacher Development Plan for involvement of countries from SSA in IMO has Mathematics, South Africa been more recent but in 2014, nine64 countries from the region took part (IMO, 2015). In response to poor student achievement in Olympians from Mexico and Brazil have been Mathematics, Science and Technology, the particularly successful in recent years with all Department of Basic Education in South Africa six members of their teams winning medals in announced in 2014 that the professional 2015. (Mexico with three bronze, two silver and development of mathematics teachers will a much-coveted gold and Brazil with three follow a ‘1+4 model’ (South Africa, 2015). silver and three bronze.) African teams65 have Under this model, one day is used to prepare not yet reached these levels of success but teachers in delivering the curriculum content increased participation and a growing number to be delivered to senior classes in the of ‘Honourable Mentions’ bode well for remaining four days of the school week. On the future. the training day, the teachers meet in a local school where a designated Lead Teacher The participation of LAC countries in the IMO presents the content and recommended has prompted the formation of a number of teaching strategies for the following four days. regional and national competitions. The The training day is highly structured and pyramidal selection process for these ensures teachers are to be tested to ensure that they that the impact of the competitions is far have mastery of the content. Teachers who reaching. For example, the National fail to demonstrate mastery will be identified Mathematical Olympiad of Brazil involves up to and supported during the week by a 18 million young people (IMU, 2014b). The ‘support team’. message that this sends out is that everyone can ‘do’ mathematics – even if only a few are According to the Minister of Basic Education, brilliant enough to win medals. this radical approach “translates into a whopping 23 days in a year dedicated to 9.4 Teacher training and support intensive training and discussion on mathematics content and methodology” (ibid). The serious weakness of initial teacher training This replaces the previous provision for programmes and in-service support services professional development which amounted to for teachers in general and mathematics approximately 10 days per year. The 1+4 teachers in particular has long been development model, which was trialled in recognised. A number of initiatives have been three66 of South Africa’s nine provinces, has developed to address these challenges – some significant implications for the organisation of of which are described here. It should be school timetables. For example, school noted that little, if any, objectively verifiable management teams have to try to arrange evidence as to the effectiveness of these teaching programmes so that no senior 64. Benin, Burkina Faso, Gambia, Ghana, Nigeria, Uganda, South Africa, Tanzania, and Zimbabwe. 65. To date, South Africa has won 49 medals and the same number of Honourable Mentions from 24 Olympiads. 66. Mpumalanga, North West and Eastern Cape. 126 mathematics classes are scheduled for the approach has the benefit of focusing efforts designated training day – a major constraint on building capacity in a limited number of key for those responsible for drawing up the institutions. It also ensures that teachers who timetable. However, this model exhibits three participate in the one-off training programme of the key characteristics associated with receive full exposure. An extended programme effective in-service training: training sessions involving a series of one- or two-day meetings are frequent and sustained over time; training over a long period would be unlikely to have forms part of a formal CPD programme; and, the same impact and, in a fragile environment, peer-to-peer support is a prominent feature. there would be a significant risk of teacher drop-out. Intensive In-service Training for Teachers, Democratic Republic of the Congo African Institute for Mathematical Sciences School Enrichment Centre, South Africa The 1+4 Development Plan for Mathematics described above is ambitious, demanding and “The African Institute for Mathematical expensive. It has required, inter alia, the radical Sciences School Enrichment Center restructuring of school timetables, the training (AIMSSEC) has been operating in South Africa of Lead Teachers, and the coordination of since 2004. AIMSSEC is a schools regular and frequent teacher development Mathematics enrichment programme offering meetings across the country. The scheme is free learning resources for learners of all ages also associated with significant direct and from 5 to 18+ years together with professional indirect costs. This sophisticated approach development courses for teachers. AIMSSEC may be sustainable in a resilient country like operates a variety of educational programmes South Africa, but it would be far harder to for teachers, including: replicate and maintain in a fragile state like DRC. In DRC, alternative approaches are being • Advanced Certificate in Education (ACE) implemented with the support of international course - an innovative two-year professional donors and development banks. A major development programme involving both initiative is the on-going Quality and Relevance residential and distance learning of Secondary and Tertiary Education Project, components. The programme uses the supported by a grant and credit from the internet, interactive TV and cell phone International Development Association. This technologies to link teachers in rural areas has as one of its aims “to improve the teaching of South Africa. and learning of mathematics and science in general secondary education” (World Bank, • Mathematical Thinking, Problem Solving and 2015, p.8). One component of the project will Technology in teaching and learning provide an intensive, six-week training Mathematics - a 10-day residential programme for secondary school teachers of programme followed by a 3-month distance mathematics and science. The programme, learning programme” (AIMS, n.d.) with newly developed content and materials, will be delivered in and by the Higher Teacher Training Institutes (Institut Supérieur Pédagogique) during the summer recess. This 127 Teacher Education in Sub-Saharan Africa OER which can be used as they are or (TESSA) initiative modified to meet specific needs and/or country-specific contexts. Ministries of The Open University, UK working in close education, Higher Education Institutions, and collaboration with international partners and TTIs can, if they wish, join the TESSA network supported by funding from philanthropic for support or they can simply ‘plunder’ the organisations67 hosts The Teacher Education in available resources to build or enhance their Sub-Saharan Africa (TESSA) initiative. TESSA own teacher training modules. For example, operates through a network of teacher the Mauritius Institute of Education has used educators and teachers working to improve OER as the basis of a ‘Creative Pedagogy’ the quality of classroom practice across SSA. module and the Ministry of Education in Togo Its focus is on supporting school-based has adapted TESSA’s freely available materials teacher education through providing to meet local needs. Further examples of the unrestricted access, through the internet, to a use of TESSA OER are given in Wolfenden et large bank of Open Educational Resources al. (2010). It is reported that the use of TESSA (OER) including: general teaching resources; materials results in “a much more diverse set subject-specific resources including teaching of teaching practices” and “increased teacher packs; audio clips; and, handbooks for preparation” (ibid, p.4). No formal evaluation teachers and teacher educators. The materials, of the impact on student achievement has, as prepared and/or adapted by African authors, yet, been conducted. are designed to enhance the training of teachers both pre-service and in-service. They UNESCO/Nokia Teacher Support through are currently available in four languages - Mobile Technology, Senegal English, French, Kiswahili (Tanzania) and Arabic (Sudan)68. Some ‘pan-Africa’ materials UNESCO and Nokia have implemented are widely applicable whilst others have been initiatives to build the capacity of primary modified to match local curricula and contexts. teachers in Mexico, Nigeria, Pakistan, and The latter are available through country- Senegal through the use of mobile specific pages of the TESSA website. technologies. In Senegal, the initiative (launched in 2012) focuses on student learning Where possible the OER promote active in Mathematics and Science. In particular, the learning and constructivist approaches to Nokia Mobile Mathematics application teaching mathematical concepts. Wolfenden (MoMath) has been adapted to match the et al. (2010) report that within two years of national curriculum. This allows students “to their completion at least some TESSA OER master mathematical concepts in a dynamic had been formally incorporated into 19 teacher digital environment that can be accessed from education programmes from the certificate any internet-enabled mobile phone” (UNESCO, level to B.Ed. level across nine partner 2013). Students can therefore practise countries. They also report that the initiative problems at home or at school at any time. has a very high degree of visibility amongst The system also stores information about the teacher educators and, increasingly, teachers. progress of students on remote servers One of the key strengths of the TESSA making this immediately available to teachers. approach is the flexibility offered by using UNESCO and Nokia worked with local partners 67. To date, TESSA has been largely funded by the Allan and Nesta Ferguson Charitable Trust, and the William and Flora Hewlett Foundation. 68. Materials are available at: http://www.tessafrica.net/. 128 RESAFAD (Réseau Africain de Formation à technology to reach greater audiences; some Distance - Sénégal) and CRFPE (Centre take advantage of the speed of technology to Régionale de Formation de Personnels de make learning and teaching faster, easier, and l’Education de Dakar) to train 100 teachers more efficient; and others connect students, from 50 schools “on using the application to teachers, and educators to those not only in gain deeper insights into the learning needs of their communities but also around the world their students and constructively respond to so they have access to more materials and these needs” (ibid). resources than ever before” (CEI, 2015a). Nowhere is the search for technological A pilot exercise yielded anecdotal evidence solutions more extensive or urgent than in that training in the use of mobile technologies SSA. Of the 130 educational technology made teachers feel that their content projects recorded on the Centre for Education knowledge had improved as a result. However, Innovations (CEI) database, more than half this finding was not tested empirically target students in SSA (ibid). Whilst national (Atchoarena, 2014). In addition, no evidence as governments are key partners in many of these to the impact of the intervention on student initiatives most are funded and/or achievement in mathematics was gathered implemented by NGOs often in collaboration because “the project didn’t target students with commercial, i.e. for-profit, organisations. directly and its duration was too short for teachers to use the improved knowledge for Some technology-based initiatives claim their students” (ibid, p.23). impressive results but caution is required when interpreting these. First, the large gains 9.5 Using technology to enhance student observed in the short-term may not persist. learning in mathematics For example, Banerjee et al. (2007) report that in India a computer-assisted mathematics There is enormous and growing interest in the learning programme increased student test use of technologies to address the serious scores by 0.47 standard deviations. However, learning deficiencies observed in low- and after one year they found that whilst gains middle-income countries (LMIC). The general remained significant for targeted children, situation is well described by the following. “they (had) faded to about 0.10 standard “Educational technology programs around the deviation” (ibid, p.1). Secondly, the large gains world — and especially in low- and middle- detected in small scale pilots may not be income countries — are taking advantage of duplicated at scale. For example, the rapid increases in internet and mobile resistance of teachers to adopt new practices connectivity to bolster students’ access to and may be overcome in small groups where quality of education. As of 2014, more than sufficient support is available but this may not 30% of households in LMIC had internet be possible when all teachers – including those access, compared to less than 10% in 2005. with little experience of using new Moreover, in 2014, there were about 90 mobile technologies - have to be persuaded to phone subscriptions for every 100 inhabitants engage with the programme and to be trained. in the developing world, as opposed to 23 just 10 years prior. Many educational technology programs utilise this growing prevalence of A few examples of initiatives designed to raise the mathematical achievement of learners are 129 described below. ‘Digital School in a Box’, Uganda ‘Academy in a Box’, Kenya “UNICEF is setting up 60 ‘Digital Schools in a Box’ to reach the most marginalised groups (in Bridge International Academies, an Uganda). These digital schools, serving 100 to international education innovation for-profit 200 children each, are set up in schools and company, targets its services at poor health centres in rural communities where communities most noticeably in Kenya and children spend most of their time so that they Uganda. It supports a chain of private, low- have access to quality educational content cost nursery and primary schools where it tries 24/7 and are more prone to learning in a to maximise efficiency and effectiveness collaborative manner. Each digital school is through the use of modern technologies. built around a solar-powered laptop with One initiative is its ‘Academy in a Box’ model, Internet connectivity, a projector, a speaker the essential elements of which are and a document camera” (UNICEF, 2013). The described below. impact of this initiative is, as yet, unclear. “The curriculum itself is standardised and Text2Teach, Philippines and Elimu kwa transformed into scripted lesson plans, which Teknolojia, Kenya69 include step-by-step instructions detailing what teachers should do and say during any The Text2Teach programme emanates from given moment of a class. Teacher scripts are the BridgeIT Project initiated by commercial delivered through data-enabled tablets, partners Nokia and Pearson. It was first piloted synced to headquarters, enabling Bridge to in the Philippines in 2003 and has since been monitor lesson pacing, record attendance, modified and expanded. The programme track assessment scores, and update or add allows teachers to download web-based TLM to their mobile phones using the Microsoft lesson scripts in real time. … Teachers come Education Delivery (MED) platform70. These from the local communities and receive generally take the form of short instructional thorough training in delivering the Bridge videos and teacher guides on mathematics, curriculum. In this way, Bridge seeks to science, and English Language for Grade 5 and contribute to the local community by driving Grade 6 students. Additional materials on job creation. Bridge’s curriculum is based on ‘Values’ are currently being added (Text2Teach, government standards, with a greater n.d.). Text2Teach videos can be used with the emphasis on basic literacy, numeracy, and whole class by connecting the mobile phone critical thinking skills in the early grades” (CEI, to a projector television. By 2014, Text2Teach 2015b). Whilst an evaluation of student had reached 1,433 schools in the Philippines achievement in Bridge schools is available and had trained more than 7,000 teachers in (Bridge, 2013), the impact of the ‘Academy in a the use of the technology. An external Box’ element is not estimated separately. evaluation of the impact of Text2Teach on student achievement found that it “leads to significantly higher learning gains in English, Maths and Science at both grade levels. The gains are very impressive for English and Science but less so in Maths although still highly significant” (Natividad, 2007). From 2015, the Department of Education will lead 69. Both Text2Teach and Elimu kwa Teknolojia emanate from the BridgeIT project from Nokia and Pearson. BridgeIT also operates in Bangladesh, Chile, Colombia, Haiti, India, Indonesia, Vietnam, and in SSA, Nigeria and South Africa. 70. Formerly the Nokia Education Delivery platform. 130 the rollout of the Text2Teach programme to all based on the national primary curriculum and 22,000 of the nation’s public elementary presented in the official language, Chichewa. schools (Text2Teach, n.d.). Its main commercial Teachers were trained in the use of the partners in this will be Microsoft, the Pearson hardware and software72. Children used the Foundation and the mobile network provider tablets on an individual basis. This meant that Globe Telecom (ibid). groups of up to 25 children were taken from their normal, large classes to work in a Since its introduction to the Philippines in dedicated room or ‘learning centre’. Each child 2003, the BridgeIT programme has been was given the opportunity to work with a introduced in a number of many low-income tablet for 30 minutes per day. The software countries including Tanzania where it is known presented the child with a well-defined as Elimu kwa Teknolojia (Education through mathematical concept. They were then given a Technology). The subjects covered include chance to show what they had learnt through Mathematics, Science and Life Skills. Where a non-threatening ‘test’. If the child was existing content was appropriate it was successful on all of the test items she/he was translated into Kiswahili. Additional content rewarded with an on-screen ‘certificate’. If any was generated to match the national items were answered incorrectly the child got curriculum. An evaluation of the programme’s a chance to try the test again. The software impact on student test scores in mathematics did not allow children to move onto the next found that those in classes where the technology had been used had made topic until they had demonstrated complete significantly more progress than their peers in mastery (Pitchford, 2015). An evaluation of the the control group (Enge, 2011). The reported Malawi pilot found that groups using the differences in mathematics scores for the two mathematics application significantly groups were relatively modest but outperformed those from normal classes (i.e. nevertheless significant with score without tablets) and a group that used tablets improvements ranging from about 8 to 17 but without the specific software (Pitchford, percentage points for the two age cohorts 2014). Effect sizes varied according to the (ibid). Similar gains were also detected when school grade and the skill being tested. All the programme was evaluated in Kenya grades showed a positive impact but this was (Bridge, 2013). bigger for students in Grades 2 and 3 than for those in the first grade. Using measures for the Descriptions of other mobile-based knowledge of the primary school curriculum, applications designed to support learning in effect sizes for students in Grade 3 ranged Mathematics, including MoMaths, Dr Maths and from 0.8 to 1.7 (ibid, p.25). According to Maths4Mobile71, can be found in Strigel and Pitchford, this is equivalent to a gain of three Pouezevara (2012). months of learning from a one-week intervention (BBC, 2014). Tablet-based mathematics learning, Malawi In a follow-up study, the same mathematics Selected schools in Malawi piloted a tablet- app (translated into English) was trialled with based mathematics learning scheme targeted a group of young learners in the UK. The at young learners with little or no previous results were very similar to those seen in the experience in the subject. The content was Malawi pilot - using the tablet-based app for 71. MoMaths was produced by Nokia in partnership with, amongst others, the Meraka Institute and the Department of Basic Education, South Africa. Math4Mobile is an app developed within the University of Haifa, Israel. Dr Maths is an online ‘question and answer’ service for mathematics learners organised by the Drexel University School of Education, USA. 72. The pilot used commercial software called Masumu developed by EuroTalk. The application is now available through the not-for-profit organisation ‘one billion’ (https://onebillion.org/about). 