Free download from www.hsrcpress.ac.za Researching mathematics education in South Africa perspectives, practices and possibilities Edited by Renuka Vithal, Jill Adler & Christine Keitel Free download from www.hsrcpress.ac.za Published by HSRC Press Private Bag X9182, Cape Town, 8000, South Africa www.hsrcpress.ac.za First published 2005 © 2005 Human Sciences Research Council All rights reserved No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers ISBN 7969 2047 Cover design by FUEL Design Design and typesetting by Christabel Hardacre Production by comPress Distributed in Africa by Blue Weaver Marketing and Distribution PO Box 30370, Tokai, Cape Town, 7966, South Africa Tel: +27 +21-701-4477 Fax: +27 +21-701-7302 email: orders@blueweaver.co.za Distributed worldwide, except Africa, by Independent Publishers Group 814 North Franklin Street, Chicago, IL 60610, USA www.ipgbook.com To order, call toll-free: 1-800-888-4741 All other inquiries, Tel: +1 +312-337-0747 Fax: +1 +312-337-5985 email: Frontdesk@ipgbook.com Free download from www.hsrcpress.ac.za Contents Preface v List of acronyms vii Part I: Research, curriculum innovation and change Mathematics curriculum research: roots, reforms, reconciliation and relevance Renuka Vithal and John Volmink Towards a framework for developing and researching groupwork in mathematics classrooms 28 Karin Brodie and Craig Pournara Mathematics education and language: policy, research and practice in multilingual South Africa 73 Mamokgethi Setati Teachers’ assessment criteria in school mathematics 110 Cassius Lubisi Ethnomathematics research in South Africa 133 Paul Laridon, Mogege Mosimege and David Mogari Part II: Researching teacher education: diverse orientations, merging messages Holding the past, living the present and creating a future: trends and challenges in research on mathematics teacher education 163 Jill Adler Pre-service mathematics teacher education: building a future on the legacy of apartheid’s colleges of education 183 Anandhavelli Naidoo Free download from www.hsrcpress.ac.za Dilemmas in the design of in-service education and training for mathematics teachers 206 Mellony Graven Dilemmas of change: seeing the complex rather than the complicated? 233 Chris Breen Part III: Psychological, sociological and historical research and perspectives 10 Examining understanding in mathematics: a perspective from concept mapping 249 Willy Mwakapenda 11 Knowledge and pedagogy: sociological research in mathematics education in South Africa 281 Paula Ensor and Jaamiah Galant 12 A history of mathematics education research in South Africa: the apartheid years 307 Bheki Khuzwayo Afterword Reflections on mathematics education research in South Africa 329 Christine Keitel Appendix: List of SAARMSE/SAARMSTE Proceedings, 1992–2004 345 About the authors 347 Index 350 Free download from www.hsrcpress.ac.za Preface The mathematics education research community in South Africa has grown markedly over the past decade Key educational concerns have been subjected to systematic study and, increasingly, researchers have become established nationally and internationally The papers brought together in this book capture some of this growth in mathematics education research in South Africa – in both human and knowledge resource terms The authors of the various chapters are located across a range of institutional settings and they address a healthy diversity of interest and concerns While many of the issues raised are resonant with issues in the wider field, each chapter, in one way or another, brings the specificity of the South African context to the fore, and so shapes the questions asked and illuminates the problems studied in particular ways In bringing together these discussions of research issues in this book, we hope, indeed intend, that we have produced a collection that will be not only a resource for graduate students, and those involved in research and policy development and implementation in South Africa, but will also be of value in the wider international field of mathematics education research What this book has come to be and represent is also a function of how it came into being The idea for the book emerged some time ago, at the University of Durban-Westville (UDW), when the Faculty of Education developed a proposal in support of Professor Christine Keitel for the (National