131 30 minutes a day for six weeks led to a The software is adaptive in that as a student learning gain of between 12 and 18 months progresses through a module, the system uses (BBC, 2014). the answers to diagnostic tests to identify strengths and weaknesses and, hence, to Khan Academy Online Learning, Sri Lanka deliver a programme tailored to the student’s specific needs. Student progress is tracked in Khan Academy is a non-profit organisation the software and the teacher has access to a based in the USA and created in 2006 with a number of tools designed to make whole-class mission “to provide a free, world-class and personalised teaching more efficient education for anyone, anywhere” (Khan (MPDA, n.d.). The ADB’s Testing e-learning as Academy, n.d.). It provides instructional videos Learning Project funded the customisation of through its website and YouTube channels, MathCloud materials to match the national practice exercises and, for registered users, a curriculum for mathematics, including dashboard to monitor progress. Materials translation to Sinhala. In the pilot phase, cover a range of subjects – including students in selected schools used MathCloud mathematics – and are freely available with for two hours per week (out of five hours open access to individual learners, parents, mathematics tuition in total) for a year. An and teachers. Originally, materials were only evaluation of the impact of the intervention provided in English. In 2013, the Asian reported that the treatment group made Development Bank (ADB) supported the Khan statistically significant gains when compared Academy Localisation Project in Sri Lanka with the control group (Chin, 2012). The effect (Pereira, n.d.). This funded the mapping of all size, estimated from the evaluation data, is Khan Academy materials to the local approximately 0.25. Whilst this may be curriculum for mathematics for Grades 3-13. considered to be ‘small’, it is comparable to Suitable videos were dubbed in Sinhala and reported effect sizes for other CAI gaps were filled with the production of interventions (Fletcher-Flinn and Gravatt, 1995, additional videos. Additional tools were put in and Cheung and Slavin, 2011). place to help teachers integrate the materials into their work. For schools with little or no 9.6 Promoting STEM through collaboration internet access, the resource is to be made with business and industry available in an offline, CD-based version (ibid). The evaluation of the first phase of The challenge of attracting more and better implementation was, at the time of writing, students74 into the areas of mathematics and underway. One of the key features of this other STEM subjects is one faced not only by approach to e-learning is that the instructional the poorer countries of SSA and beyond, but and practice materials are not the preserve of also some of the world’s most highly teachers – students can learn independently developed economies. In any country, the state out of school. education system is by far the most important and influential player but, in general, it cannot MathCloud e-learning, Sri Lanka on its own meet the needs of the highly specialised and fast-changing world of STEM- MathCloud is an e-learning platform developed based commercial sector. In particular, the by the for-profit company MPDA73 in Korea. private sector is uniquely placed to provide: 73. My Personal Data Analysis (MPDA) is the parent company responsible for MathCloud. MPDA Angels is a not-for-profit subsidiary which partners the Sri Lankan Ministry of Education and the Asian Development Bank in the implementation of the Testing e-learning as Learning Project. 74. Attracting students on to advanced study programmes in STEM subjects and into STEM-based careers is an almost universal challenge. However, this problem is particularly acute when it comes to attracting girls. In recognition of this, many countries have public initiative and/or public-private partnerships specifically targeted at encouraging young women into the STEM sector. 132 additional finance to support schools and policies and programs” (Change the Equation, universities in the teaching of STEM subjects; 2016a, p.1.) It does this by identifying sponsored places for students in institutions of educational policies and practices which have further and higher education; opportunities for been shown to be effective in producing students to gain exposure to modern STEM STEM-literate students and then advocating environments; and technical expertise in the their adoption by schools, communities and development of authentic teaching aids for states. In addition, member companies invest modern technologies. In return for investment, in a wide range of programmes. These include the private sector benefits from an increased events designed to engage young learners flow of applicants who are better prepared in (e.g. National Science Olympiads, state science Mathematics and other STEM subjects. For fairs, inter-school robotics championships, example, The Mastercard Foundation etc.) and activities to support teachers announced in 2015 that it was committing USD through the provision of materials and ideas. In 25 million to supporting the work of the some cases, for example the Denver Public African Institute for Mathematical Sciences Schools CareerConnect program, students are (MasterCard Foundation, 2015). The given the opportunity to experience what it is investment is to “enable 500 academically like to work in a STEM environment (Change talented students from economically the Equation, 2016b). It is estimated that the disadvantaged communities to pursue their member companies of the consortium invest Masters level education in science, technology, around USD 750 million per year in STEM engineering and mathematics. It will also initiatives. Further details of the organisation’s support the creation of a teacher training work and the resources it offers to educational program which will improve the quality of policy makers, businesses, schools and secondary-level math and science teaching in teachers can be found at http:// Cameroon” (ibid, p.1). changetheequation.org/resources. ‘Change the Equation’ is a particularly 9.7 Summary interesting example, from the USA, of the way in which industry and commerce can be Throughout SSA, a large number of diverse engaged to support state initiatives in the field and innovative interventions are being tried to of STEM education. ‘Change the Equation’ is tackle the systemic problems that contribute an organisation formed in response to to low levels of student achievement in President Obama’s Educate to Innovate mathematics. Many focus on supporting initiative (United States, 2009). Its members in-service teachers by providing them with are Chief Executive Officers (CEOs) of forty better training and access to more and better major, multi-national and US-based companies teaching and learning materials through the including BP, DuPont, IBM, Intel, Microsoft, use of modern technologies. Some effect Rolls Royce, Time Warner Cable and Xerox76. optimism but, as yet, little objectively The consortium’s mission is to “work at the verifiable evidence is available as to the intersection of business and education to returns on investment offered by the ensure that all students are STEM literate by various programmes. collaborating with schools, communities, and states to adopt and implement excellent STEM For a full list see: http://changetheequation.org/our-members. 133 Developing and delivering technological solutions for implementation at scale is both technically demanding and expensive. As a result, few such initiatives are solely owned or controlled by national governments. Many rely on external sources of funding from international NGOs and/or philanthropic groups. Governments may also need to form partnerships with for-profit companies including, for example, software developers and the providers of internet services and mobile networks. Such arrangements may in the longer-term raise questions as to intellectual property rights and have implications for sustainability. The sustainability of technological solutions is of concern especially in the resource-poor and often insecure context of SSA’s schools. The problem is generally less serious in e-learning programmes where teachers and/or learners access materials through their own digital devices and in m-learning programmes where TLM’s are delivered through a mobile phone (e.g. Elimu kwa Teknolojia). However, sustainability is of major concern in programmes which require schools to be equipped with highly specialised and/or expensive equipment (e.g. Digital School in a Box and Tablet-based Learning). In this case, many fundamental questions have to be asked including: Who within the school is to be responsible for the safe keeping of the equipment? How will the hardware be maintained and what happens if something goes wrong with the software? How will obsolete equipment be replaced and who will pay? The long-term sustainability of programmes designed to enhance learning in SSA through the use of educational technologies is an area worthy of further research. 134 135 136 Mathematics Education in Sub-Saharan Africa: 10 Findings and recommendations 10.1 Summary of findings access to high quality schooling for all would inevitably raise achievement levels in There is a consensus that investment in mathematics along with those in all other education yields significant returns for subjects. The umbrella term ‘quality of individuals, communities, and nations. Returns schooling’ covers many factors: adequate are maximised when the education system financial resources; good physical structures; promotes the acquisition of critical cognitive access to utilities and services (e.g., potable skills - linguistic literacy, numeracy, and water, electricity, and internet services); problem solving skills. Of these, research availability of TLMs and educational suggests that, in an increasingly technological technologies; effective school managers; and, world, mathematical literacy is the most above all else, well trained and highly important. Unfortunately, a large body of motivated teachers. Financial investment in evidence supports the view that mathematics schools serving poor and disadvantaged education in SSA is in a precarious state. communities is of particular importance as The learning deficit between countries in the highlighted by Spaull (2011) who shows that region and international norms is so large that, the socio-economic status (SES) of the school without extensive and sustained interventions is a significantly more important factor in across all phases of education, the gap may determining outcomes than the SES of never be narrowed let alone closed. the student. The factors that contribute to low levels of Notwithstanding the above, mathematics student achievement in mathematics in SSA education in SSA requires special attention for are numerous, varied, and interconnected in three reasons. First, it is a priority because the complex ways. There is no panacea; there is no economic well-being of a nation depends on magic bullet. Any solution will require the capacity of its education system to simultaneous actions on many fronts. produce workers and consumers who are Mounting a comprehensive and coherent mathematically literate. Secondly, the learning campaign to raise the quality of mathematical deficit in mathematics for most countries in education will require careful strategic the region is huge and shows no sign of planning and significant investment. Even with diminishing. Thirdly, widely-held negative a suitable plan in place it will be difficult to attitudes towards mathematics and an overcome the inertia associated with large acceptance of failure increase resistance to education systems, so governments and other change and hamper progress. stakeholders should be prepared to sustain their efforts over the long term. There are no Whilst the need to address poor outcomes in quick fixes. mathematics is urgent, many of the most important interventions will only be effective Mathematics education is not an island in the in the longer-term. However, there are areas ocean: it is inextricably linked to the quality of where interventions could be implemented in schooling experienced by learners. Providing the short- to medium-term. Some of these 137 require little investment and whilst they may increased per student expenditure is not on their own make a significant impact, associated with better mathematical they would send an important message at the outcomes. Therefore, additional funding, over start of what is likely to be a protracted and above that for general education, should campaign. Suggested interventions are be allocated to interventions specifically presented below. It should be noted that the targeted at improving mathematical outcomes order in which they appear is not intended to at the primary, secondary and tertiary levels as suggest a hierarchy of priorities. All will need a matter of priority. to be included in any comprehensive action plan. This shift in priorities should be reflected in the policies and actions of the many international 10.2 Suggested interventions banks, donor agencies, NGOs and philanthropic organisations that play a vital Raising the status of education in role in supporting governments in the mathematics to that of a national priority implementation of educational reforms. For example, those preparing any programme and/ This study has shown that raising or project to be supported by an international mathematical achievement from the current development bank should be required to low levels found throughout SSA is now a describe if/how proposed actions will address critically important issue. This should be the acute issue of promoting increased recognised by governments in their strategic engagement with, and achievement in, plans where improving standards in STEM subjects77. mathematics should be explicitly classified as a national priority. The difficulty in achieving Changing attitudes towards mathematics ambitious strategic objectives related to the numbers pursuing and succeeding in It has been suggested that one of the key mathematics and other STEM-related courses factors contributing to the success of the should not be underestimated. For example, in countries of East Asia which consistently top 1970 the Government of Malaysia implemented the TIMSS and PISA rank orders for a ’60:40 Policy’ aimed at having 60% of mathematics is the prevailing ‘culture’. This students at the upper secondary level enrolled manifests itself in three ways which are in a STEM stream (with 40% in the Arts and relevant here. First, education is highly prized Humanities stream). Four decades later, this and teaching is a respected profession. target has not been reached – currently 42% Secondly, hard work is recognised as the are in the STEM stream – but significant means by which educational success is progress from a low baseline has been made achieved. Thirdly, mathematics is no exception and the explicit policy objective continues to to the rule; as in any other subject success in guide the actions of the Ministry of Education76 mathematics can be achieved with hard work and to serve as a signpost as to the desired and does not depend upon a special ‘natural direction of travel (MOE, Malaysia, 2016). ability’. Therefore, as a first step in tackling underachievement in mathematics in SSA, Budgets for education in SSA tend to be governments and their ministries of education severely constrained but the evidence is that should implement a public relations campaign 76. Under the 60:40 policy students who achieve the highest grades in mathematics and science in the examinations administered at the end of the lower secondary phase are automatically placed in the STEM stream unless they or their parents object. One consequence of this is that a disproportion number of girls are placed in the STEM stream because they outperform boys in both mathematics and science in the lower secondary phase. In addition, a study conducted in 2015 found that the arrangement had “raised the girls’ self esteem and confidence (MOE, Malaysis, 2016, p.19). 77. This requirement to reflect on a programme’s likely impact on a critical issue is akin to the World Bank’s approach to the vitally important issues of, for example, gender equality and HIV-AIDS. 138 incorporating three key messages: (a) It pays Improving initial teacher training to invest in the mathematical education of your children because, amongst other benefits, Improving the quality of teaching is the most success in mathematics is linked to greater important challenge facing those attempting economic returns; (b) Everyone can be to improve the outcomes of mathematical successful in mathematics - you don’t need to education. Whilst some advantage can be be born with a special ability; (c) Hard work achieved through training teachers who are will bring better results in mathematics. already in service, it is vital that new entrants to the profession are properly prepared Other countries are already trying to change through the pre-service courses offered by attitudes towards the subject in this way. In teacher training institutions. Unfortunately, in 2015, the UK Education Secretary said in an many countries of SSA such colleges have not interview, “there is no such thing as having a risen to the challenge and perpetuate an ‘Maths brain’. With the right support we can all unacceptable status quo by preparing get better at Maths. For too long, being bad graduates who, as evidenced by the poor with numbers has been something to brag outcomes of their students, are not effective about” (McTague, 2015). Similarly, the Minister teachers of mathematics. TTIs which currently of Education in Jamaica in launching a serve as a block against progress must be campaign to tackle low standards in transformed so that they fulfil their potential mathematics has warned teachers that and become a significant part of the solution. “phrases such as “Mathematics is hard” or “Mathematics is boring” should not be Currently, the general impression is that the encouraged around students” (Linton, 2014). curricula and instructional practices of TTIs are primarily designed to produce teachers who When addressing attitudes towards know how to do the mathematics required by mathematics, special attention should be paid school curricula and, hence, can demonstrate to changing the view that this (along with the to their students the right way (sic) to solve natural sciences) is predominantly a subject mathematical problems. This is at odds with for boys. Schools, institutions of further and current thinking about the skills and deep higher education, and potential employers knowledge required by good mathematics should reinforce the message that careers in teachers. In addition, it does not reflect the STEM-related fields offer valuable constructivist/child-centred approaches to opportunities to all regardless of gender. teaching mathematics incorporated in many of Highlighting good female role models, using the revised school curricula of SSA. Generating gender-appropriate learning materials, and a new vision of the type of graduate that TTIs adopting interactive teaching methods will should produce is essential, but there is likely improve the confidence (i.e. self-efficacy) of to be much resistance to change. Four key girls and, hence, their achievement. The areas in need of reform are: revising curricula countries of SSA cannot afford to continue to of TTIs; revising the way in which curricula are ignore the valuable human capital represented delivered; making better use of new by girls and young women. educational technologies; and, crucially, changing the profile of TTI tutors – especially 139 those who are preparing teachers for the clear that the current management and tutors primary phase of education. of TTIs are in a position to deliver a radically different approach to preparing new teachers. A number of observers have commented that A key deficiency is that TTI tutors receive little much of the pre-service curriculum is currently or no training in how to teach primary and dedicated to teaching trainees how to do the secondary level teachers. An additional mathematics that they should have learned in concern is the lack of tutors who have school, i.e. strengthening their subject content experience of teaching in primary grades. It is knowledge. Instruction as to how to teach difficult to see how a teacher trainer who does mathematics to young learners (e.g. through not have first-hand experience of how young the effective use of alternative methods, TLM, learners think about mathematics can advise and formative assessment) often receives less trainees on effective teaching strategies. attention. This means that trained teachers Correcting this will be neither easy nor quick. lack the knowledge and skills necessary “to First, the rights of teacher trainers currently in build bridges between the meaning of the post will need to be respected. Secondly, there subject content and the construction students is no obvious supply of potential tutors who make of that meaning” (Moreno, 2005, p.12). are both well qualified and have experience of Akyeampong et al. (2011) suggest that what is primary school teaching. lacking in initial teacher training is a comprehensive treatment of theory so that It should be possible to retrain selected TTI trainees can make sense of practice. The tutors through a suitable professional importance of stressing the complementary development programme - including a nature of theory and practice in training practicum. If necessary, financial incentives mathematics teachers is further explored in could be offered to those who successfully Ogwel (n.d.). complete a certified course in, for example, ‘the teaching of mathematics in primary In terms of mathematical content, trainees schools’. Appointing new teacher trainers from should be helped to develop a far deeper the primary sector is likely to require the understanding of the mathematical concepts formal recognition of a new career path and they will teach even though this may mean the amendment of the selection criteria sacrificing the breadth of the content currently applied by TTIs. One strategy would somewhat. At the same time, trainees must be be to identify outstanding primary school provided with a range of strategies for helping teachers and/or school principals and to learners who when presented with a encourage them to join TTIs in order to better mathematical problem may choose to tackle it prepare the next generation of teachers78. in different ways because they conceptualise it differently. In short, the curricula of TTIs and Whilst the structural changes advocated above the way in which they are delivered should may only be effective in the medium- to reflect best practice in the classroom. longer-term, there is an immediate opportunity to strengthen teacher training through the use Revising curricula and teaching programmes of educational technologies. Unfortunately, for TTIs does not require great investment and many TTIs do not seem well-placed to take could begin immediately. However, it is not advantage of this in that they are under 78. In some countries, e.g. Ghana, there are plans to give good primary and secondary school teachers incentives to stay in their classroom rather than seeking promotion to non-teaching administrative roles. 140 resourced (in terms of hardware and software) clips of model lessons and to download and have not yet developed sufficient materials for their own education and for use technical capacity. As ministries of education in their practicum. increasingly explore the opportunities offered by technology in partnership with NGOs and Supporting practising teachers commercial partners, there is a danger that TTIs will fall further behind and will not be able Whilst the reform of initial teacher training is to prepare their trainees to make best use of of paramount importance the needs of the e-learning and m-learning (mobile learning) majority of teachers who are currently in tools. Fortunately, examples of good practice service must not be neglected. Research from are emerging in SSA. For example, in some both SSA and beyond shows that in-service countries TTIs are already incorporating open training can be effective if it has the right educational resources freely available from, for characteristics. Walter and Briggs (2012) example, the TESSA initiative in their taught suggest that “The professional development programmes. Harnessing the potential benefits that makes the most difference to teachers: (1) of e-based TLM and helping trainees to is concrete and classroom-based; (2) brings in appreciate that they can use such technologies expertise from outside the school; (3) involves in their own work should be a priority for teachers in the choice of areas to develop and all TTIs. activities to undertake; (4) enables teachers to work collaboratively with peers; (5) provides The natural inertia of large organisations such opportunities for mentoring and coaching; (6) as TTIs may make it difficult to achieve is sustained over time; and (7) is supported by significant progress over a short period. In effective school leadership” (Walter and particular, it may be some time before reforms Briggs, 2012, p1.). In mathematics education, of formal study programmes yield positive peer support and collaboration between results. Individual trainees, however, can teachers appears to be of particular respond far more quickly if they are importance. Evidence suggests that high levels encouraged to take greater responsibility for of achievement in China are due, at least in their own professional development. Therefore, part, to the fact that teachers of mathematics TTIs should be advocating and facilitating collaborate routinely – something which does self-development as an adjunct to their taught not seem to be the norm in, for example, North courses. Most importantly, trainees should be America and Europe (Cai, Lin, & Fan, 2004). It exposed to current ideas about teaching is interesting to note that the 1+4 teacher mathematics effectively by being given free development plan for South Africa discussed access to a wide range of materials and in the previous chapter provides, within its resources. These should include both design, the opportunity for teachers to meet traditional TLM79 including textbooks, teachers’ regularly in order to discuss teaching and guides, exemplar worksheets, etc and e-based learning strategies. It will be interesting to see learning materials for both teachers and whether this initiative translates into students. Free (i.e. unfettered and free of significantly better teaching and learning. charge) internet access is the key to this since it allows trainees to see, for example, video 79. Akyeampong et al (2011) report that “Another factor contributing to the misalignment of school and college curricula is that neither college tutors nor trainees are likely have access to the materials, such as teacher guides and textbooks used in schools. Access to the primary curriculum documents and guides was also not always guaranteed” (Akyeampong et al, 2011, p.18). 141 Providing more and better mathematics Notwithstanding the above, research shows textbooks that simply supplying more textbooks will not, on its own, raise mathematical achievement In countries where, especially in the primary significantly. The textbook has to be the right phase, the student:textbook ratio for textbook and determining whether this is the mathematics is greater than 2:1, there is case or not requires systematic evaluation. probably benefit in investing in the provision Currently the pre-publication evaluation of of more books (Fehrler, Michaelowa and new textbooks tends to focus on alignment Wechtler, 2007). Fredriksen and Brar (2015) with the content of the curriculum, suggest strategies for meeting the demand for attractiveness to learners, physical quality and, textbooks in SSA. of course, cost of production. However, there is little evidence that new textbooks in SSA are Whilst there is currently a great need for systematically evaluated as to their physical textbooks in many countries of SSA, effectiveness as aids to learning i.e. that they the internet offers a parallel route for allowing are closely aligned with instructional teachers, students and parents free access to objectives. A description of a model used in the books. For example, The National Council the USA to evaluate textbooks in mathematics for Educational Research and Training and science is given by Kulm, Roseman, and (NCERT) in India commissions physical Treistman (1999). This involved training a cadre textbooks for use in schools on a commercial of reviewers (school teachers and university basis. However, it also makes e-versions freely mathematics specialists) in the application of a available to individuals provided that these are structured evaluation procedure. The first step not offered for resale. The books, and in the process was to identify from the national supplementary learning materials, are available standards the specific learning goal or goals to through an e-portal80. They are available in be analysed. Then the relevant section in the formats suitable for download to mobile textbook was analysed to ascertain the degree devices and PCs. There is, as yet, little data on of alignment between the textbook’s content the use of these resources but the principle of and the selected learning goal(s). Then, and allowing free access to TLMs produced with most importantly, the material was analysed the support of the state is sound. The potential for alignment between the book’s mode of advantages of such a system in the countries instruction and the selected learning goal(s). of SSA context are significant. For example, Evaluators were required “to estimate how well tutors in TTIs and their trainees would have each activity addresses the targeted learning access to the curricula and textbooks being goal from the perspective of what is known used in schools; serving teachers would have about student learning and effective teaching” free access to textbooks in multiple (Kulm, Roseman, and Treistman, 1999, p1.). 81 languages when preparing their lessons; and students fortunate enough to have access to Systematically investigating the effectiveness the internet would have free access to of a textbook before publication may add to textbooks and other materials for self-tuition. the initial costs of production, but this may be a small price to pay for greater returns in terms of educational outcomes. 80. Materials are available at: http://epathshala.nic.in/e-pathshala-4/. 81. For example, the Indian NCERT website gives teachers free access to Hindi, Urdu and English versions of the textbook for Grade 3 Mathematics – extremely useful, for example, for teachers presenting lessons in English rather than their Mother Tongue. 142 Supporting mathematics teachers through The informal, decentralised, and uncontrolled technology approach advocated here may not sit well with more conservative policy makers. However, it As described in Chapter 9, many initiatives reflects the reality of a digital universe where have been launched in recent years to try to teaching communities are not limited by turn the potential of digital technologies into national borders and where the best teaching/ improved teaching and learning. It is not yet learning materials emerge through a process clear which, if any, of these should be taken to akin to natural selection: the best survive and scale in any particular country. It is also are used by teachers whilst the worst simply unclear which will be sustainable in the long fade from view. run. However, it is clear that technological tools are emerging that individual teachers Harnessing the power of assessment: regional can, with support, use to enhance their and national assessments teaching of mathematics. Typically these teaching tools and materials are not being Participating in international large-scale created by government agencies: they are assessments may bring benefits but for being generated by not-for-profit countries in SSA where it is known that organisations, academic institutions, and achievement in mathematics currently lies far, commercial entities. Commercial and far below international norms it is not clear professional competition tends to ensure that that the potential benefits outweigh the costs. they are, in general, of high quality. Given the In the longer-term, new initiatives such as PISA fact that the available pool of resources is for Development may make the proposition constantly growing and changing, perhaps the more attractive. In the shorter-term, best short-term strategy is not to be too alternatives include the development of directive and simply to facilitate teachers’ national assessments and participation in access to ideas, models, materials and tools. regional assessments. The advantage of For example, ministries of education may wish joining an existing regional assessment is that to guide teachers towards particular resources individual countries do not have to develop through, for example, a national education capacity in the highly technical fields portal. In addition, online communities of associated with such assessments – especially mathematics teachers should be encouraged the capacity to apply IRT to student in order to facilitate the sharing of resources responses. Over recent years, the two regional that have been found, by teachers, to work in assessments currently available – SACMEQ and the classroom. A good example of this is the PASEC – have become increasingly resource-sharing website hosted by the Times sophisticated and potentially more powerful. Educational Supplement82 in the UK. Teachers Collaboration between SACMEQ and PASEC from all phases of education and in all subjects should be strengthened through formal upload resources they have made and used. agreements to work towards common These can be accessed and used, many operational standards, and the use of a without charge, by teachers from anywhere in common reporting scale. At the same time, the world. more countries should be encouraged to join the consortia. Co-operation and expansion would move SSA towards a pan-African 82. The Times Educational Supplement is a newspaper/magazine specifically aimed at schools and teachers. Its resources for teachers are available at: https://www.tes.com/teaching-resources/ [Accessed 5 February 2016]. As at February 2016, there were 35,000 Mathematics TLMs available, suitable for learners from 3-11 years old. 143 comparative assessment programme capable should instruct national examination boards of measuring student achievement and, of and other assessment agencies to put in place, paramount importance, monitoring trends without delay, comprehensive feedback over time. systems to supply teachers and other practitioners with both qualitative and Notwithstanding the above, a significant quantitative information as to student number of countries in SSA have attempted to performance in mathematics (and all other conduct national assessment programmes, and subjects). Anonymised datasets should also be in some cases succeeded in doing so. However, made freely available to bona fide researchers in many cases it is not clear that these yield wishing to conduct secondary analysis since, the information that policymakers require and as Fehrler, Michaelowa and Wechtler (2009) there is little evidence that they are providing conclude “any kind of measures to enhance schools and mathematics teachers with sound transparency about… learning outcomes and practical advice that can be used to appears to be valuable” (Fehrler, Michaelowa improve learning. All countries that are and Wechtler 2009, p.27). currently investing in national assessments should immediately review these to ensure Where they do not already do so, examination that they are providing value for money. In boards should be instructed to make materials particular, steps should be taken to ensure that which would help teachers and students all national assessments provide mathematics prepare for examinations in mathematics (and teachers with concrete examples of student all other subjects) freely available via the performance at different achievement levels. internet. These should include examination Examples of test items, descriptions of programmes (syllabuses), reports of examiners alternative solutions and popular and, most importantly, past papers83 (with misconceptions, and supporting statistical their marking schemes). data are all necessary if national assessments are to have a positive impact on Supporting student self-learning through classroom practices. technology Allowing access to materials and data related When it comes to knowledge and education, to high-stake examinations the advent of the internet has begun to undermine the hegemony of schools, teachers, In many countries of SSA, high-stake ministry-approved textbooks, etc. Students examinations act as gatekeepers at the who have access to the internet can now easily transition points of the education system. The supplement their formal education with agencies responsible for them are under great information and resources from elsewhere. pressure to maintain the security of their This should not be seen as a threat but as an systems and to ensure that individual students opportunity to raise levels of achievement (at receive the correct result in a timely fashion. In least for some) without significant additional focusing on this they tend to neglect their role investment from the state. This is particularly in enhancing education by providing materials true in SSA where many students are currently and information to teachers and students. being taught by teachers who lack confidence Governments and their ministries of education and/or competence in mathematics. Three 83. Examination boards that currently charge for past papers (hard copy) should be encouraged to accept a small loss in income for the greater national good. 144 initial steps are recommended. First, students, their transformation are driven by long-term parents and local communities should be processes that involve several actors and often made aware of the possibilities for self- impersonal factors and large social groups, learning. They should be encouraged to access leading to a slow pace of change subject to suitable learning materials – possibly through a various forces, some of which cannot be easily user-friendly, national education portal. controlled even by a benevolent national Secondly, key players in education, both authority” (ibid, p.16). Therefore, they suggest government agencies and NGOs, should be that fragile states wishing to build resilience encouraged to provide free access to existing should “focus in the near term on more open educational resources. Thirdly, NGOs and ‘narrowly defined’ institutions that can be commercial partners should be encouraged to reformed within a decade or so through the collaborate with, for example, ministries of action of a well-identified authority” (ibid, education in the generation of age-appropriate p.16). The evidence presented in this report learning materials compatible with the content suggests that two categories of institution are and philosophy of national curricula for of critical importance in raising educational mathematics84. outcomes in mathematics: institutions responsible for the pre-service and in-service 10.3 Challenges associated with training of teachers; and, institutions implementation in fragile states responsible for examinations and other forms of educational assessment. As mentioned previously, the OECD (2015a) classifies 28 states in SSA as being ‘fragile’. Chapter 7 highlights the fact that the majority Gelbard et al (2015) define a fragile state as of TTIs are currently so weak that they one “in which the government is unable to represent a significant barrier to progress. deliver basic services and security to the Therefore, in any development strategy, these population” and suggest that such states should be radically reformed and strengthened “display an elevated risk of both political - as a matter of priority - so that they are instability (including civil conflict), and capable of preparing competent and confident economic instability” (Gelbard et al, 2015, p.7). teachers of mathematics who, in turn, are In such states, the implementation of complex, capable of inspiring learners and inculcating a long-term educational reforms, as advocated deeper understanding of mathematics. in this report, is extremely problematic. The probability of success is enhanced by Chapters 5 and 8 reveal the important roles addressing three key issues: poor governance played by examination boards and national in the education sector; failure to allocate assessment agencies. Examination boards and adequate and sustainable resources to the agencies responsible for the conduct of education; weakness of key educational national and regional assessments have the institutions. A detailed analysis of these issues potential to provide valuable information to and evaluation of possible solutions is beyond policy makers and practitioners on standards the scope of this report. However, the of achievement and on the factors which importance of strengthening institutional contribute to better outcomes. Unfortunately, capacity is worth highlighting. Gelbard et al this potential is rarely fulfilled. Therefore, (ibid) note that, in general, “institutions and strengthening the professionalism and 84. A relevant example is the long-standing collaboration between South Africa’s Department of Basic Education, Sesameworkshop ®, and the South African Broad casting Corporation in producing child-friendly TV programmes, on-line video clips, and workbooks to support early childhood development in a number of areas – including numeracy. (See http://www.takalanisesame.co.za/) 145 technical capacity of these institutions should How do learners understand mathematical be a priority. In countries where there is concepts as demonstrated by their teachers? currently no capacity to conduct regional How do they approach mathematical assessment programmes and/or design and problems? conduct national assessments, developing a new institution for these purposes should be A recurring theme in this study has been the considered from the outset. mismatch between teaching practice and the constructivist approach advocated by modern 10.4 Areas worthy of further research curricula. Some examples of alternative ways in which students may view particular The issue of low levels of achievement in mathematical concepts are given in academic numeracy and mathematics in SSA has been papers. However, there appears to be little widely acknowledged for some time and, as a evidence, and few examples, gathered in the result, the underlying factors have been the context of typical classrooms in SSA. In subject of much research. There remain, addition, Akyeampong et al. (2011) point out however, areas where further research could that the use of TLMs has been “ritualised to make a positive contribution to the the point where how they communicate formulation of strategies for remedial action. conceptual understanding is lost” Some of the research questions which, during (Akyeampong et al., 2011, p.39). Both of these the preparation of this report, have emerged issues should be subject to action research. as being worthy of study are described below. How effective are the textbooks currently How can countries monitor trends in being used to teach basic mathematics mathematical achievement? in SSA? As countries invest in reforms designed to Whilst many argue that the availability of significantly raise levels of mathematical mathematics textbooks is an important factor achievement they will need to know whether in raising student achievement, quantitative progress is being made or not. It is our research repeatedly suggests that the direct contention that, to date, national and regional benefits are, at best, small. One hypothesis is assessments in SSA have not been able to that investing in textbooks is of value only if provide sufficiently precise and reliable data the prescribed textbook is effective. There are, on trends in student achievement. The however, few rigorous evaluations of textbook question is: ‘How can education systems effectiveness. This is an area where further establish quick and effective mechanisms for study would be of value. monitoring mathematical achievement over time?’ What will be necessary to establish sufficiently precise baseline measurements and how can subsequent measurements be systematically linked with those baselines? 