Research Foundation) NRF-Humboldt scholarship Christine Keitel is well known for bringing collections of research together into handbooks that have enabled the growth of the international mathematics education community Her expertise in assisting the community here to collect developing experience into a resource for wider dissemination was one key contribution identified as something that she could offer, should she win the award And she did The NRF-Humboldt scholarship is a prestigious award, and this was the first time it was made not only to a Faculty of Education, but also to a historically disadvantaged university Christine’s input in the conceptualisation of this book and her assistance in its coming to fruition have been a v R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A critical part of its development We have all benefited from the time Christine has spent in South Africa as a result of the award, and these benefits have extended beyond UDW and the development of this book Free download from www.hsrcpress.ac.za A first step in its development, and indeed one of the first tasks that Christine undertook on her visit here, was a review of all the conference proceedings of the Southern African Association for Research in Mathematics and Science Education (SAARMSE) and which later became the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE) as a means of beginning to conceptualise a book about research in mathematics education in South Africa Some of her reflections on this task are captured in the Afterword to this collection, as an outsider’s perspective on South African mathematics education research Her initial thinking, however, formed the basis for conversations between us as co-editors and enabled us to generate an overall conception for a book and so start the process of soliciting papers We simultaneously sent out a call (extending here as widely as possible), and invited particular people to respond to the call The rest is history The authors who, over time, developed and reworked chapters have not only contributed to the realisation of this initial goal, but each has been enormously patient with a process that has taken longer than we had initially hoped We thank you! As editors, our task was to work to shape a book, to construct an overall coherence across diverse chapters, while enabling individual researchers and their diverse interests, styles and orientations to come to the fore We trust we have done justice to this dual task The publishing of academic texts is a financially fraught undertaking, here and elsewhere We were, however, determined that the book be published here, carrying a South African stamp on all its features This book appears through a generous grant from the National Research Foundation for its origination costs, and thanks to the interest of the Human Sciences Research Council in seeing such work come to be part of the public domain We are most grateful to both these organisations In particular, we thank Beverly Damonse for her vision and response from the NRF, and John Daniel and Garry Rosenberg of the HSRC Renuka Vithal Jill Adler Christine Keitel vi Free download from www.hsrcpress.ac.za List of acronyms ACE ALLE AMESA ANC C2005 CNE DET FDE FLLE FP ICME INSET LOlT MATIP MDM ME MEP MES MLMMS NCS NCTM NECC NED NEPI NETF OBE OE ORPF PDME Advanced Certificate in Education additional language learning environments Association of Mathematics Education in South Africa African National Congress Curriculum 2005 Christian national education Department of Education and Training (South Africa, pre-1994) Further Diploma in Education foreign language learning environments fundamental pedagogics International Congress of Mathematics Education in-service education and training language of learning and teaching Mathematics Teacher In-service Training Project mass democratic movement mathematical English Mathematics Education Project Mathematics Education Society mathematical literacy, mathematics and mathematical sciences National Curriculum Statement National Council of Teachers of Mathematics National Education Co-ordinating Committee Natal Education Department (South Africa, pre-1994) National Education Policy Investigation National Education Training Forum outcomes-based education ordinary English official pedagogic recontextualising fields people’s education