146 How can national assessments of student Which of the e-learning and m-learning achievement in mathematics be improved so technologies in the classroom have the that they provide policy makers and teachers greatest potential to raise levels of numeracy with the information needed to improve and mathematical competence? What are the outcomes in mathematics? challenges of introducing e- and m-learning technologies - especially in fragile states? Whilst commentators such as Kellaghan and Greaney (2004) highlight the potential Over recent years, a significant number of benefits of conducting national assessments initiatives to raise levels of numeracy and and UNESCO (2015) applauds the fact that a student achievement in basic Mathematics significant number of countries across SSA through the use of digital technologies have have carried out such assessments, there is been piloted across SSA. Few of these have little evidence as to the technical quality of been subjected to fully independent scrutiny. these. Few governments appear to be asking There is a need to evaluate any such initiative these fundamental questions: Do our national before investing in implementing it at scale. assessments serve their intended purposes? Evaluative studies should not only investigate Do they offer value for money? Have they the returns to learning but also the costs and had a discernible impact on educational policy risks associated with adoption on a large- and/or practice? Answering these scale. These are the key questions: Which questions will require both qualitative and technologies/approaches yield the greatest quantitative research. benefits in terms of improved outcomes? What are the costs associated with implementing Where OER have been used as the basis of, the proposed technological solution at the or to supplement, formal teacher education regional and/or national levels? Given the development programmes, have they prevailing context, is the proposed been effective? technological solution viable and sustainable? In ‘fragile states’ which technologies/ Open Educational Resources produced by approaches are likely to be effective international development partners have been and sustainable? used in some TTIs as the basis of new initial teacher training programmes or to supplement existing programmes. In other cases, OER have been built into in-service professional development programmes for teachers. Independent evaluations of these initiatives are required to determine whether they have contributed to the production of better graduates or not. If such programmes can be shown to be effective and offer good value for money then the approach is more likely to be adopted by other countries and other TTIs. 147 148 Mathematics Education in Sub-Saharan Africa: Appendix A. Case studies for six countries A.1 Overview Republic of the Congo, Ethiopia, Nigeria, Rwanda, and Uganda – were selected to The case studies documented here were represent some of the diversity which can be carried out in 2015 to gather evidence to found across SSA. In particular, countries supplement that available in the many nominally designated as anglophone and research reports and other documents francophone were chosen although, as shown reviewed in the preparation of the main study. in Table A.1, policies with regards to the use of The six countries – Cameroon, Democratic language in education are more complicated. Table A.1: Overview of the locations and educational language policies of the study’s six focus countries Location Language policy for education Cameroon Central Government policy is to promote bilingualism (French and English) for all official functions including Africa education. According to Rosendal (2008), “The law guarantees education in either English or French, depending on the linguistic zone, from first grade throughout secondary school. Teaching the second official language starts in Grade 6. The teachers, as state employees, must use the official languages in communication with the learners. Pupils are prohibited from speaking to teachers in a national language” (Rosendal, 2008, p.37). DRC Central There appears to be no official policy with regard to the language of instruction. In general, however, in the Africa first two years of primary school, one of the national languages (Kikongo, Lingala, Luba-Kasai, and Congo Swahili) is used with the official language, French, being introduced from Grade 3. French is the language of instruction for secondary and higher education. (Language Education Policy Studies, n.d.) Ethiopia East Africa National languages at primary level (to Grade 4 at least but with some variation thereafter by administrative (Horn of area). English is the language of instruction for secondary and higher levels (Vujcich, 2013). Africa) Nigeria West Africa Mother Tongue or local language at the pre-primary and in the early stages of primary education. Thereafter transitioning to English which is the language of instruction for secondary and higher levels (Orekan, 2010). Rwanda East Africa From 2008, English has been designated the official language of instruction for education beyond the lower (Great Lakes primary phase replacing earlier French or French/English bilingual practices. In the early years of primary Region) education, Kinyarwanda is used as the language of instruction but English is studied as a subject from Grade 1. (Samuelson and Freedman, 2010). Uganda East Africa From 2007, rural primary schools have been required to teach pupils in the first three grades in the (Great Lakes dominant local language. During the fourth year, English is introduced as one of the languages of instruction Region) and from Grade 5 it is the sole language of instruction. Urban primary schools are exempt and many choose to teach in English from Grade 1. In each country the survey focused on operating in a range of geo-social contexts classroom practices and teacher attitudes taking into account the limited time and towards mathematics and the teaching of resources available. We do not claim that the mathematics. Each case study is based on findings are generalisable with any great observations made in a sample of schools and degree of precision, but they do allow us to on questionnaires completed by teachers. The check whether the general claims made by samples were not drawn using probabilistic researchers and agencies involved in the methods and we do not claim that they are implementation of educational reforms are representative. National co-ordinators used confirmed by observations made in the field. their local knowledge to select schools 149 Three mechanisms were used to collect data: more extensive studies – especially the classroom observations; teacher influential report ‘Teacher Preparation and questionnaires; and a questionnaire for Continuing Professional Development in Africa’ institutions providing initial teacher training. prepared by Akyeampong et al (2011). Classroom observations and teacher interviews were conducted in public schools only. The Each country-specific profile starts with a target within each country was to observe 50 table containing contextual information. This is mathematics lessons in the primary phase and followed by a description of “lesson 20 mathematics lessons in the upper signatures” following the model used in the secondary phase. The classroom observations 1999 TIMSS video study (Hiebert, et al, 2003). were structured to focus on the question: Statements made within the lesson signatures “What actually happens in classrooms where are, where appropriate, supported by statistics mathematics is being taught?” Following each from the classroom observations in order to observed lesson the teacher responsible was give some indication of the frequency of the invited to complete the teacher questionnaire. described behaviour. Information from the In each country, three institutions responsible attitudinal questionnaires completed by for delivering pre-in-service training for teachers is then summarised. Finally, responses teachers were invited to complete from teacher training institutions questionnaires. We do not suggest that this are summarised. small sample is representative of the country, but we were able to check whether their responses were consistent with the findings of Table A.2: Cameroon: Country key facts Indicator Value Year Size (area): 472,710 km2 Population: 22.77 million 2014 Urban population growth (annual %) 3.6% 2014 GDP (current USD): USD 32.55 billion 2014 GDP growth (annual %) 5.9% 2014 GDP per capita (current USD) USD 1,429.3 2014 Expenditure on education as a % of GDP 3% 2012 Expenditure on education as a % of total government expenditure 15.2% 2012 Government expenditure per primary pupil (USD) USD 73.8 2012 Mobile cellular subscriptions (per 100 people) 76 2014 Internet users (per 100 people) 11 2014 Structure of education system (years primary + lower secondary + upper secondary) 6 + 4 + 3 (Fr) 6 + 5 + 2 (En) School enrolment, pre-primary (% gross) 34% 2014 School enrolment, primary (% gross) 113% 2014 Primary completion rate, total (% of relevant age group) 72% 2014 School enrolment, secondary (% gross) 52% 2013 Ratio of girls to boys in primary and secondary education (%) 87% 2012 Pupil:teacher ratio in primary education (headcount) 44.2 2014 Pupil:teacher ratio in secondary education (headcount) 21.4 2012 Average number of pupils per mathematics textbook in primary education 13.9 2012 150 A.2 Case study: Cameroon concept of interest by lecturing (98%) and by writing on the chalkboard (86%). Pupils were A.2.1 Primary mathematics ‘lesson being questioned and asked to respond (90%). signature’ (Grades 3 and 6) A minority (40%) used some form of TLM to aid their explanation. At this time, the majority This description is based on 50 classroom of pupils (86% of cases) were orally answering observations made in 25 schools. questions asked by the teacher and, in about two-thirds of cases (68%), reciting their Typically, the mathematics lessons observed answers in unison. It was relatively rare (-20% of lasted for about 40 minutes. On average, 42 cases) to find pupils working in pairs students were on the class register but there or groups. was a great degree of variation and the maximum number observed in one class was About halfway through the lesson, little had 90. In nearly all cases (>90%) children had changed with nearly all teachers (90%) still chairs or benches to sit on and a hard surface using the chalkboard, lecturing and on which to write. In general the lighting, questioning pupils. Most students (-85% of temperature and ventilation were adequate and cases) were involved in answering questions the majority of classrooms (72%) were and/or doing mathematics problems in their described as “cheerful and bright environments exercise books. Pair and group work was not decorated with wall charts etc“. Chalkboards frequently observed (20%). Throughout the were available and used in all classrooms lesson, very few incidents of pupil indiscipline (100%) and the majority of teachers (90%) had were observed. their own copy of the textbook. In about a half of cases (52%) measuring instruments and At the end of the lesson, the majority of teachers concrete teaching aids for mathematics were summarised the contents of the lesson (84%) available. None of the classrooms visited was and the majority (72%) set a homework task. In equipped with any form of educational general, the end of the lesson was as orderly as technology. Nearly all pupils (-95%) had a the beginning with, according to observers, 76% pencil/pen and an exercise book. In two-thirds having “a clear and orderly end”. of cases (68%) most or all of the pupils had a mathematics textbook. The overall impression was generally favourable. The vast majority of teachers (96%) appeared The start of each lesson was orderly and well to understand the concept they were teaching structured. About three-quarters of teachers and were able to explain it to their classes. (78%) referred back to the previous lesson with Compared with the results seen in other a significant number (60%) handing back, or countries, a relatively high proportion of talking about, pupils’ homework. The majority teachers (76%) incorporated at least one ‘real of teachers (-80%) started by giving a clear life’ example in their explanations. Our description of what the lesson was to be about. observers considered that in about three- quarters of the lessons the majority of students About 15 minutes into the lesson nearly all not only understood what had been taught teachers were explaining the mathematical (80%) but had also enjoyed the lesson (72%). 151 A.2.2 Secondary mathematics ‘lesson About 15 minutes into the lesson the vast signature’ (Grades 9, 10 and 11) majority (>90%) of teachers were explaining the mathematical concept of interest by This description is based on 20 classroom writing on the chalkboard and lecturing to observations made in 10 schools. their pupils. In addition, they were asking pupils questions and listening to their oral On average, the observed mathematics lessons responses. In about three-quarters of the lasted for about 60 minutes. Relative to other classrooms, students were also set problems countries in this study, classes were relatively to solve. At this time, the majority of pupils large with an average of 57 students attending (85% of cases) were orally answering the lesson. However, class sizes varied and in questions asked by the teacher. Answering in one case 130 students were present! chorus was a very frequent activity and was Notwithstanding the large numbers of observed in nearly all (95%) lessons. It was students present, there was generally enough relatively rare (-20% of cases) to find pupils seating available and students had a hard working in pairs or groups and even rarer surface on which to write. However, few (10%) to see them handling/using teaching classrooms (15%) were described as being and learning materials. “bright and cheerful learning environments”. Apart from the omnipresent chalkboard, About halfway through the lesson, the teachers had few TLM available to them save observed teaching pattern was largely for drawing equipment for the chalkboard unchanged with most teachers (85%) still which was available in about half the using the chalkboard to explain the concept of classrooms (55%). Only 40% of teachers interest and questioning pupils to judge their appeared to have their own copy of the understanding. The majority of pupils were textbook. Not surprisingly, none (0%) of copying from the chalkboard (90% of cases) classrooms was equipped with any form of and/or attempting to solve problems in their educational technology i.e. overhead exercise books (90%). At this stage of the projectors, televisions, and computer lesson pair or group work was not observed. projection equipment were not available. Compared with the teachers, the students Without exception, the lessons observed were appeared relatively equipped with all, or nearly brought to “a clear and orderly end”. Nearly all all, having writing materials and textbooks. In (95%) of teachers summarised the contents of addition, in all of the classrooms observed, all the lesson and about three-quarters (70%) set or nearly all students had calculators. a homework task. The start of each lesson was, in general, The overall impression was that the teachers orderly with all (100%) teachers giving a clear were technically competent in that they all description of what the lesson was to be appeared to understand the concept they about. Nearly all teachers (95%) explicitly were teaching and they rarely, if ever, made referred back to the previous lesson and a mathematical mistakes. However, in only two large number (65%) handed back, or talked cases were teachers observed using ‘real life’ about, pupils’ homework. examples in their teaching. 152 A.2.3 Teacher characteristics and attitudes The primary school teachers in the survey reported, with very few exceptions, that they In Cameroon, attitudinal questionnaires were were very well prepared, or at least partially completed by 50 teachers teaching at the prepared, to teach the required concepts of primary level and 20 teaching mathematics at the basic mathematics curriculum. Not the secondary level. Most (86%) of the surprisingly, the vast majority (>85%) of teachers interviewed were between 30 and 59 mathematics specialists teaching at the years old. They were also relatively secondary level reported that they were very experienced with the majority (72%) having at well prepared to teach any of the concepts least five years’ teaching experience. Prior to required by the curriculum. embarking on their pre-service training, 28% had graduated from senior secondary school, When asked about the value of group work 46% had completed A-levels or the equivalent, and/or pair work in the classroom, there was and 21% had gained a first degree. Of the almost unanimous agreement that this was secondary school teachers nearly two-thirds “somewhat important” or “very important”. (63%) had gained a degree level qualification. Similarly, the use of concrete practical equipment in the teaching/learning of At the primary level nearly all of our teachers Mathematics was considered to be very (96%) reported that whilst they are fluent in important by 97% of teachers. It is interesting the language of instruction, they are not to contrast what teachers say is important teaching in their mother tongue. The vast with what they do in practice as described in majority (86%) claim that their students do not the lesson signatures above. face any significant problems because they all understand the language of instruction. A Prior to teaching, a significant minority of our similar pattern was found amongst secondary primary teachers (19%) had received no formal school teachers. teacher training and another 15% had been trained through short courses amounting to In order to judge the readiness of our teachers less than one-year. About one-third (36%) had to use educational technologies they were completed a one-year programme and a asked about their ownership of mobile phones further 23% a two-year pre-service training and the way they saw their own computer course. Our small sample of secondary level skills. All reported having a mobile phone and, teachers displayed a remarkably wide range of of these, almost 50% have smart phones with pre-service experience. 40% said they had not internet access. In contrast with some of the been trained (sic) or had followed short other countries in our study, PC ownership courses only, 20% reported two years of amongst teachers appears to be relatively training and 40% had received three or more high. 61% reported owning a PC, laptop or years of training. tablet computer and half of these have internet access. Only a small number (9%) The primary school teachers who had been classed themselves as non-users but a trained generally displayed positive attitudes relatively large proportion (62%) considered towards their pre-service training with the themselves to be beginners with limited skills. majority agreeing or strongly agreeing with However, more than a quarter (29%) claimed statements such as: “My own mathematical to be confident or expert users. skills improved a lot as a result of my training” 153 (56%); “My pre-service training left me well positive about their students’ attitude towards prepared to teach mathematics” (68%); and, “I mathematics and their progress, the vast enjoyed my pre-service training”(87%). There majority (80%) agree that “most pupils need was less agreement on the content of training additional tutoring”. Thirdly, most (74%) courses. For example, whilst 36% of our teachers obviously feel under pressure to primary teachers agreed with the statement cover the syllabus and nearly half feel that “nearly all my pre-service training was about they do not have enough time to cover the improving my mathematical skills”, 26% curriculum and sometimes have to move on disagreed. Similarly, the statement “We did not before their pupils have mastered the current get enough practice teaching mathematics in topic. Fourthly, nearly all mathematics the classroom” split the group with 28% teachers (91%) believe that more in-service agreeing and 34% disagreeing. support is required if student achievement is to be enhanced. At present, peer-support The table below summarises how the 70 looks to be very important with nearly all teachers in our survey responded to selected (94%) of teachers reporting that they regularly statements in our attitudinal questionnaire. exchange ideas related to the teaching of This raises several points of interest. First, mathematics. Finally, most (64%) of the there is a general consensus that all students teachers in our sample are confident that have the potential to be good at mathematics computers and other educational technologies and that this does not require a special sort of will help to improve results in mathematics. brain. Secondly, whilst teachers are very Table A.3: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 44 22 1 0 2 (62.9%) (31.4%) (1.4%) (0.0%) (2.9%) Everyone has the potential to be good at mathematics. 19 31 8 7 3 (27.1%) (44.3%) (11.4%) (10.0%) (4.3%) You have to have the right sort of brain to be good at mathematics. 1 7 8 32 19 (1.4%) (10.0%) (11.4%) (45.7%) (27.1%) Very few pupils are naturally good at mathematics. 7 40 10 8 1 (10.0%) (57.1%) (14.3%) (11.4%) (1.4%) The current curriculum for Mathematics is too difficult for my students. 3 16 15 22 8 (4.3%) (22.9%) (21.4%) 31.4%) (11.4%) My pupils are making good progress in mathematics. 6 47 7 5 1 (8.6%) (67.1%) (10.0%) (7.1%) (1.4%) Students seem to be interested in learning mathematics. 12 29 10 10 1 (17.1%) (41.4%) (14.3%) (14.3%) (1.4%) Most pupils need additional tutoring in mathematics. 19 37 6 5 0 (27.1%) (52.9%) (8.6%) (7.1%) (0.0%) We are under a lot of pressure to cover the syllabus so that pupils are ready 12 40 3 9 2 for examinations. (17.1%) (57.1%) (4.3%) (12.9%) (2.9%) Sometimes you have to move onto the next topic even if some pupils do 4 29 7 19 9 not understand the current topic. (5.7%) (41.4%) (10.0%) (27.1%) (12.9%) I have enough time to teach everything in the mathematics curriculum. 12 25 3 20 4 (17.1%) (35.7%) (4.3%) (28.6%) (5.7%) Teachers need more in-service support to improve the teaching of 36 28 1 2 0 mathematics in our schools. (51.4%) (40.0%) (1.4%) (2.9%) (0.0%) I regularly exchange ideas on how to teach mathematics with my fellow 37 29 2 1 0 teachers. (52.9%) (41.4%) (2.9%) (1.4%) (0.0%) Using computers and other new technologies in the classroom will improve 22 23 11 8 3 results in mathematics (31.4%) (32.9%) (15.7%) (11.4%) (4.3%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 154 A.2.4 Teacher Training Institutions their training. In all colleges, trainees are required to pass examinations at the end of In Cameroon, questionnaires were completed their first year. by representatives of three institutions for initial teacher training – two for the basic The colleges in our study reported significant phase and one for the secondary phase. deficiencies in terms of educational Compared with the TTIs questioned in other technologies. They do not have libraries of countries, the TTIs in Cameroon were very video material for teaching/learning small with between 106 and 320 trainees in mathematics for use by trainees and none total with an average annual intake of just 80 reported having computers with internet trainees. They employ, on average, 25 tutors access available for use by trainees. The but none of the three reported having more colleges in our sample volunteered that they than one or two mathematics specialists. The do not have adequate technical resources to minimum qualification required for tutors is a teach their trainees how to use educational first degree and some previous teaching software in the classroom. experience. No college requires its tutors to periodically refresh their skills in a school environment or to undergo formal appraisals to check that their knowledge is up-to-date. The minimum entry requirement for prospective primary school teachers is a qualification gained after four years of secondary education (i.e. equivalent to O-level). Somewhat surprisingly, it was reported that a pass in mathematics at this level is not a requirement. Both colleges for the preparation of primary teachers reported that in the current academic year they were “undersubscribed and many places were left unfilled”. All respondents agreed with the statement “we face problems attracting high quality applicants to train as teachers”. During the initial three-year teacher training programme for primary school teachers, the colleges reported that just one to two hours per week are dedicated to the subject of mathematics. This is far fewer than the level reported in other countries in our study. Trainees are required to undergo a practicum of between six to nine weeks in each year of 155 A.3 Case study: Democratic Republic of the Congo (DRC) Table A.4: Democratic Republic of the Congo: Country key facts Indicator Value Year Size (area): 341,500 km2 Population: 4.50 million 2014 Urban population growth (annual %) 3.1% 2014 GDP (current USD): USD 14.14 billion 2014 GDP growth (annual %) 6.5% 2014 GDP per capita (current USD) USD 3,137.7 2014 Expenditure on education as a % of GDP 6.2% 2010 Expenditure on education as a % of total government expenditure 29% 2010 Government expenditure per primary pupil (USD) USD 10.4 2010 Mobile cellular subscriptions (per 100 people) 108 2014 Internet users (per 100 people) 7 2014 Structure of education system (years primary + lower secondary + upper secondary) 6+4+3 School enrolment, pre-primary (% gross) 14% 2012 School enrolment, primary (% gross) 109% 2012 Primary completion rate, total (% of relevant age group) 73% 2012 School enrolment, secondary (% gross) 54% 2012 Ratio of girls to boys in primary and secondary education (%) 100% 2012 Pupil:teacher ratio in primary education (headcount) 37.1 2013 Pupil:teacher ratio in secondary education (headcount) 14.2 2013 Average number of pupils per mathematics textbook in primary education 1.65 2013 PASEC: 5th Grade mathematics – median score (100 scale) 46.9 2010 A.3.1 Primary mathematics ‘lesson signature’ dramatically from a class where just five (Grades 3 and 6) children attended to one in which there were 90 pupils. In only 70% of cases did all the This description is based on 50 classroom children have a chair or bench to sit on and a observations made in 25 schools. hard surface on which to write. In general the lighting, temperature and ventilation were Typically, the mathematics lessons observed considered “adequate” but only one in five lasted for about 40 minutes. On average, 38 (20%) of classrooms were described as being students were present but the number varied “cheerful and bright environments decorated 156 with wall charts, etc“. Chalkboards were but it was also very common (72% of cases) for available and used in all classrooms (100%) and pupils to be invited to the board to answer a the majority of teachers (80%) had their own question whilst the rest of the class watched. copy of the textbook. In about one-quarter of Pair or group work was never observed and classrooms (26%) measuring instruments such even individual work on problem solving was as rulers, scales and measuring jugs were relatively rare (36%). Our observers reported present but other forms of mathematical that nearly all teachers (92%) were involved in teaching aid (e.g. models, Cuisenaire rods, etc.) “disciplining” pupils but given that pupil were less frequently available (16%). It was very misbehaviour was, to all intents and purposes, rare (<5%) to see a classroom equipped with never observed this probably refers to ‘strict any form of educational technology. In the control’ rather than punitive action. majority of classrooms (-95%) all or most pupils were equipped with writing materials. However, About halfway through the lesson, most our observers did see two lessons in which it teachers (-90%) were still using the chalkboard appeared that none of the children had pen or and questioning their pupils. However, about paper. In about one-third of classrooms (34%) three-quarters (74%) were also setting tasks for at least some of the pupils were seen to have a their pupils to solve. Once again “disciplining mathematics textbook. At the same time, in students” was reported in nearly all classrooms 34% of classrooms no child appeared to have suggesting that teachers in DRC adopt an a textbook85. authoritative approach to classroom control. The start of each lesson was orderly and well At the end of the lesson, nearly all teachers structured. Nearly all teachers referred back to (96%) summarised the contents of the lesson. the previous lesson (90%) and gave a clear About a half (56%) set their pupils a task to be description of what the lesson was to be about done as homework. According to our observers, (94%). In only about a quarter of lessons the vast majority of lessons (-80%) had “a clear observed (24%) was homework returned or and orderly end”. discussed – a lower proportion than observed in the other five countries covered by The overall impression was generally favourable. our survey. The vast majority of teachers (96%) appeared to understand the concept they were teaching About 15 minutes into the lesson nearly all and were able to explain it to their classes with teachers (99%) were explaining the a significant number (50%) incorporating at mathematical concept by writing on the least one ‘real life’ example. However, our chalkboard and talking to their pupils. About a observers believe that they detected half (52%) were using some form of TLM to aid mathematical errors or points which the their explanation. In addition, all teachers teacher could not explain adequately in about a (100%) were asking pupils questions and quarter of the lessons observed (24%). listening to their oral responses. At this time, Notwithstanding this, observers considered the majority of pupils were engaged in teacher- that in nearly all lessons (-90%) the majority of led question/answer activities. Individual students not only appeared to understand what answering (92% of cases) coupled with whole- had been taught but had also enjoyed class answering in chorus (78%) were prevalent the lesson. 85. In the remaining classrooms, observers could not be sure whether children had access to textbooks or not. 157 A.3.2 Secondary mathematics ‘lesson addition, they were asking pupils questions and signature’ (grades 9 and 11) listening to their oral responses. As in the primary lessons, our observers noted the strict This description is based on 20 classroom approach of teachers with “disciplining observations made in 10 schools. students” being recorded in 85% of cases even though student misbehaviour was extremely Typically, a single mathematics lessons lasted rare. At this time, the majority of pupils (85% of for between 45 and 50 minutes. On average, 34 cases) were orally answering questions asked students were present but the number varied by the teacher and/or attempting to solve significantly from a class where just seven mathematical problems in their exercise books children attended to one in which there were (50% of cases). Pair or group work was 68 pupils. Somewhat surprisingly for secondary never observed. phase classes, the physical conditions for pupils were not good. In only about 60% of cases did About halfway through the lesson, the all pupils have chairs or benches to sit on and a observed teaching pattern was largely hard surface on which to write. In about three- unchanged with most teachers (95%) still using quarters of classrooms, the lighting, the chalkboard to explain the concept of temperature and ventilation were considered as interest and questioning pupils to judge their adequate but only 25% of classrooms were understanding. The pupils were copying from described as being bright and cheerful learning the chalkboard (100% of cases) and/or environments. Chalkboards were available in all answering questions orally (85%). Somewhat classrooms (100%) and 75% of teachers had surprisingly, “answering in unison” was their own copy of the textbook. Basic TLMs observed in a significant number of classes were available in a minority of classrooms (40%). On only one occasion were students (15%-30%) but none (0%) of the classrooms seen to be working in pairs or groups. was equipped with any form of educational technology i.e. overhead projectors, televisions, At the end of the lesson, about three-quarters and computer projection equipment were not of the teachers summarised the contents of the available. Nearly all pupils had writing materials lesson (80%) and set a homework task (75%). but in 80% of classrooms textbooks were either In about two-thirds of cases (65%) the lesson not available or in short supply. In only 10% of had, according to observers, “a clear and classrooms did all students have a textbook. orderly end”. The majority of teachers (75%) did have a copy of the textbook. The overall impression was relatively good. Nearly all teachers (95%) appeared to The start of each lesson was orderly and well understand the concept they were teaching structured. All teachers referred back to the and our observers detected very few previous lesson and nearly all (90%) gave a mathematical errors or problems in the clear description of what the lesson was to be teacher’s explanation. In addition, they judged about. In half the lessons (50%) homework was that students appeared to understand what had returned to pupils and/or discussed. been taught in more than three-quarters (80%) About 15 minutes into the lesson the vast of the lessons observed. majority of teachers (95%) were explaining the mathematical concept of interest by writing on the chalkboard and lecturing to their pupils. In 158 A.3.3 Teacher characteristics and attitudes a PC, laptop or tablet computer was extremely rare (-9%) with only four of our teachers having In DRC, attitudinal questionnaires were a computer with internet access. The vast completed by 52 teachers teaching at the majority (79%) admitted that they could not primary level and 18 teaching mathematics at use a computer with a further 16% operating at the secondary level. The vast majority (84%) of the level of a beginner with limited skills. the teachers in our survey fell into the age range 30-59 years old. They were also relatively The primary school teachers in the survey experienced with the majority (97%) having at reported, with very few exceptions, that they least three years’ teaching experience. However, were very well prepared, or at least partially their educational experience prior to taking up prepared, to teach all the required concepts of training was, by the standards observed in the basic mathematics curriculum. Not other countries in our study, extremely limited. surprisingly, the vast majority (-90%) of More than half (57%) reported having mathematics specialists teaching at the completed primary school only with a further secondary level reported that they were very 20% not studying beyond the junior secondary well prepared to teach any of the concepts level or its equivalent. Only a small minority required by the curriculum. (7%) had a post-secondary qualification before training to become teachers. When asked about the value of group work and/or pair work in the classroom, 81% of At the primary level only a very small minority teachers agreed that this was “very important”. of our teachers (6%) are teaching in their This is in stark contrast to the practices mother tongue. However, nearly all (92%) claim observed in the classroom where any form of to be fluent in the language of instruction. collaborative learning was extremely rare. Of all About 40% of primary teachers report that the teaching practices included in the teacher their pupils face some difficulties due to the questionnaire the two that were considered language of instruction with almost one in five most important were “homework assignments” (17%) teaching in more than one language to and “doing quizzes, tests and examinations in help their pupils. At the secondary level, 94% of school” with 96% of teachers rating these as teachers in our sample are teaching in a being “very important”. language which is not their mother tongue but all claim to be fluent in the language Prior to teaching, the majority of our primary of instruction. teachers (65%) had completed a three-year teacher training programme. However, a In order to judge the readiness of our teachers sizeable minority (23%) reported that they had to use educational technologies they were received no pre-service training. A similar asked about their ownership of mobile phones pattern emerged amongst secondary teachers and the way they saw their own computer skills. with 56% having had three or more years of Nearly one-fifth (19%) do not have a mobile initial teacher training and 33% having phone – a larger proportion than reported in had none. the other countries in our survey. Just over half (51%) of our teachers have phones without In general, the teachers in our sample who had internet access with the remainder (30%) received formal training displayed positive having smart phone with internet. Ownership of attitudes towards their pre-service training with 159 60% agreeing or strongly agreeing with mathematics. For example, 45% of teachers do statements such as: “My own mathematical not agree that “everyone has the potential to skills improved a lot as a result of my training”; be good at mathematics” and a staggering 91% “My pre-service training left me well prepared agree that “you have to have the right sort of to teach mathematics”; and, “I enjoyed my brain to be good at mathematics”. Secondly, pre-service training”. In terms of content, 43% whilst teachers are very positive about their agreed with the statement “nearly all my students’ attitude towards mathematics and pre-service training was about improving my their progress, nearly three-quarters (71%) mathematical skills”. In addition, a third (31%) agree that “most pupils need additional agreed that in their pre-service training they tutoring”. This may be because a similar “did not get enough practice teaching proportion (74%) feels that the mathematics mathematics in the classroom”. curriculum is too difficult for their pupils. Thirdly, 78% believe that more in-service The table below summarises how the 70 support is required if student achievement is to teachers in our survey responded to selected be enhanced. Finally, in DRC opinion appears to statements in our attitudinal questionnaire. This be divided on the likely impact on mathematics raises several points of interest. First, whilst achievement of introducing new educational there is consensus that “mathematical skills are technologies. This may well reflect our teachers’ useful for everyone” there is a divergence of lack of confidence in their own computing skills. opinion over what it takes to be successful in Table A.5: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 35 26 4 5 0 (43.8%) (32.5%) (5.0%) (6.3%) (0.0%) Everyone has the potential to be good at mathematics. 15 15 4 25 11 (18.8%) (18.8%) (5.0%) (31.3%) (13.8%) You have to have the right sort of brain to be good at mathematics. 29 36 0 3 2 (36.3%) (45.0%) (0.0%) (3.8%) (2.5%) Very few pupils are naturally good at mathematics. 6 33 3 27 1 (7.5%) (41.3%) (3.8%) (33.8%) (1.3%) The current curriculum for mathematics is too difficult for my students. 19 40 7 4 0 (23.8%) (50.0%) (8.8%) (5.0%) (0.0%) My pupils are making good progress in mathematics. 21 46 1 2 0 (26.3%) (57.5%) (1.3%) (2.5%) (0.0%) Students seem to be interested in learning mathematics. 17 44 3 5 0 (21.3%) (55.0%) (3.8%) (6.3%) (0.0%) Most pupils need additional tutoring in mathematics. 24 33 2 11 0 (30.0%) (41.3%) (2.5%) (13.8%) (0.0%) We are under a lot of pressure to cover the syllabus so that pupils are ready 8 15 2 33 12 for examinations. (10.0%) (18.8%) (2.5%) (41.3%) (15.0%) Sometimes you have to move onto the next topic even if some pupils do 1 5 2 45 17 not understand the current topic. (1.3%) (6.3%) (2.5%) (56.3%) (21.3%) I have enough time to teach everything in the mathematics curriculum. 23 33 1 13 0 (28.8%) (41.3%) (1.3%) (16.3%) (0.0%) Teachers need more in-service support to improve the teaching of 33 29 2 5 1 mathematics in our schools. (41.3%) (36.3%) (2.5%) (6.3%) (1.3%) I regularly exchange ideas on how to teach mathematics with my fellow 46 21 1 1 0 teachers. (57.5%) (26.3%) (1.3%) (1.3%) (0.0%) Using computers and other new technologies in the classroom will improve 26 9 9 3 23 results in mathematics (32.5%) (11.3%) (11.3%) (3.8%) (28.8%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree. Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 160 A.3.4 Teacher Training Institutions the statement “ideally our trainees should spend more time practising in schools before In DRC, questionnaires were completed by they qualify”. representatives of three institutions for teacher training all of which are government institutions The colleges in our study reported significant subordinated to the Ministry of Education. Of deficiencies in terms of educational these, two prepare teachers for the primary/ technologies. Two stated that video material for junior secondary phase only, and one prepares teaching/learning mathematics, computers and teachers for the secondary phase. The teaching/learning software are simply not institutions offer training for, on average, 1,200 available. The other reported having some trainees per year. The minimum qualification resources but that these were not for use by required for tutors is a first degree. Two trainees. All colleges in our sample volunteered colleges reported that their tutors are required that they do not have adequate technical to have some prior teaching experience but one resources to teach their trainees how to use allows for the appointment of tutors from a educational software in the classroom and that non-teaching route. they do not use technology to a significant extent in their training. The colleges reported that trainee primary school teachers are typically aged 20-23 on admission. The minimum entry requirement is a qualification gained after 13 years of education (i.e. equivalent to A-level). In all cases a pass in mathematics is said to be required. Two colleges said that they were undersubscribed for the current academic year and that it was difficult to attract sufficient applicants. The other college said that supply and demand were roughly balanced. All colleges agreed with the statement “we face problems attracting high quality applicants to train as teachers”. During the initial three-year teacher training programme for primary school teachers, up to four hours per week only are dedicated to the subject of mathematics. Trainees undergo a short practicum (between two to four weeks) in each of the first two years and a longer practicum (between 8-12 weeks) in the third year. In all colleges, trainees are required to pass examinations at the end of their first year. The reported failure rate at this point was between 10-16%. All respondents agreed with 161 A.4 Case study: Ethiopia Table A.6: Ethiopia: Country key facts Indicator Value Year Size (area): 1,000,000 km2 Population: 96.96 million 2014 Urban population growth (annual %) 4.8% 2014 GDP (current USD): USD 54.80 billion 2014 GDP growth (annual %) 9.9% 2014 GDP per capita (current USD) USD 565.2 2014 Expenditure on education as a % of GDP 4.7% 2010 Expenditure on education as a % of total government expenditure 22% 2010 Government expenditure per primary pupil (USD) USD 72.0 2010 Mobile cellular subscriptions (per 100 people) 32 2014 Internet users (per 100 people) 3 2014 Structure of education system (years primary + lower secondary + upper secondary) 8 + 2 +2 School enrolment, pre-primary (% gross) 2% 2006 School enrolment, primary (% gross) 84% 2006 Primary completion rate, total (% of relevant age group) 47% 2006 School enrolment, secondary (% gross) 29% 2006 Ratio of girls to boys in primary and secondary education (%) 81% 2006 Pupil:teacher ratio in primary education (headcount) 53.7 2012 Pupil:teacher ratio in secondary education (headcount) 38.8 2012 Average number of pupils per mathematics textbook in primary education 1 2012 A.4.1 Primary mathematics ‘lesson signature’ average, 43 students were in attendance but (Grades 3 and 6) the number varied dramatically from just 8 to 78! In the vast majority of cases (>90%) This description is based on 50 classroom children had chairs or benches to sit on and a observations made in 25 schools. hard surface on which to write. In general the lighting and temperature were described as Typically, the mathematics lessons observed satisfactory but ventilation was inadequate in lasted for between 35 and 40 minutes. On one-third of classrooms and less than half 162 (42%) were described as “cheerful and bright About halfway through the lesson, the pattern environments decorated with wall charts etc“. of teaching remained largely unchanged with Compared with some of the other countries in most teachers still using the chalkboard (86%) this study the physical equipment in classrooms and lecturing (78%). Pupils were still answering was relatively poor. For example one third of teachers’ questions (86%) and our observers classrooms observed did not have a chalkboard reported seeing ‘rote’ responses in nearly or its equivalent, drawing instruments for the two-thirds (64%) of cases. However, around this board were not seen, and concrete teaching time pupils were also solving mathematical aids and models were not available for teachers problems in their exercise books. It was to use. About half (52%) of teachers had their extremely rare (6%) to see students handling own textbook. None of the primary classrooms any form of physical teacher/learning material. observed was equipped with any form of educational technology. The vast majority of In contrast with some of the other countries in students (-90%) had a pencil/pen and an this study, our observers considered that exercise book and in 60% of classrooms all, teachers spent considerable time “disciplining or nearly all, of the students had a students”. However, it is not clear what this mathematics textbook. means because significant misbehaviour was seen rarely. It is possible that teachers in The start of each lesson was, in general, orderly Ethiopia adopt a more authoritative stance than and well structured. Nearly all teachers (- 90%) their counterparts in other countries. made some reference back to a previous lesson and/or handed back, or talked about, pupils’ At the end of the lesson, the majority of homework (54%). The vast majority of teachers teachers (> 80%) ensure a quiet and orderly (96%) started by giving a clear description of end to the lesson. However, only half (54%) what the lesson was to be about. explicitly summarised the contents of the lesson. About 15 minutes into the lesson the majority of teachers (>90%) were at the chalkboard, The overall impression was that the vast explaining the mathematical concept of interest majority of teachers (92%) appeared to by talking to their pupils (i.e. lecturing) and understand the concept they were teaching asking pupils questions and listening to their and were able to explain it to their classes. oral responses (94%). At this time, nearly all However, most relied on the textbook as their pupils (92% of cases) were orally answering main teaching aid and only a quarter (28%) questions asked by the teacher and, in about used real-life examples when explaining the two-thirds of cases (66%), reciting their topic. The observers considered that in about answers in unison. There was, however, some three-quarters of the lessons (80%) the variation and in about half of classrooms there majority of students appear to understand what was some evidence of collaborative work had been taught. Notwithstanding the between pairs or small groups of pupils. apparently strict control exercised by teachers, the majority of students also appeared to have enjoyed the lesson. 