for people’s power vii political dimensions of mathematics education Programme for Leader Educators in Senior-phase Mathematics Education PME psychology of mathematics education PRESET pre-service education and training RADMASTE Centre for Research and Development in Mathematics, Science and Technology Education RIEP Research Institute for Educational Planning SAARMSE Southern African Association for Research in Mathematics and Science Education SAARMSTE Southern African Association for Research in Mathematics, Science and Technology Education TE teacher education TIMSS Third International Mathematics and Science Study URPF unofficial pedagogic recontextualising fields ZPD zone of proximal development Free download from www.hsrcpress.ac.za PEPP PLESME viii Free download from www.hsrcpress.ac.za Part I Research, curriculum innovation and change Free download from www.hsrcpress.ac.za R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Mutimucuio IV (ed) (2001) Proceedings of the ninth annual conference of the Southern African Association for Research in Mathematics, Science and Technology Education Volume & Volume Maputo, 17–20 January Free download from www.hsrcpress.ac.za Malcolm C & Lubisi C (eds) (2002) Proceedings of the tenth annual conference of the Southern African Association for Research in Mathematics, Science and Technology Education University of Natal, 22–26 January Putsoa B, Dlamini B, Dlamini M & Kelly V (eds) (2003) Proceedings of the eleventh annual conference of the Southern African Association for Research in Mathematics, Science and Technology Education Volume & Volume Waterford-KaMhlaba, Swaziland, 11–15 January Buffler A & Laugksch RC (eds) (2004) Proceedings of the twelfth annual conference of the Southern African Association for Research in Mathematics, Science and Technology Education University of Cape Town, 13–17 January 346 Free download from www.hsrcpress.ac.za About the authors Professor Jill Adler holds the Chair of Mathematics Education in the School of Education at the University of the Witwatersrand and presently serves as vice-president of the International Congress of Mathematical Instruction (ICMI) Her research interests are in the broad field of mathematics teacher education and specifically in teaching and learning in multilingual classrooms She is also a member of the South African research team of the ‘Learners’ Perspective Study’ Professor Chris Breen is an associate professor in mathematics education at the University of Cape Town, where he also directed the Mathematics Education Project (MEP) His present research interests are adults’ fear of mathematics, researching one’s own practice, and enactivism as a theory of learning and an alternative framework of research Ms Karin Brodie teaches education and mathematics education in the School of Education at the University of the Witwatersrand She is currently a doctoral student at Stanford University, where she is involved in a project studying the differences between reform and traditional mathematics curricula Her research interests include learner-centred mathematics teaching Professor Paula Ensor is associate professor in mathematics education in the School of Education at the University of Cape Town Her research interests are in the sociology of education, especially in relation to curriculum and pedagogy She also publishes in teacher education and higher education studies Ms Jaamiah Galant worked as a mathematics educator at the Mathematics Education Project (MEP) Schools Development Unit at the University of Cape Town, where she was involved in mathematics teacher development and materials development Currently she is a senior researcher at the Centre for Interdisciplinary Studies at Stellenbosch University, focusing on research in higher education 347 R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Free download from www.hsrcpress.ac.za Dr Mellony Graven is a lecturer in the School of Education at the University of the Witwatersrand, where she works in post-graduate mathematics education courses and does in-service work with the Centre for Research and Development in Mathematics Science and Technology Education (RADMASTE) She has been involved in a longitudinal study on the nature of mathematics teacher learning Professor Christine Keitel is professor of mathematics education in the Department of Education and Psychology at the Freie Universität in Berlin She has a broad range of research interests including studies on political and socio-cultural aspects of mathematics education, mathematical literacy, gender and internationalisation and globalisation, with a special focus on international comparative studies in mathematics education She is the German research team leader of the ‘Learners’ Perspectives Study’ Dr Herbert Bheki Khuzwayo is a lecturer in the Faculty of Education at the University of KwaZulu-Natal teaching mathematics education to both under-graduate and post-graduate students His current research interest is in the history of mathematics teaching and learning, and he is also a member of the research team of the ‘Learners’ Perspective Study’ Professor Paul Laridon is currently a director of the Centre for Research and Development in Mathematics Science and Technology Education (RADMASTE) at the University of the Witwatersrand His research interests focus mainly on curriculum and include ethnomathematics, assessment and mathematical literacy Dr Cassius Lubisi was based in the School of Education at the University of KwaZulu-Natal before he joined the Department of Education (DoE) as special advisor to the Minister in 2003 He currently serves as deputy general of General Education and Training in the DoE His research interests include teacher assessment and curriculum change Dr David Mogari is a senior lecturer in mathematics education at the University of Venda for Science and Technology His research interests include ethnomathematics, teacher education and mathematics teaching and learning 348 Free download from www.hsrcpress.ac.za ABOUT THE AUTHORS Dr Mogege Mosimege is based in the national Department of Science and Technology as Manager: Indigenous Knowledge Systems His research interests include ethnomathematics, socio-cultural issues in mathematics education, teacher education and intellectual property rights Dr Willy Mwakapenda is a lecturer in mathematics education at the University of the Witwatersrand His research interests include contextualisation in mathematics education, and researching possibilities for change in teaching and learning as a consequence of changes in the mathematics curriculum Professor Anandhavelli Naidoo is dean of the Faculty of Education at the Univesity of Port Elizabeth Currently her research interests include mathematics education and students’ academic writing Mr Craig Pournara works in the College of Education at the University of the Witwatersrand, where he is involved in pre-service mathematics teacher education He develops mathematics courses for teacher education programmes and is specifically interested in learners’ thinking in the areas of trigonometry and functions Dr Mamokgethi Setati is associate professor in mathematics education in the School of Education at the University of the Witwatersrand Her main research interest is in discursive practices in mathematics teaching and learning in multilingual classrooms Dr Renuka Vithal is associate professor in the School of Educational Studies (Westville Campus), at the University of KwaZulu-Natal, where she coordinates the doctoral programme Her research interests include educational research and mathematics teacher education, with a special focus on social, cultural and political perspectives in mathematics education She is the South African research team leader of the ‘Learners’ Perspective Study’ Professor John Volmink is pro vice-chancellor and director of the KwaZuluNatal University Development Fund and has also been involved in the leadership of the Centre for the Advancement of Science and Mathematics Education (CASME) at the University of KwaZulu-Natal His research interests include mathematical curricular reforms, mathematical literacy and adult education 349 Free download from www.hsrcpress.ac.za Index A action research 166, 174, 176 additional language learning environment (ALLE) 95 procedural discourse 102 Afrikaans as the medium of instruction 75, 315 Anglo-American influence 339–340, 341 anti-intellectualism and education policy 334 apartheid education 9, 31–32, 163, 183, 184, 284 inequalities in 12, 310, 315, 342 mathematics 307–325 mathematics education research 329 ‘occupation of our minds’ 323–325 apprenticeship into mathematics 293–294, 297–298, 302 assessment criteria see mathematics