163 A.4.2 Secondary mathematics ‘lesson TLM to support their explanation. In addition, signature’ (Grades 9, 10 and 11) they were asking pupils questions and listening to their oral responses. In addition, it was This description is based on 20 classroom common (80%) to see teachers setting a observations made in 10 schools. mathematical problem for pupils to solve. At this time, the majority of pupils (85% of cases) Typically, a single mathematics lesson lasted for were orally answering questions asked by the about 40 minutes. On average, 43 students teacher with a significant incidence of ‘rote’ attended the lesson. In all cases pupils had responses (60%). However, it was also common chairs or benches to sit on and a hard surface to see pupils “doing mathematics items in their on which to write. In general the lighting, exercise books” (80% of cases) with pair or temperature and ventilation were adequate and small group working seen in about half of the the majority of classrooms (70%) were observed lessons. described by observers as being bright and cheerful learning environments. As in the About halfway through the lesson, the primary phase classrooms, physical equipment observed teaching pattern was largely was relatively limited. For example 25% of unchanged with most teachers (>90%) still classrooms observed did not have a chalkboard lecturing from the front of the class and or its equivalent, drawing instruments for the questioning pupils to judge their understanding. board were not seen, and concrete teaching Copying from the board, responding to the aids and models were not available for teachers teacher’s questions and attempting to solve to use. The textbook was, to all intents and problems in their exercise books were the most purposes, the only TLM available to teachers common pupil activities observed. and pupils. About half (55%) of teachers used the textbook as a teaching aid and in 50% of At the end of the lesson, two-thirds of the classrooms all, or nearly all, of the students had teachers (65%) summarised the contents of the a mathematics textbook. Televisions were lesson and a similar proportion set a homework available in a significant number of classrooms task. In general, the vast majority of teachers but other forms of educational technology were (90%) ensured that the lesson came to “a clear extremely rare. On the positive side, the only and orderly end”. overhead projector seen by observers was used by the teacher! According to our observers, nearly all teachers (-90%) appeared to understand fully the The start of each lesson was, in general, orderly concept they were teaching and in only one with nearly all (95%) teachers giving a clear case was a possible mathematical error or a description of what the lesson was to be about. problem in the teacher’s explanation detected. The majority (80%) of teachers explicitly referred back to the previous lesson and a third A.4.3 Teacher characteristics and attitudes (35%) handed back, or talked about, pupils’ homework. In Ethiopia, attitudinal questionnaires were completed by 48 teachers teaching at the About 15 minutes into the lesson the vast primary level and 20 teaching mathematics at majority of teachers were explaining the the secondary level. The group displayed a very mathematical concept of interest by writing on wide range of ages with teachers distributed in the chalkboard and lecturing to their pupils. age groups of under 25 years to more than 60. Very few (15%) used a concrete model or other Nearly two-thirds (65%) of our teachers 164 reported having at least six years’ teaching The primary school teachers in the survey experience. Prior to embarking on their pre- reported, with very few exceptions, that they service training, 31% had studied only up to the were very well prepared, or at least somewhat end of junior secondary school. The largest prepared, to teach the required concepts of the group (41%) had completed senior secondary basic mathematics curriculum. Not surprisingly, school before training. Of the secondary school the majority (>75%) of mathematics specialists teachers nearly half (44%) had gained a degree teaching at the secondary level reported that level qualification. they were ‘very well prepared’ to teach any of the concepts required by the curriculum. At the primary level nearly three-quarters (71%) of our teachers are teaching in their mother When asked about the value of group work tongue and nearly all (96%) claim to be fluent and/or pair work in the classroom, there was in the language of instruction. Unlike the almost unanimous agreement (97%) that this findings in other countries, the vast majority of was “very important”. Similarly, the use of primary teachers in our sample (84%) claim concrete practical equipment in the teaching/ that students have no or few problems learning of mathematics was considered to be understanding the language in which lessons very important by 76% of teachers. It is are presented. At the secondary level, the interesting to contrast what teachers say is picture is markedly different. Only 10% of important with what they do in practice as teachers in our sample are teaching in their described in the lesson signatures above. There mother tongue with a significant number (30%) was also near unanimous support for assigning admitting that they have at least some difficulty homework and “doing quizzes, tests and in the language of instruction. When it comes examinations in schools”. to their pupils, 70% suggest that their students encounter at least some difficulties in The majority (61%) of our secondary teachers understanding the language of instruction with had at least three years of pre-service training half of these using code switching to help their but, somewhat surprisingly, the rest (39%) students. This reflects the educational language reported having received initial training policy of Ethiopia where after Grade 6 the amounting to less than one year. language of instruction in many administrative areas switches to English (Vujchic, 2013). Both primary and secondary school teachers in our sample displayed very positive attitudes In order to judge the readiness of our teachers towards their pre-service training with about to use educational technologies they were asked about their ownership of mobile phones three-quarters (70 - 74%) agreeing or strongly and the way they saw their own computer skills. agreeing with statements such as: “My own Nearly all (91%) reported having a mobile mathematical skills improved a lot as a result of phone and, of these, 62% have phones with my training” and “My pre-service training left internet access. None of our teachers reported me well prepared to teach mathematics”. owning a PC, laptop or tablet computer with However, 71% also agreed with the statement internet access. A large majority (82%) “nearly all my pre-service training was about admitted that they either could not use a improving my mathematical skills”. There was computer or that they considered themselves slightly less agreement when it came to to be beginners with limited skills. practice in the classroom with 41% of our teachers agreeing they “did not get enough practice teaching mathematics in the classroom” in their pre-service training. 165 The table below summarises how the 70 teachers are positive about their students’ teachers in our survey responded to selected attitude towards mathematics and their statements in our attitudinal questionnaire. This progress, nearly everyone (94%) agrees that raises several points of interest. First, and “most pupils need additional tutoring”. Thirdly, unsurprisingly, there is a great deal of nearly all mathematics teachers (94%) believe consensus that “mathematical skills are useful that more in-service support is required if for everyone”. However, opinion is divided when student achievement is to be enhanced. Finally, it comes to students’ capacities to be these teachers in Ethiopia are convinced that successful in mathematics. For example, nearly computers and other educational technologies one-quarter (24%) disagree to some extent will help to improve results in mathematics. with the statement “everyone has the potential However, it should be remembered that this to be good at mathematics”. Similarly, 80% particular group of teachers admit to having think that “you have to have the right sort of weak technological skill so this begs the brain to be good at mathematics” and 72% question ‘who will be able to use these agree that “very few pupils are naturally good new technologies?’ at mathematics”. Secondly, whilst most Table A.7: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 53 13 2 1 0 (75.7%) (18.6%) (2.9%) (1.4%) (0.0%) Everyone has the potential to be good at mathematics. 18 26 8 13 4 (25.7%) (37.1%) (11.4%) (18.6%) (5.7%) You have to have the right sort of brain to be good at mathematics. 41 15 4 6 4 (58.6%) (21.4%) (5.7%) (8.6%) (5.7%) Very few pupils are naturally good at mathematics. 20 30 3 10 3 (28.6%) (42.9%) (4.3%) (14.3%) (4.3%) The current curriculum for mathematics is too difficult for my students. 9 16 4 26 12 (12.9%) (22.9%) (5.7%) (37.1%) (17.1%) My pupils are making good progress in mathematics. 12 34 9 10 2 (17.1%) (48.6%) (12.9%) (14.3%) (2.9%) Students seem to be interested in learning mathematics. 23 25 4 12 6 (32.9%) (35.7%) (5.7%) (17.1%) (8.6%) Most pupils need additional tutoring in mathematics. 34 32 3 1 0 (48.6%) (45.7%) (4.3%) (1.4%) (0.0%) We are under a lot of pressure to cover the syllabus so that pupils are ready 14 18 4 22 10 for examinations. (20.0%) (25.7%) (5.7%) (31.4%) (14.3%) Sometimes you have to move onto the next topic even if some pupils do 4 19 5 27 14 not understand the current topic. (5.7%) (27.1%) (7.1%) (38.6%) (20.0%) I have enough time to teach everything in the mathematics curriculum. 19 22 1 22 4 (27.1%) (31.4%) (1.4%) (31.4%) (5.7%) Teachers need more in-service support to improve the teaching of 44 22 3 1 0 mathematics in our schools. (62.9%) (31.4%) (4.3%) (1.4%) (0.0%) I regularly exchange ideas on how to teach mathematics with my fellow 27 34 2 3 4 teachers. (38.6%) (48.6%) (2.9%) (4.3%) (5.7%) Using computers and other new technologies in the classroom will improve 36 23 2 4 5 results in mathematics (51.4%) (32.9%) (2.9%) (5.7%) (7.1%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree. Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 166 A.4.4 Teacher Training Institutions The three colleges in our study reported significant deficiencies in terms of educational In Ethiopia, questionnaires were completed by technologies. They all admitted that they do representatives of three institutions for teacher not use technological aids (video, broadcast training – two preparing teachers for the material, etc) extensively in their training. Only primary/junior secondary phase only, and the one reported having a library of video material smallest one preparing teachers for the senior for teaching/learning mathematics for use by secondary phase. In addition, all three trainees. All said that they have at least some institutions offer in-service courses. The computers with internet access but that these institutions offer training for between 820 and are rarely used by trainees. None reported 4500 trainees in total with an average of 1100 having any specialist software available for trainees in their first year. The largest of them teaching mathematics. employs about 185 tutors. Relatively few (up to 12) of these are specialists in mathematics and/ or mathematics education. The minimum qualification required for tutors is a first degree. The colleges preparing primary teachers require their tutors to have some teaching experience at the primary level. The other college also requires its tutors to have prior teaching experience. All three colleges said that their tutors are required to participate in some form of continuous professional development but none requires its tutors to periodically refresh their skills in a school environment or to undergo any form of periodic appraisal. During the initial three-year teacher training programme for primary school teachers, three to four hours per week are dedicated to the subject of mathematics. In all colleges, trainees are required to pass examinations at the end of their first year but the reported failure rates were extremely low (-3%). Whilst acknowledging that our sample is small and probably not representative, the responses to the attitudinal part of the questionnaire were not encouraging. None agreed that “teaching in primary schools is a highly respected profession” and all agreed that they faced difficulties in “attracting high quality applicants to train as teachers”. 167 A.5 Case study: Nigeria Table A.8: Nigeria: Country key facts Indicator Value Year Size (area): 910,770 km2 Population: 177.48 million 2014 Urban population growth (annual %) 4.5% 2014 GDP (current USD): USD 568.5 billion 2014 GDP growth (annual %) 6.3% 2014 GDP per capita (current USD) USD 3,203.3 2014 Expenditure on education as a % of GDP n.a. Expenditure on education as a % of total government expenditure n.a. Government expenditure per primary pupil (USD) n.a. Mobile cellular subscriptions (per 100 people) 78 2014 Internet users (per 100 people) 43 2014 Structure of education system (years primary + lower secondary + upper secondary) 6+3+3 School enrolment, pre-primary (% gross) 13% 2010 School enrolment, primary (% gross) 85% 2010 Primary completion rate, total (% of relevant age group) 76% 2010 School enrolment, secondary (% gross) 44% 2010 Ratio of girls to boys in primary and secondary education (%) 91% 2010 Pupil:teacher ratio in primary education (headcount) 37.6 2010 Pupil:teacher ratio in secondary education (headcount) 33.1 2010 Average number of pupils per mathematics textbook in primary education n.a. A.5.1 Primary mathematics ‘lesson signature’ In nearly all cases (96%) children had chairs or (Grades 3 and 6) benches to sit on and a hard surface on which to write. In general the lighting, temperature This description is based on 50 classroom and ventilation were adequate and the vast observations made in 25 schools. majority of classrooms (84%) were described as “cheerful and bright environments decorated Typically, the mathematics lessons observed with wall charts, etc“. Chalkboards were lasted for between 35 and 40 minutes. On available and used in nearly all classrooms average, 39 students were on the class register. (98%) and the majority of teachers (82%) had 168 their own copy of the textbook. In about a third About halfway through the lesson, most of cases (34-40%) measuring instruments and teachers (-80%) were still using the chalkboard concrete teaching aids for mathematics were and lecturing. However, most students (-80 of available. Very few classrooms (-5%) were cases) were copying problems from the equipped with any form of educational chalkboard and solving them in their exercise technology. However, in the rare cases where an books. Pair and group work was still rare. Once overhead projector or computer with projector again, we observed no significant bad were available, the teachers used them! Nearly behaviour or inattention. all pupils (-95%) had a pencil/pen and an exercise book. In nearly all cases, at least some At the end of the lesson, two-thirds of the of the pupils had a mathematics textbook. In teachers (68%) summarised the contents of the more than half (54%) most, if not all, had a lesson and the majority (82%) set a homework textbook. task. In general, the end of the lesson was as orderly as the beginning with, according to The start of each lesson was orderly and well observers, 88% having “a clear and structured. Nearly all teachers (> 94%) referred orderly end”. back to the previous lesson with a significant number (48%) handing back, or talking about, The overall impression was generally favourable. pupils’ homework. The vast majority of teachers The vast majority of teachers (92%) appeared (-90%) started by giving a clear description of to understand the concept they were teaching what the lesson was to be about. and were able to explain it to their classes with a significant number (42%) incorporating at About 15 minutes into the lesson the majority of least one ‘real life’ example. However, our teachers (-90%) were explaining the observers believe that they detected mathematical concept of interest by talking to mathematical errors or points which the their pupils (i.e. lecturing) and by writing on the teacher could not explain adequately in about a chalkboard. 40% were using some form of TLM quarter of the lessons observed (24%). to aid their explanation. In addition, they were Notwithstanding this, observers considered asking pupils questions and listening to their that in about three-quarters of the lessons the oral responses (76%). At this time, the majority majority of students not only understood what of pupils (86% of cases) were orally answering had been taught but had also enjoyed questions asked by the teacher and, in about the lesson. half of cases (48%), reciting their answers in unison. It was also very common (-80% of A.5.2 Secondary mathematics ‘lesson cases) for pupils to be invited to the board to signature’ (Grades 9, 10 and 11) answer a question whilst the rest of the class watched. It was rare (<15% of cases) to find This description is based on 20 classroom pupils working in pairs or groups. At this stage observations made in 10 schools. of the lesson, we observed very few cases where students were disrupting the lesson to Typically, a single mathematics lessons lasted any significant extent. for about 40 minutes. On average, 45 students were on the class register with 42 attending the lesson. In all cases pupils had chairs or benches 169 to sit on and a hard surface on which to write. blackboard (80%). Answering in chorus was In general the lighting, temperature and rarely observed during lessons at the secondary ventilation were adequate and the majority of level. It was rare (-15% of cases) to find pupils classrooms (85%) were described by observers working in pairs or groups, or handling/using as being bright and cheerful learning teaching and learning materials. environments. Chalkboards together with suitable drawing instruments were available in About halfway through the lesson, the all classrooms (100%). 80% of teachers had observed teaching pattern was largely their own copy of the textbook even though unchanged with most teachers (-90%) still only half used them during the lesson. In more using the chalkboard to explain the concept of than 60% of classrooms, concrete teaching aids interest and questioning pupils to judge their and other TLMs for Mathematics were available understanding. The vast majority of pupils were (note, however, that only one-third of teachers copying from the chalkboard (95% of cases) used them). However, no (0%) classroom was and/or attempting to solve problems in their equipped with any form of educational exercise books (95%). It was rare (10% of cases) technology i.e. overhead projectors, televisions, to find students working in pairs or groups. and computer projection equipment were not available. All, or nearly all, pupils had writing At the end of the lesson, nearly three-quarters materials. In all of the classrooms observed, at of the teachers (70%) summarised the contents least some pupils had a Mathematics textbook of the lesson and all (100%) set a homework and in 70% of cases all, or nearly all, had a task. In general, the end of the lesson was textbook. In three-quarters of classrooms at orderly with 85% having, according to least some pupils had calculators. observers, “a clear and orderly end”. The start of each lesson was, in general, orderly The overall impression was somewhat mixed. with all (100%) teachers giving a clear Nearly all teachers (95%) appeared to description of what the lesson was to be about. understand the concept they were teaching All teachers explicitly referred back to the but, in about one-third of cases (35%-45%), our previous lesson and a large number (70%) observers believed that they detected a handed back, or talked about, pupils’ homework. mathematical error or a problem in the teacher’s explanation. In addition, they judged About 15 minutes into the lesson the vast that students appeared to understand what had majority of teachers were explaining the been taught only in half (55%) of the mathematical concept of interest by writing on lessons observed. the chalkboard and lecturing to their pupils. About half (55%) used a concrete model or A.5.3 Teacher characteristics and attitudes other TLM to support their explanation. In addition, they were asking pupils questions and In Nigeria, attitudinal questionnaires were listening to their oral responses. At this time, completed by 40 teachers teaching at the the majority of pupils (95% of cases) were primary level and 30 teaching mathematics at orally answering questions asked by the teacher the senior secondary level. Most of the teachers and/or watching as others answered at the interviewed were more than 30 years old and were relatively experienced with the majority 170 (96%) having at least five years’ teaching teach any of the concepts required by experience. Prior to embarking on their pre- the curriculum. service training, 38% had studied up to the end of senior secondary school, 28% had completed When asked about the value of group work A-levels and 30% had gained a first degree. Of and/or pair work in the classroom, there was the secondary school teachers nearly half almost unanimous agreement that this was (47%) had gained a degree level qualification. “very important”. Similarly, the use of concrete practical equipment in the teaching/learning of At the primary level only a very small minority mathematics was considered to be very of our teachers (8%) are teaching in their important by 96% of teachers. It is interesting mother tongue. Most (80%) claim to be fluent to contrast what teachers say is