assessment criteria Association for Mathematics Education of South Africa (AMESA) 133, 216, 282, 321 B Bantu Education 12, 310 language of learning and teaching 75 Bantu Education Act 309–310 behaviourism 5, 6, 10 ‘best practice’ 224, 236, 239, 243, 296, 298 350 bilingual classroom 90, 95–96 mathematics achievement in 89–90 in urban context 90 see also multilingual classroom; language of learning and teaching C Christian National Education 5, 184 classification of symbolic systems 288 classroom culture 50–51, 52, 53 classroom practice 190, 198–199, 234, 237 recontextualisation 294–297 teacher-learner interaction 192–193 code-switching 56, 91–98 criticism of 92 definition 91 socio-political aspects 97–98 uses of 93–94 see also multilingual classroom cognitive assessment criteria see mathematics assessment criteria cognitive conflict 39, 51, 54 collaborative approach to groupwork 36, 39–41, 50–54, 60 see also groupwork colleges of education 183 and constructivism 187–189 didactics syllabus 187 and Fundamental Pedagogics 186–187 lecturers’ qualifications 186–187 Free download from www.hsrcpress.ac.za INDEX Committee on Teacher Education Policy 200 community of practice 214–217 complexity theory 233, 238–243 concept maps analysis of 256–269, 270 definition of 253 examples of student 258, 260, 265, 266 follow-up interview 256–269, 270, 273 and mathematics 254, 269–273 as a methodological tool 249–274 use of 253 see also mathematical concepts constructivism 6, 7, 25, 200–203, 330 challenge to 300 in colleges of education 187–189 limitations of 7, 120–121 as a method 188–189 in post-apartheid South Africa 201–202 see also socio-cultural constructivism co-operative approach to groupwork 36–38, 48–50, 60 see also groupwork criterion-referenced assessment see mathematics assessment criteria criterion-referencing democratic paradox of 126–127 critical mathematics education 7, 45–46, 136 cross-curricular themes 290 cultural models 100–101 culture definition 134 and mathematics 135, 316–320, 338 see also ethnomathematics; sociocultural research curriculum classification of 288 see also mathematics curriculum Curriculum 2005 (C2005) 10, 11, 15, 76–77, 284, 335, 338 assessment 124 cascade training model 212 characteristics of 32 cross-subject integration 290–291 outcomes 77, 110, 128–129 relevance of content 285 and sociology of education 290–291 and teachers’ role 48–59, 221 curriculum critique 290–291 curriculum reform 13–17 and ideology 16–17 see also mathematics curriculum; Curriculum 2005 D De Lange Commission 9, 315–316 mathematics sub-committee 315–316 developing countries access to mathematics 331 discourses 302 vertical/horizontal 286, 289 see also mathematics discourse distance education 237 diversity in education 31, 44–46 E economics education education policy and business 341–342 reform 17–25, 233 and research 17–25 Education Renewal Strategy 351 R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Free download from www.hsrcpress.ac.za enactivism 240, 242, 243 English language as second language 318 ordinary English/mathematical English 78–82 status of 75–76, 99, 101 see also language; language of learning and teaching ethnomathematics 7, 133–155 and academic mathematics 135, 138–139 and access to the curriculum 139–140, 145 and critical mathematics education 136 and cultural artefacts 137, 141–146 Curriculum 2005 154–155 definition 135 dilemmas in 137–140 and games 137, 146–154 and geometry 143–146, 149–150 and language 153–154 learners’ attitude 139–140, 146, 154 learners’ performance 145–146, 154 mentoring 138 National Curriculum Statement 155 pedagogy 136, 138 RADMASTE Ethnomathematics Project 137, 140, 146, 154 research 133-155 research methodology 140–141, 150–152 socio-cultural constructivism 136 String Figure Gates (Malepa) 149–154 teachers’ attitude 138–139, 145, 146, 154 wire cars 143–146 352 Euro-centrism 331, 339 European Research in Mathematics Education 166 F foreign language learning environment (FLLE) 95 formalism framing of symbolic systems 288 Fundamental Pedagogics 5, 138, 184–186, 198, 199 Christian National Education 184–185 colleges of education 186–187 indoctrination 313 lesson structure 314 learners’ role 314 and mathematics education 313–315 need for change 199–120 teacher-pupil relationship 185 Further Diploma in Education 237 further education and training (FET) and mathematical literacy 11, 17 G games and culture 147–148 and pedagogy 298 general education and training (GET) and mathematical literacy 11, 17 globalisation and mathematics 8, 341–342 groupwork 28-65 approaches to 35–48, 60 classroom culture 50–51, 52, 57 cognitive conflict 39–40, 51, 54–55 curriculum 2005 30–33 definitions of 35–36 diversity issues 44–45, 57–58 Free download from www.hsrcpress.ac.za INDEX form/substance distinction 33 future research 64–65 goals 34 language of communication 42–44, 56 learner achievement 59, 61–63 limitations of 38, 39 means/end distinction 34–35 purpose of 34–35 report-backs 56–57 research on 59–63, 64–65 selection of tasks 37, 38, 40–41, 45–46, 51, 60 teachers’ role 48–60, 63–64 theory of learning 60 H higher education restructuring of 184, 236 ‘homelands’ mathematics teachers in 319–320 Human Sciences Research Act 312 Human Sciences Research Council analysis of reports 299–300 mandate of 312 I in-service education and training (INSET) 166, 168, 169, 170–172, 235–238 access to resources 228 curriculum reforms 211 classroom vs workshop 212–213 community of practice 226 design dimensions of 206–228 funding for 172 life-long learning 222–225, 227 long-term vs short-term 211–213, 226 professional identity 172, 227 recontextualisation 294–297 ‘teacher as person’ 238, 240 teacher change 172, 222–225 teacher-in-context 241, 242 see also Programme for Leader Educators in Senior-phase Mathematics Education (PLESME) integrated curriculum International Congress of Mathematics Education (ICME) 331 J journal writing analysis of 298–299 as pedagogy 234 K knowledge 290 forms of 286–287, 289 integration of 287 recontextualisation of 286 transfer of 286 see also mathematical knowledge L language and Curriculum 2005 77 diversity see multilingual classroom and mathematics education 73–104 and National Curriculum Statement 77 socio-political role of 97, 98, 99–103 see also English language; language of learning and teaching; multilingual classroom Language in Education Policy (LiEP) 74–76, 77, 93, 103 353 R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Free download from www.hsrcpress.ac.za language of learning and teaching (LoLT) 42–44, 73, 84 ANC policy 75 dominance of English 75–76, 89, 94–95, 99, 103 historical background 74–75 socio-political aspects 99–103 see also English language learner contribution to research 332–333 Learner Perspective Study (LPS) 322 learner-centred teaching 31, 33 need for a challenge to 300 learning community of practice 208–210 context of 253, 257, 272, 273 social theory of 208–209 learning areas 284 see also mathematics learning area logical language 79 M Malepa see String Figure Gates Mass Democratic Movement (MDM)12 mathematical concepts 251, 274 assessment of 114 analysis of student errors 252 conceptual links 269–273 contextual links 269–273 linking of 253–274 see also concept mapping; mathematics mathematical knowledge 31, 115, 270, 273 context 273–274 learners’ access to 168, 270 of teachers 251, 334 mathematical literacy 8, 11–12, 17, 168, 200 354 mathematical symbols 80–81 see also mathematics language mathematics access to 3, 168 assessment see mathematics assessment criteria and culture 316–320 definition of learners’ attitude 7, 122, 124, 139, 272 and mathematical literacy 11–12 meaningful learning of 271–272 neutral subject 321, 324 problem-orientated approach to 272 students’ understanding of 249, 269–273, 316–320 traditional teaching of 272 ‘way of thinking’ 117–118, 129 see also mathematical concepts mathematics assessment criteria 110–129, 335 alternative 128 apprenticing 118–121, 124, 125–126 behavioural 122 cognitive 114–118, 123–124, 125 context of 128, 129 core assessment criteria 124 democratic paradox of criterion referencing 126–127 explicit/implicit 127–128 framing 126 and groupwork 60–63 learner autonomy 122–123, 124, 126 mathematical competence 112 mathematical thinking 118–120 neatness 123 non-cognitive 118–123, 125–126 ‘official’ criteria 110 Free download from www.hsrcpress.ac.za INDEX research case study 112–128 skills 116–117 socio-behavioural 121–123, 124–125, 126 theoretical perspectives 110–112 written work 118–121 Mathematics Association of South Africa (MASA) 321, 325 Mathematics Commission 13, 321 mathematics curriculum constructivism 202 effectiveness of reforms 23 FET 11, 17, 168 GET 11, 17 policy research 299–300 and