important with in the language of instruction but a significant what they do in practice as described in the minority (12%) report that they themselves have lesson signatures above. some difficulty in the language in which they have to teach. About 40% of primary teachers Prior to teaching, the majority of our primary report that their pupils face difficulties due to teachers (66%) completed a three-year teacher the language of instruction. At the secondary training programme with a further 18% having level, 86% of teachers in our sample are followed a two-year course. The vast majority teaching in a language which is not their (80%) of our secondary teachers had three or mother tongue but, with few exceptions, they more years of initial teacher training. claim to be fluent in the language of instruction. Both primary and secondary school teachers in In order to judge the readiness of our teachers our sample displayed very positive attitudes to use educational technologies they were towards their pre-service training with typically asked about their ownership of mobile phones -90% agreeing or strongly agreeing with and the way they saw their own computer skills. statements such as: “My own mathematical All reported having a mobile phone and, of skills improved a lot as a result of my training”; these, 60% have smart phones with internet “My pre-service training left me well prepared access. One-fifth (21%) reported owning a PC, to teach mathematics”; and, “I enjoyed my laptop or tablet computer with internet access. pre-service training”. However, 80% also agreed Perhaps surprisingly, a large majority (80%) with the statement “nearly all my pre-service admitted that they either could not use a training was about improving my mathematical computer or that they considered themselves skills”. There was slightly less agreement when to be beginners with limited skills. it came to practice in the classroom. More than a third of our teachers (39%) agreed that in The primary school teachers in the survey their pre-service training they “did not get reported, with very few exceptions, that they enough practice teaching mathematics in were very well prepared, or at least partially the classroom”. prepared, to teach the required concepts of the basic mathematics curriculum. Not surprisingly, The table below summarises how the 70 the vast majority (-90%) of mathematics teachers in our survey responded to selected specialists teaching at the secondary level statements in our attitudinal questionnaire. This reported that they were very well prepared to raises several points of interest. First, it is 171 interesting to note that whilst there is a great curriculum and sometimes have to move on deal of consensus that, for example, “everyone before their pupils have mastered the current has the potential to be good at mathematics”, topic. Fourthly, nearly all mathematics teachers there is an equally strong feeling that “very few (96%) believe that more in-service support is pupils are naturally good at mathematics”. required if student achievement is to be Secondly, whilst teachers are very positive enhanced. Finally, these teachers in Nigeria are about their students’ attitude towards confident that computers and other mathematics and their progress, nearly educational technologies will help to improve everyone agrees that “most pupils need results in mathematics. This feeling appears to additional tutoring”. Thirdly, most teachers be stronger than in other, perhaps poorer, obviously feel under pressure to cover the countries where teachers have less faith syllabus and a significant minority (34%) feel in technology. that they do not have enough time to cover the Table A.9: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 49 19 1 0 0 (70%) (27.1%) (1.4%) (0%) (0%) Everyone has the potential to be good at mathematics. 22 29 11 8 0 (31.4%) (41.4%) (15.7%) (11.4%) (0%) You have to have the right sort of brain to be good at mathematics. 22 27 10 7 4 (31.4%) (38.6%) (14.3%) (10%) (5.7%) Very few pupils are naturally good at mathematics. 22 32 4 10 2 (31.4%) (45.7%) (5.7%) (14.3%) (2.9%) The current curriculum for mathematics is too difficult for my students. 2 10 9 32 17 (2.9%) (14.3%) (12.9%) (45.7%) (24.3%) My pupils are making good progress in mathematics. 20 44 6 0 0 (28.6%) (62.9%) (8.6%) (0%) (0%) Students seem to be interested in learning mathematics. 6 27 20 17 0 (8.6%) (38.6%) (28.6%) (24.3%) (0%) Most pupils need additional tutoring in mathematics. 31 34 1 1 1 (44.3%) (48.6%) (1.4%) (1.4%) (1.4%) We are under a lot of pressure to cover the syllabus so that pupils are ready 20 29 10 9 2 for examinations. (28.6%) (41.4%) (14.3%) (12.9%) (2.9%) Sometimes you have to move onto the next topic even if some pupils do 5 19 11 24 11 not understand the current topic. (7.1%) (27.1%) (15.7%) (34.3%) (15.7%) I have enough time to teach everything in the mathematics curriculum. 3 14 15 29 7 (4.3%) (20%) (21.4%) (41.4%) (10%) Teachers need more in-service support to improve the teaching of 46 21 2 0 0 mathematics in our schools. (65.7%) (30%) (2.9%) (0%) (0%) I regularly exchange ideas on how to teach mathematics with my fellow 27 32 8 2 1 teachers. (38.6%) (45.7%) (11.4%) (2.9%) (1.4%) Using computers and other new technologies in the classroom will improve 37 22 5 3 3 results in mathematics (52.9%) (31.4%) (7.1%) (4.3%) (4.3%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree. Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 172 A.5.4 Teacher Training Institutions pedagogical methods whilst the other claimed that content and methodology were given In Nigeria, questionnaires were completed by equal weight. In all colleges, trainees are representatives of three institutions for teacher required to pass examinations at the end of training – two preparing teachers for the their first year. Two colleges reported that at primary/junior secondary phase only, and one this point around 20% of students fail. All preparing teachers for the secondary phase. In respondents agreed with the statement “when addition, all three institutions offer in-service they start their courses most of our trainees courses. The institutions offer training for have inadequate knowledge of the school between 2,200 and 3,700 trainees in total with mathematics curriculum”. between 1,400 and 1,800 trainees in their first year. They employ between 115 and 380 tutors. The colleges in our study reported significant Relatively few (between 8 and 15) of these are deficiencies in terms of educational specialists in mathematics and/or mathematics technologies. None has a library of video education. The minimum qualification required material for teaching/learning Mathematics for for tutors is a first degree. The colleges use by trainees. Only one of the three reported preparing primary teachers require their tutors having computers with internet access available to have some teaching experience at the for use by trainees. All colleges in our sample primary level. The other college also requires its volunteered that they do not have adequate tutors to have prior teaching experience. All technical resources to teach their trainees how three colleges said that their tutors are required to use educational software in the classroom to participate in some form of continuous but that they do not use technology to a professional development. No college requires significant extent in their training. its tutors to periodically refresh their skills in a school environment. All colleges reported that trainee primary school teachers are typically aged 16-17 on admission. The minimum entry requirement is a qualification gained after four years of secondary education (i.e. equivalent to O-level). In all cases a pass in mathematics is required. All colleges reported being heavily oversubscribed in the current academic year with one saying that entry requirements have been raised in recent years. During the initial three-year teacher training programme for primary school teachers, at least five hours per week are dedicated to the subject of mathematics. Two colleges admitted that the majority of this time (>66%) is dedicated to mathematical content rather than 173 A.6 Case study: Rwanda Table A.10: Rwanda: Country key facts Indicator Value Year Size (area): 24,670 km2 Population: 11.34 million 2014 Urban population growth (annual %) 5.9% 2014 GDP (current USD): USD 7.89 billion 2014 GDP growth (annual %) 7% 2014 GDP per capita (current USD) USD 695.7 2014 Expenditure on education as a % of GDP 5% 2014 Expenditure on education as a % of total government expenditure 16.6% 2013 Government expenditure per primary pupil (USD) USD 45.5 2013 Mobile cellular subscriptions (per 100 people) 64 2014 Internet users (per 100 people) 11 2014 Structure of education system (years primary + lower secondary + upper secondary) 6+3+3 School enrolment, pre-primary (% gross) 14% 2013 School enrolment, primary (% gross) 134% 2013 Primary completion rate, total (% of relevant age group) 59% 2013 School enrolment, secondary (% gross) 33% 2013 Ratio of girls to boys in primary and secondary education (%) 103% 2013 Pupil:teacher ratio in primary education (headcount) 59.8 2013 Pupil:teacher ratio in secondary education (headcount) 22.8 2013 Average number of pupils per mathematics textbook in primary education 1.4 2012 A.6.1 Primary mathematics ‘lesson signature’ were on the class register with 40 attending the (Grades 3 and 6) lesson. In all cases (100%) children had chairs or benches to sit on and a hard surface on which This description is based on 53 classroom to write. In general the lighting, temperature observations made in 25 schools. and ventilation were adequate but a quarter of classrooms (25%) were too crowded to allow Typically, the mathematics lessons observed easy movement. In addition only two-thirds lasted for 40 minutes. On average, 44 students (68%) were described as “cheerful and bright 174 environments decorated with wall charts, etc“. good with no significant disruption of Chalkboards were available in all classrooms the lesson. (100%) and nearly all teachers (93%) had their own copy of the textbook. In the majority of About halfway through the lesson, the teaching classrooms (>66%) concrete teaching aids for pattern in many cases was largely unchanged mathematics were not visible. To all intents and but there were exceptions. More cases of purposes, none of classrooms was equipped students solving problems in their exercise with any form of educational technology i.e. books were noted (55%) and in 38% of lessons overhead projectors, televisions, and computer students were working in pairs or groups. Once projection equipment were not available. In again, we observed no significant only one classroom was an overhead projector bad behaviour. available but in that case the teacher did use it! All pupils (100%) had a pencil/pen and an At the end of the lesson, three-quarters (75%) exercise book. In the majority of classrooms of the teachers summarised the contents of the (53%) all or most of the students had a lesson and 42% set a homework task. mathematics textbook. According to observers, the vast majority of lessons (85%) had “a clear and orderly end”. The start of each lesson was orderly and well structured. All teachers referred back to the The overall impression was generally favourable. previous lesson and the vast majority (> 94%) All teachers (100%) appeared to understand started by giving a clear description of what the concept they were teaching and were able the lesson was to be about. In only 15% of cases to explain it to their classes. However, fewer did teachers hand back pupils’ homework or than a half (40%) incorporated ‘real life’ talk about a homework task. examples in their teaching. Whilst these things are difficult to judge, observers considered that About 15 minutes into the lesson our observers in nearly all lessons (>85%) the majority of noted a wide range of teacher and pupil students not only understood what had been activities (in sharp contrast with the taught but had also enjoyed the lesson. observations made in, for example, Uganda). Whilst a majority of teachers were lecturing A.6.2 Secondary mathematics ‘lesson their pupils (53%) and writing on the signature’ (Grades 9 and 11) chalkboard (66%), they were also setting tasks and moving around the classroom observing This description is based on 19 classroom and/or helping pupils (55%). At this time, pupils observations made in 10 schools. (>53% of cases) were engaged in answering questions asked by the teacher and in many Typically, the mathematics lessons observed cases watching while a classmate answered a lasted for 40 minutes but with some “double question on the board. Reciting answers in lessons” lasting for up to 100 minutes. On unison was not very common (21% of cases). It average, 34 students were on the class register was rare (<20% of cases) to find pupils working with 31 attending the lesson. In practically all in pairs or groups or handling/using teaching cases the learning environment was good with and learning materials. Pupil behaviour was sufficient space, chairs and desks, lighting and 175 ventilation. Three-quarters (74%) of classrooms About halfway through the lesson, the were described by observers as being bright observed teaching pattern was largely and cheerful learning environments. unchanged with most teachers (68%) still using Chalkboards were universally available and the chalkboard and lecturing to explain the almost all teachers (95%) had their own copy of concept of interest and/or set of problems for the textbook. In a minority of classrooms (26% their pupils. Many pupils were still copying from to 32%) some concrete teaching aids were the chalkboard (53% of cases) and/or visible. None (0%) of the classrooms was attempting to solve problems in their exercise equipped with any form of educational books (58% of cases). Pair or group work was technology i.e. overhead projectors, televisions, observed in a significant number of classrooms and computer projection equipment were not (42% of cases). available. All pupils (100%) had writing materials. In almost half (47%) of the At the end of the lesson, about three-quarters classrooms observed, all or most of the of the teachers (74%) summarised the contents students present had a mathematics textbook. of the lesson with about half (53%) setting a In over 40% of classrooms at least some pupils homework task. With very few exceptions, all had calculators. lessons had, according to observers, “a clear and orderly end”. The start of each lesson was, in general, orderly with all (100%) teachers giving a clear The overall impression was generally favourable. description of what the lesson was to be about. Nearly all teachers (90%) appeared to The vast majority (79%) also referred back to understand the concept they were teaching the previous lesson or an earlier associated and were, in general, able to present it to their topic. It was relatively rare (16%) for teachers to classes without any discernible errors. Only a be seen handing back homework or talking minority (16%) used ‘real life’ examples in their about it. teaching. Observers judged that in about 80% of lessons the majority of students not only About 15 minutes into the lesson the vast appeared to understand what had been taught majority of teachers were explaining the but also seemed to enjoy the lesson. mathematical concept of interest by writing on the chalkboard (79%) and lecturing to their A.6.3 Teacher characteristics and attitudes pupils (63%). In addition, they were asking pupils questions and listening to their oral In Rwanda, attitudinal questionnaires were responses. At this time, the majority of pupils completed by 52 teachers teaching at the (58% of cases) were copying from the primary level and 18 teaching mathematics at chalkboard and/or orally answering questions the senior secondary level. Of the primary asked by the teacher (63%). Answering by rote teachers, 39 (75%) were male and 13 (25%) was rarely observed during lessons at the were female. Of the secondary teachers, nine secondary level. In about a quarter (26%) of the (50%) were male and nine (50%) were female. cases observed there was some evidence of In both cases, there was a wide range of ages students working in pairs or small groups. from under 25 to 59. In the case of primary teachers there was also a wide range in their pre-service educational experience. 13% had only completed primary education; 35% had 176 completed junior secondary; 37% had to teach the required concepts of the basic completed senior secondary education. mathematics curriculum. Not surprisingly, the vast Somewhat surprisingly, the secondary school majority (-80%) of mathematics specialists teachers in our sample also displayed a wide teaching at the secondary level reported that they range of pre-service educational experience. were very well prepared to teach any of the Nine teachers (53%) reported that they had not concepts required by the curriculum. gone beyond the junior secondary level. The teachers in our sample were relatively When asked about the value of group/pair experienced with the majority (93%) having at work, and the use of practical equipment in the least three years’ teaching experience and 33% teaching/learning of mathematics, there was having more than 10 years. almost unanimous agreement that these aspects are “very important”. Fewer teachers At the primary level about a fifth (21%) of our (39%) felt that pupils working alone to solve teachers are teaching in their mother tongue. mathematical problems is “very important” with Most (65%) claim to be fluent in the language 15% suggesting that it is “not important”. It is of instruction but a significant minority (35%) interesting to contrast what teachers say is report that they themselves have some important with what they do in practice as difficulty in the language in which they have to described in the lesson signatures above. teach. About 40% of primary teachers report that their pupils face difficulties due to the Prior to teaching, the majority of our primary language of instruction. At the secondary level, teachers (75%) hsd completed a three-year only a minority (17%) are teaching in their teacher training programme. 78% of our mother tongue. Of the rest, half claimed to be secondary teachers had also followed a three- fluent in the language of instruction. However, year programme. 40% of teachers admitted that their command of the language of instruction presents them Both primary and secondary school teachers in with some difficulties. our sample displayed very positive attitudes towards their pre-service training with typically In order to judge the readiness of our teachers 80% agreeing or strongly agreeing with to use educational technologies they were statements such as: “My own mathematical asked about their ownership of mobile phones skills improved a lot as a result of my training”; and the way they saw their own computer skills. “My pre-service training left me well prepared 99% reported having a mobile phone and 61% to teach mathematics”; and, “I enjoyed my have smart phones with internet access. One- pre-service training”. However, about 70% also fifth (20%) said that they own a PC, laptop or agreed with the statement “nearly all my tablet computer with internet access. A pre-service training was about improving my significant majority (67%) admitted that they mathematical skills”. There was slightly less either could not use a computer or that they agreement when it came to practice in the considered themselves to be beginners with classroom. About a quarter of our teachers limited skills. (23%) agreed that in their pre-service training they “did not get enough practice teaching The primary school teachers in the survey, with mathematics in the classroom”. very few exceptions, reported that they were very well prepared, or at least partially prepared, 177 The table below summarises how the 70 good at mathematics. Secondly, whilst teachers teachers in our survey responded to selected are very positive about their students’ attitude statements in our attitudinal questionnaire. This towards Mathematics and their progress, the raises several points of interest. First, it is majority (79%) agree that “most pupils need interesting to note that whilst there is a great additional tutoring”. Thirdly, most teachers deal of consensus that “mathematical skills are obviously feel under pressure to cover the useful for everyone” there is less agreement syllabus and nearly half (47%) say that they when it comes to questions concerning the sometimes have to move on before their pupils potential/aptitude of learners. For example, have mastered the current topic. Fourthly, 27% of the teachers in our sample do not agree nearly all mathematics teachers (87%) believe with the statement “Everyone has the potential that more in-service support is required if to be good at mathematics” and 69% seem to student achievement is to be enhanced. think that you need a special sort of brain to be Table A.11: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 46 20 1 3 0 (65.7%) (28.6%) (1.4%) (4.3%) (0%) Everyone has the potential to be good at mathematics. 19 19 13 19 0 (27.1%) (27.1%) (18.6%) (27.1%) (0%) You have to have the right sort of brain to be good at mathematics. 24 24 5 8 5 (34.3%) (34.3%) (7.1%) (11.4%) (7.1%) Very few pupils are naturally good at mathematics. 19 28 4 16 2 (27.1%) (40%) (5.7%) (22.9%) (2.9%) The current curriculum for mathematics is too difficult for my students. 7 15 16 25 7 (10%) (21.4%) (22.9%) (35.7%) (10%) My pupils are making good progress in mathematics. 18 48 3 0 0 (25.7%) (68.6%) (4.3%) (0%) (0%) Students seem to be interested in learning mathematics. 20 40 8 2 0 (28.6%) (57.1%) (11.4%) (2.9%) (0%) Most pupils need additional tutoring in mathematics. 21 34 5 7 1 (30%) (48.6%) (7.1%) (10%) (1.4%) 22 We are under a lot of pressure to cover the syllabus so that pupils are ready 28 4 11 4 for examinations. (31.4%) (40%) (5.7%) (15.7%) (5.7%) Sometimes you have to move onto the next topic even if some pupils do 6 27 5 21 10 not understand the current topic. (8.6%) (38.6%) (7.1%) (30%) (14.3%) I have enough time to teach everything in the mathematics curriculum. 8 31 5 23 2 (11.4%) (44.3%) (7.1%) (32.9%) (2.9%) Teachers need more in-service support to improve the teaching of 41 25 2 1 0 mathematics in our schools. (58.6%) (35.7%) (2.9%) (1.4%) (0%) I regularly exchange ideas on how to teach mathematics with my fellow 31 37 1 0 0 teachers. (44.3%) (52.9%) (1.4%) (0%) (0%) Using computers and other new technologies in the classroom will improve 30 16 11 8 4 results in mathematics (42.9%) (22.9%) (15.7%) (11.4%) (5.7%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree. Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 178 A.6.4 Teacher Training Institutions (>66%) is dedicated to mathematical content rather than pedagogical methods and Questionnaires were completed by strategies. Trainees are required to spend time representatives of three institutions for teacher in schools observing and/or practising in each training – two preparing teachers for the year of their training. The length of this primary phase only, and one preparing teachers practicum varies but in the final year of the for both the primary and secondary phases. In course, trainees spend between 10-14 weeks in addition, all three institutions offer in-service schools. In all colleges, trainees are required to courses. The institutions varied in size offering pass examinations at the end of their first year training for between 670 and 5400 trainees in in order to continue their studies. total with between 215 and 900 trainees in their first year. They employ between 19 and 170 The colleges in our study reported significant tutors but relatively few of these are specialists deficiencies in terms of educational in mathematics and/or mathematics education. technologies. None had a library of video Indeed the largest college reported having just material for teaching/learning mathematics for nine mathematics specialists on its staff. The use by trainees and none had specialist minimum qualification required for tutors is a software for mathematics instruction for use by first degree. Somewhat surprisingly, none of the tutors or trainees. Computers with internet responding colleges said that their tutors are access were said to be available for use by required to have prior teaching experience. trainees. Two colleges volunteered that they do Equally surprisingly, two colleges said that their not have adequate technical resources to teach tutors are not required to participate in some their trainees how to use educational software form of continuous professional development. in the classroom and that they do not use No college requires its tutors to periodically technology (i.e. video, low-cost material, refresh their skills in a school environment. computer software applications, etc) to any great extent in their training. All colleges reported that trainee primary school teachers are typically aged 16 on admission. The minimum entry requirement is a qualification gained after four years of secondary education (i.e. equivalent to O-level). In two cases a pass in mathematics is required. One college reported being heavily oversubscribed in the current academic year with the others saying that the numbers of applicants was approximately equal to the number of available places. During the initial three-year teacher training programme for primary school teachers, between five and six hours per week are dedicated to the subject of mathematics. All colleges admitted that the majority of this time 179 A.7 Case study: Uganda Table A.12: Uganda: Country key facts Indicator Value Year Size (area): 241,550km2 Population: 38.84 million 2014 Urban population growth (annual %) 5% 2014 GDP (current USD): USD 26.31 billion 2014 GDP growth (annual %) 5% 2014 GDP per capita (current USD) USD 677.4 2014 Expenditure on education as a % of GDP 2.2% 2013 Expenditure on education as a % of total government expenditure 12.9% 2013 Government expenditure per primary pupil (USD) USD 33.7 2012 Mobile cellular subscriptions (per 100 people) 52 2014 Internet users (per 100 people) 18 2014 Structure of education system (years primary + lower secondary + upper secondary) 7+4+2 School enrolment, pre-primary (% gross) 11% 2013 School enrolment, primary (% gross) 107% 2013 Primary completion rate, total (% of relevant age group) 54% 2013 School enrolment, secondary (% gross) 27% 2013 Ratio of girls to boys in primary and secondary education (%) 99% 2013 Pupil:teacher ratio in primary education (headcount) 45.6 2013 Pupil:teacher ratio in secondary education (headcount) 21.3 2013 Average number of pupils per mathematics textbook in primary education 3.1 2011 SACMEQ III mean performance on the mathematics scale 481.9 2007 SACMEQ III proportion functionally innumerate (level 1 + level 2) 38.8% 2007 A.7.1 Primary mathematics ‘lesson signature’ chairs or benches to sit on and a hard surface (Grade 3 and 6) on which to write. In contrast, nearly a quarter of teachers (23%) did not have their own chair This description is based on 48 classroom and table. In general the lighting, temperature observations made in 24 schools. and ventilation were adequate but only three- quarters of classrooms (77%) were described as Typically, the mathematics lessons observed “cheerful and bright environments decorated lasted for 40 minutes. On average, 77 students with wall charts, etc“. Chalkboards were were on the class register with 66 attending the available and used in all classrooms (100%) but lesson. In nearly all cases (92%) children had teachers had few other resources at their 180 disposal. Most (63%) had their own copy of the About halfway through the lesson, the teaching textbook but in the majority of classrooms pattern was largely unchanged with most (>75%) concrete teaching aids for mathematics teachers (-90%) still using the chalkboard and were not visible. None (0%) of the classrooms oral questioning to explain the concept of was equipped with any form of educational interest and judge the understanding of pupils. technology i.e. overhead projectors, televisions, However, in 30% of lessons students were at and computer projection equipment were not this stage working in pairs or groups and/or available. Nearly all pupils (-85%) had a pencil/ using some form of learning aid. Once again, pen and an exercise book. In over three-quarters we observed no significant bad behaviour. (77%) of the classrooms observed, none of the students had a mathematics textbook. At the end of the lesson, fewer than half of the teachers (42%) summarised the contents of the The start of each lesson was orderly and well lesson but the majority (63%) did set a structured. Nearly all teachers (> 85%) referred homework task. In general, the end of the back to the previous lesson with a significant lesson was somewhat less orderly than the number (38%) handing back, or talking about, beginning with just about half (46%) having, pupils’ homework. The vast majority of teachers according to observers, “a clear and (> 90%) started by giving a clear description of orderly end”. what the lesson was to be about. The overall impression was generally favourable. About 15 minutes into the lesson the majority of The vast majority of teachers (96%) appeared teachers (-90%) were explaining the to understand the concept they were teaching mathematical concept of interest by talking to and were able to explain it to their classes with their pupils (i.e. lecturing) and by writing on the about half (54%) incorporating at least one ‘real chalkboard. In addition, they were asking pupils life’ example. Whilst these things are difficult to questions and listening to their oral responses. judge, observers considered that in about Without exception, the teachers were standing three-quarters of the lessons the majority of up and interacting with their pupils. At this students not only understood what had been time, the majority of pupils (88% of cases) were taught but had also enjoyed the lesson. orally answering questions asked by the teacher and, in three-quarters of cases, reciting their A.7.2 Secondary mathematics ‘lesson answers in unison. It was also common (-50% of signature’ (Grades 9 and 10) cases) for pupils to be invited to the board to answer a question whilst the rest of the class This description is based on 20 classroom watched. It was rare (<20% of cases) to find observations made in 10 schools. pupils working in pairs or groups or handling/ using teaching and learning materials. At this Typically, the mathematics lessons observed stage of the lesson, we observed no cases lasted for 40 minutes but with some “double where students were misbehaving and lessons” lasting for 80 minutes. On average, 74 disrupting the lesson to any significant extent. students were on the class register with 63 attending the lesson. In all cases pupils had chairs or benches to sit on and a hard surface on which to write. In contrast, nearly a half of 181 teachers (45%) did not have their own chair working in pairs or groups, or handling/using and table. In general the lighting, temperature teaching and learning materials. and ventilation were adequate but none of the classrooms (0%) was described by observers as About halfway through the lesson, the being bright and cheerful learning observed teaching pattern was largely environments. Chalkboards were available and unchanged with most teachers (-90%) still used in all classrooms (100%) but teachers had using the chalkboard to explain the concept of few other resources at their disposal. About a interest and questioning pupils to judge their half (45%) had their own copy of the textbook understanding. The majority of pupils were but in the vast majority of classrooms (95%) copying from the chalkboard (80% of cases) concrete teaching aids for mathematics were and/or attempting to solve problems in their not visible. None (0%) of classrooms was exercise books (95%). It was rare (10% of cases) equipped with any form of educational to find students working in pairs or groups. technology i.e. overhead projectors, televisions, and computer projection equipment were not At the end of the lesson, about half of the available. All pupils (100%) had writing teachers (55%) summarised the contents of the materials. In almost half (45%) of the lesson and the majority (70%) set a homework classrooms observed, none of the students had task. In general, the end of the lesson was a mathematics textbook. In nearly three- somewhat less orderly than the beginning with quarters of classrooms at least some pupils just about half (55%) having, according to had calculators. observers, “a clear and orderly end”. The start of each lesson was, in general, orderly The overall impression was generally favourable. but perhaps less well-structured than those All teachers (100%) appeared to understand observed in the primary grades. Only 60% of the concept they were teaching and were, in teachers explicitly referred back to the previous general, able to explain it to their classes. Only lesson and only a minority (30%) handed back, a minority (30%) used ‘real life’ examples in or talked about, pupils’ homework. However, their teaching. All teaching appeared to be the vast majority of teachers (> 95%) started by directed at the whole class with no evidence of giving a clear description of what the lesson teachers working with individual pupils. was to be about. Observers judged that in about 80% of lessons the majority of students not only appeared to About 15 minutes into the lesson the vast understand what had been taught but also majority of teachers were explaining the seemed to enjoy the lesson. mathematical concept of interest by writing on the chalkboard and lecturing to their pupils. In A.7.3 Teacher characteristics and attitudes addition, they were asking pupils questions and listening to their oral responses. At this time, In Uganda, attitudinal questionnaires were the majority of pupils (>60% of cases) were completed by 50 teachers teaching at the orally answering questions asked by the teacher primary level and 20 teaching mathematics at and/or solving problems in their exercise books the senior secondary level. Of the primary or on paper. Answering by rote was rarely teachers, 34 (68%) were male and 16 (32%) observed during lessons at the secondary level. were female. Of the secondary teachers, 18 It was rare (<10% of cases) to find pupils (90%) were male and only two (10%) were 182 female. In both cases, most of the teachers specialists teaching at the secondary level interviewed were aged 30 to 39 years. Prior to reported that they were very well prepared to embarking on their pre-service training, the a teach any of the concepts required by majority of primary school teachers (78%) had the curriculum. completed senior secondary education. Of the secondary school teachers 65% had completed When asked about the value of group work A-levels or some other post-secondary study and/or pair work in the classroom, there was and a further 25% had gained a degree level almost unanimous agreement that this was qualification. The teachers in our sample were “very important”. Similarly, the use of concrete relatively experienced with the majority (93%) practical equipment in the teaching/learning of having at least three years’ teaching experience mathematics was considered to be very and 39% having more than 10 years. important by 90% of teachers. Fewer teachers (21%) felt that pupils working alone to solve At the primary level only a small minority of mathematical problems was “very important”. It teachers (16%) are teaching in their mother is interesting to contrast what teachers say is tongue. Most (72%) claim to be fluent in the important with what they do in practice as language of instruction but a significant described in the lesson signatures above. minority (12%) report that they themselves have some difficulty in the language in which they Prior to teaching, the majority of our primary have to teach. About half of primary teachers teachers (78%) completed a two-year teacher (52%) report that their pupils face difficulties training programme. 35% of our secondary due to the language of instruction. At the teachers also followed a two-year programme, secondary level, 95% of teachers are teaching in but the majority (55%) had three or more years a language which is not their mother tongue of initial teacher training. but, almost without exception, they claim to be fluent in the language of instruction. Both primary and secondary school teachers in our sample displayed very positive attitudes In order to judge the readiness of our teachers towards their pre-service training with typically to use educational technologies they were 80% agreeing or strongly agreeing with asked about their ownership of mobile phones statements such as: “My own mathematical and the way they saw their own computer skills. skills improved a lot as a result of my training”; 99% reported having a mobile phone but only “My pre-service training left me well prepared 50% have smart phones with internet access. to teach mathematics”; and, “I enjoyed my Only 13% said that they own a PC, laptop or pre-service training”. However, about three- tablet computer with internet access. A large quarters (78%) also agreed with the statement majority (81%) admitted that they either could “nearly all my pre-service training was about not use a computer or that they considered improving my mathematical skills”. There was themselves to be beginners with limited skills. slightly less agreement when it came to practice in the classroom. About a quarter of The primary school teachers in the survey, with our teachers (27%) agreed that in their pre- very few exceptions, reported that they were service training they “did not get enough very well prepared, or at least partially practice teaching mathematics in prepared, to teach the required concepts of the the classroom”. basic mathematics curriculum. Not surprisingly, the vast majority (-80%) of mathematics 183 The table below summarises how the 70 majority (66%) agree that “most pupils need teachers in our survey responded to selected additional tutoring”. Thirdly, most teachers statements in our attitudinal questionnaire. This obviously feel under pressure to cover the raises several points of interest. First, it is syllabus and a significant minority (>35%) feel interesting to note that whilst there is a great that they do not have enough time to cover the deal of consensus that, for example, “everyone curriculum and sometimes have to move on has the potential to be good at mathematics”, before their pupils have mastered the current there is less agreement when it comes to the topic. Fourthly, nearly all mathematics teachers statement “very few pupils are naturally good (87%) believe that more in-service support is at mathematics”. Secondly, whilst teachers are required if student achievement is to be very positive about their students’ attitude enhanced. towards mathematics and their progress, the Table A.13: Teacher responses to selected statements using a five-point Likert scale Indicator SA A N D SD Mathematical skills are useful for everyone. 63 7 0 0 0 (90%) (10%) (0%) (0%) (0%) Everyone has the potential to be good at Mathematics. 21 32 7 9 1 (30%) (45.7%) (10%) (12.9%) (1.4%) You have to have the right sort of brain to be good at Mathematics. 23 19 6 17 5 (32.9%) (27.1%) (8.6%) (24.3%) (7.1%) Very few pupils are naturally good at Mathematics. 14 22 6 20 7 (20%) (31.4%) (8.6%) (28.6%) (10%) The current curriculum for Mathematics is too difficult for my students. 4 7 10 38 11 (5.7%) (10%) (14.3%) (54.3%) (15.7%) My pupils are making good progress in Mathematics. 17 46 3 4 0 (24.3%) (65.7%) (4.3%) (5.7%) (0%) Students seem to be interested in learning Mathematics. 8 47 12 2 0 (11.4%) (67.1%) (17.1%) (2.9%) (0%) Most pupils need additional tutoring in Mathematics. 12 37 9 11 1 (13.1%) (52.9%) (12.9%) (15.7%) (1.4%) We are under a lot of pressure to cover the syllabus so that pupils are ready 13 36 5 10 6 for examinations. (18.6%) (51.4%) (7.1%) (14.3%) (8.6%) Sometimes you have to move onto the next topic even if some pupils do 5 24 6 23 12 not understand the current topic. (7.1%) (34.3%) (8.6%) (32.9%) (17.1%) I have enough time to teach everything in the Mathematics curriculum. 4 29 12 21 4 (5.7%) (41.4%) (17.1%) (30%) (5.7%) Teachers need more in-service support to improve the teaching of 28 33 7 2 0 Mathematics in our schools. (40%) (47.1%) (10%) (2.9%) (0%) I regularly exchange ideas on how to teach Mathematics with my fellow 41 24 1 2 2 teachers. (58.6%) (34.3%) (1.4%) (2.9%) (2.9%) Using computers and other new technologies in the classroom will improve 20 30 10 7 3 results in Mathematics (28.6%) (42.9%) (14.3%) (10%) (4.3%) SA = strongly agree; A = agree; N = neither agree nor disagree; D = disagree; SD = strongly disagree. Note: Percentages may not add to 100% due to teachers who chose not to respond to a particular statement (i.e. ‘missing’ responses). 184 A.7.4 Teacher Training Institutions During the initial teacher training programme (two years for primary school teachers and In Uganda, questionnaires were completed by three for secondary school mathematics representatives of three government specialists) a significant amount of time is institutions for teacher training – two preparing dedicated to the subject of mathematics - at teachers for the primary phase and one least five hours per week for the duration of the preparing mathematics teachers for the course. Two colleges admitted that the majority secondary phase. In addition, all three of this time (>66%) is dedicated to institutions offer in-service courses. The mathematical content rather than pedagogical institutions varied in size offering training for methods and strategies. One college said that between 400 and 1,000 trainees in total with their programme struck a balance between between 160 and 530 trainees in their first year. content and methodology. Trainees are required They employ between 22 and 62 tutors but to spend time in schools observing and/or relatively few are specialists in mathematics practising in each year of their training. The and/or mathematics education. Indeed the length of this practicum varies from four to nine smallest college reported having just one weeks per year. In two colleges, trainees are mathematics specialist on its staff. The required to pass examinations at the end of minimum qualification required for tutors is a their first year in order to continue their studies. first degree. In addition, tutors are required to However reported failure rates are low (<5%). have some teaching experience but not necessarily at the primary level. Tutors in all the The colleges in our study reported significant colleges in our sample are required to deficiencies in terms of educational participate in professional development technologies. None had a library of video courses, but no college requires its tutors to material for teaching/learning mathematics periodically refresh their skills in a which could be used by trainees. Computers school environment. with internet access were available and regularly used by trainees, but specialist Colleges reported that their trainees are aged software for mathematics instruction was not between 18 and 21 on admission. One college available. All colleges volunteered that they did preparing primary teachers required a minimum not have adequate technical resources to teach of O-level (i.e. a qualification gained after four their trainees how to use educational software years of secondary education) while the other in the classroom. They also admitted that they had raised its entry requirement to a minimum did not use technology (i.e. video, low-cost of A-level (i.e. the qualification gained after six material, computer software applications, etc) years of secondary education). In all cases a to any great extent in their training. pass in mathematics is required. All three colleges reported that in the current academic year they were heavily oversubscribed and so had to reject many applicants. That having been said, they also reported that they face problems attracting high quality applicants to train as teachers. 185 186 Mathematics Education in Sub-Saharan Africa: Appendix B. References Adu-Yeboah, C., 2011. Learning to Teach Reading Altinok, N. and Kingdon, G., 2009. New and Mathematics and Influences on Practice: A Evidence on Class Size Effects: A Pupil Fixed Study of Teacher Education in Ghana. Centre for Effects Approach. Centre for the Study of International Education, University of Sussex. 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Available at: http://documents. worldbank.org/curated/ en/2014/09/20240847/decade-development- sub-saharan-african-science-technology- engineering-Mathematics-research [Accessed 17 December 2015]. 205 Cambridge Education, 22 Station Road, Cambridge CB1 2JD, United Kingdom T +44 (0)1223 463500 F +44 (0)1223 461007 W www.camb-ed.com This report and the corresponding overview were prepared by Cambridge Education for the World Bank, with George Bethell as the author. It was commissioned by Sukhdeep Brar and supervised by Ryoko Tomita (World Bank)