reconciliation 12–17 reforms 4, 8–13, 23 relevance 17, 285–286 research 17–25 roots 5–8 mathematics discourse 85–88, 101–102, 268, 269 conceptual 86–88, 101–102 dilemma of mediation 86–87 dilemma of transparency 87 ‘discourse guide’ see multilingual classroom domains of 292–293 procedural 85, 88, 101–102, 104 role of the teacher 86 see also mathematics language; mathematics register mathematics education access by black pupils to 310–311 for Africans 308 assessment see mathematics assessment criteria and concept maps 274 and cultural models 100–101 Fundamental Pedagogics 313–315, 323–324 government policy 18, 19, 22–24 and groupwork see groupwork humanistic view 334 in the ‘homelands’ 317–320 inclusion in 250 influence from the West 330 internationalisation of 341–342 and language see language political dimensions of 336 pre-apartheid 312 psychological research in 283 quality in black schools 311 research see mathematics education research sociological research in 281–302 socio-political issues 336 ‘universal’ theories 329–330 Mathematics Education and Society (MES) 331, 333 Mathematics Education Project 234 mathematics education research 17–25, 64–65, 329–343 alternative forms 330 on assessment see mathematics assessment criteria ‘black-on-black’ 320–321 ‘black-on-white’ 321–322 in developing countries 22 ethnomathematics 133–155 funding 21 355 R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Free download from www.hsrcpress.ac.za on groupwork see groupwork history of 307–325 policy reform 17–25 political emphasis 332–334 qualitative studies 21 reference to race 311–312 socio-political emphasis 332 status of 308 traditional forms 330 ‘white-on-white’ 309–315 ‘white-on-black’ 315–320 mathematics language 78–82, 268 formal/informal 82–85 see also mathematics discourse; mathematics register mathematics learning area 11, 16, 31, 76–77 mathematics register 73, 78, 80, 82 see also mathematics discourse; mathematics language mathematics teacher education see teacher education Mathematics Teachers In-service Training Project (MATIP) 309, 317, 319–320 mediation dilemma of 86–87 meta-language 79 minority groups access to mathematics 331 motivational approach see co-operative approach to groupwork multiculturalism 331 multilingual classroom 44, 56, 73, 83, 87, 89–98 356 code-borrowing 91 code-mixing 91 code-switching 91–98 ‘discourse guide’ 96, 97 integration 91 role of teacher 96 102 N National Curriculum Statement (NCS) and mathematics 11, 77 National Education and Training Forum (NETF) 14 National Education Co-ordinating Committee (NECC) 9, 13, 14 National Education Crisis Committee 12 National Education Policy Investigation (NEPI) 9, 13 National Qualifications Framework (NQF) 284, 285, 290 New Curriculum Model for South Africa (CUMSA) New-Math movement 5, non-governmental organisations (NGOs) funding 235 and mathematics education 235 novice teachers classroom practices of 189–199 O Official Pedagogic Recontextualising Field 19, 22, 24 outcomes-based education (OBE) 8, 10, 15, 200, 202, 338 government statement on 284 Free download from www.hsrcpress.ac.za INDEX P Palestinian struggle 323 pedagogic identities 298–300, 301 peer-teaching 37, 38, 40, 42–43, 50, 60 people’s education 12–14 People’s Education for People’s Power (PEPP) 320–321 see also Mathematics Commission people’s mathematics 6, 8, 202 PLESME 206–228 aim of 207, 213–214 community of practice 214–217 design dilemmas of 210–225 educational redress 217–218 and learning 209–210 and life-long learning 222–225 mathematical competence of participants 218–219 pedagogical forms 219 professional community 215–217 professional identity of participants 220–222 and teacher change 222–225 teachers’ role 221 see also INSET Political Dimensions of Mathematics Education Conference (PDME) 133, 331, 333 political struggle and schools 233, 251 post-apartheid education 10, 15, 30–33, 129, 284–285 educational redress 217 predicate logic 79 pre-service education and training (PRESET) 167, 170–171, 173, 183–203, 296 and classroom practices 183 problem-solving approach to mathematics 5, 7, 40, 285 and learner attitude see also socio-constructivism; collaborative approach to groupwork professional community 215–217 professional development of teachers see INSET Programme for Leader Educators in Senior-phase Mathematics Education see PLESME Psychology of Mathematics Education (PME) 332 publication of Grade 12 results 342 R race and course grading 298–299 of researcher 217–218 radical constructivism see constructivism RADMASTE 207 see also ethnomathematics realistic mathematics reconciliation and curriculum reform 12–17 relevance of mathematical curriculum 285, 287 Research Institute for Educational Planning (RIEP) 309, 319 Review Committee on Curriculum 2005 219 rural schools mathematics case study 189–199 357 R E S E A R C H I N G M AT H E M AT I C S E D U C AT I O N I N S O U T H A F R I C A Free download from www.hsrcpress.ac.za S Schools Development Unit 236 semiotic mediation 41 separate development and education 310 situated approach to groupwork 36, 47, 58–59, 60 see also groupwork skills see mathematical assessment criteria socio-behavioural assessment criteria see mathematical assessment criteria socio-constructivism 25 see also constructivism; socio-cultural constructivism socio-cultural approach to groupwork 36, 41–44, 54–57, 60 see also groupwork socio-cultural constructivism and mathematics 136 socio-cultural research on educational policy 331 on mathematics education 330, 331 socio-political approach to groupwork 36, 44–46, 57–58, 60 see also critical mathematics education; groupwork sociology of education and mathematics education 281–302 and psychology 282–283 at the University of Cape Town 301 Southern African Association for Research in Mathematics and Science Education (SAARMSE) seeSouthern African Association for Research in Mathematics, Science and Technology Education 358 Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE ) 4, 18, 22, 25, 165, 216, 250, 321, 332, 335 conference proceedings 23, 164, 250–252, 282, 336–339 limitations of conference papers 170, 175–176 research culture in 250, 332, 333 review of conference proceedings 170–176, 336–339 teacher education research 170–176 Soweto riots 12, 75, 315 String Figure Gates (Malepa) language used 153–154 mathematical concepts 149–150 see also ethnomathematics structuralism T teacher as authority 193, 198 teacher as facilitator 48–54, 57–59 teacher as mediator 48, 54–57, 58–59 teacher as researcher 168, 174, 332–333 teacher education and complexity theory 242 funding 172 and higher education 23, 184, 203, 312 mathematics curriculum 169, 172–173, 236 mathematics method course 296 recontextualisation of practices 294–297 see also colleges of education; INSET; PRESET Free download from www.hsrcpress.ac.za INDEX teacher education research 163–178 analysis framework 170–172, 175–176 case study research 170, 171, 175 categories of 166–167, 171 entry of teachers into the profession 168, 174 funding 172 INSET/PRESET 170, 171, 172, 173 international 164, 166–169 methodology 175–176, 175 and policy 168, 169, 174 and teachers’ professional knowledge 166, 167, 171, 172–173, 177 TIMSS 175 primary/secondary level 170, 171 relationship with practice 167, 168, 169, 171, 177 SAARMSTE conference proceedings 164, 165, 170–176 teachers as researchers 168, 171, 174 teacher shortages 168, 169, 174 teacher-in-context 234, 241 textbook analysis 296 and gender 299 and relevance 300–301 Third International Mathematics and Science Study (TIMSS) 4, 19–20, 175 implications for South Africa 19–20, 102–103, 175, 340–342 ‘Third World’ see developing countries transparency dilemma of 87 U unit standard 290 ‘universal’ theories 329–330 Unofficial Pedagogic Recontextualising Field 19, 22 V Verwoerd, Hendrik F 3, 310 Vygotsky, L S approach to learning 41–42, 44 see also socio-constructivism; sociocultural approach to groupwork W Western imperialism 323, 330 see also Euro-centrism wire cars and geometry 143–146 see also ethnomathematics Z zone of proximal development (ZPD) 41–42, 51 359 Free download from www.hsrcpress.ac.za 360 ... in- service education and training language of learning and teaching Mathematics Teacher In- service Training Project mass democratic movement mathematical English Mathematics Education Project Mathematics. .. of Education and Training (South Africa, pre-1994) Further Diploma in Education foreign language learning environments fundamental pedagogics International Congress of Mathematics Education in- service... perspectives 10 Examining understanding in mathematics: a perspective from concept mapping 249 Willy Mwakapenda 11 Knowledge and pedagogy: sociological research in mathematics education in South Africa