Table Of ContentIN SEARCH OF A PEDAGOGY OF CONFLICT AND DIALOGUE
FOR MATHEMATICS EDUCATION
Mathematics Education Library
VOLUME 32
Managing Editor
A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board
J.P. Becker, Illinois, U.S.A.
G. Leder, Melbourne, Australia
A. Sfard, Haifa, Israel
O. Skovsmose, Aalborg, Denmark
S. Turnau, Krakow, Poland
The titles published in this series are listed at the end of this volume.
IN SEARCH OF A PEDAGOGY OF
CONFLICT AND DIALOGUE
FOR MATHEMATICS EDUCATION
by
RENUKA VITHAL
University of Durban-Westville,
Durban, South Africa
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
ISBN 978-94-010-3987-1 ISBN 978-94-010-0086-4 (eBook)
DOI 10.1007/978-94-010-0086-4
Printed on acid-free paper
All Rights Reserved
©2003Springe r Scienc e+Busines s Media Dordrecht
OriginallypublishedbyKluwerAcademicPublishersin2003
Softcover reprint of the hardcover 1st edition 2003
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
CONT ENTS
Acknowledgements IX
Dedication XI
Foreword XIII
Chapter 1: AN EMERGENT SOCIAL, CULTURAL, POLITICAL 1
APPROACH: Sketching a theoretical landscape
1. MATHEMATICS EDUCATION AFTER APARTHEID? 1
2. FOUR STRANDS OF A SOCIAL, CULTURAL, 3
POLITICAL APPROACH
2.1. A critical mathematics education for all 6
2.2. A “critical ethnomathematics” education 16
2.3. Dimensions of diversity: a critical perspective in 22
mathematics education through a focus on gender
2.4. A critical perspective in the South African context: 27
People’s Mathematics
3. PULLING THE THEORETICAL STRANDS TOGETHER 35
THROUGH EDUCATIONAL PRACTICE: THE CASE
OF PROJECT WORK
4. CONTEXTUALISING THIS LANDSCAPE 39
Chapter 2: METHODOLOGICAL “THEORETICAL TOOLS” FOR 45
RESEARCHING A SOCIAL, CULTURAL, POLITICAL
APPROACH
1. A RESEARCH JOURNEY 45
2. THE ACTUAL CURRENT SITUATION 47
2.1. Teacher education, student teachers and teaching 48
practice
2.2. School mathematics curricula and reforms 50
3. THE IMAGINED HYPOTHETICAL SITUATION 55
3.1. Initiating student teachers’ hypothetical imagination 56
– during coursework
3.2. Developing student teachers’ hypothetical 59
imagination – getting ready for practice
4. THE ARRANGED SITUATION 62
4.1. In the arranged situation 63
4.2. After the arranged situation 65
5. REFLECTIONS ON THE SITUATIONS 67
5.1. Potentiality 68
5.2. Intervention, implementation or imposition 69
5.3. Connecting the situations 70
5.4. Transformacy 71
6. CONCLUSION 72
V
VI CONTENTS
Chapter 3: METHODOLOGICAL CHALLENGES AND CRITERIA 75
FOR RESEARCHING A SOCIAL, CULTURAL,
POLITICAL APPROACH
1. INTRODUCTION: RESEARCH PARADIGMS 75
2. A CRITICAL APPROACH TO RESEARCH VERSUS A 76
CRITICAL APPROACH TO EDUCATION
3. SOURCES FOR DEVELOPING A RESEARCH 78
METHODOLOGY FOR A CRITICAL PERSPECTIVE
IN MATHEMATICS EDUCATION
3.1. The search inside mathematics education 78
3.2. The search outside mathematics education 79
4. THE RESEARCHER; RESEARCH PARTICIPANTS; 80
AND THE RESEARCH PROCESS
4.1. Researcher and the research participants 81
4.2. Research participants and the research process 82
4.3. The researcher and the research process 84
5. IS MY RESEARCH CRITICAL RESEARCH? 85
6. CRITERIA IN A RESEARCH METHODOLOGY FOR A 88
CRITICAL PERSPECTIVE IN MATHEMATICS
EDUCATION
6.1. Validity in transformation and in action 89
6.2. Validity concerns in my research 92
6.3. Democratic participatory validity 95
6.4. Generalisability and generativity 99
7. CONTEXT IN A RESEARCH METHODOLOGY FOR A 103
CRITICAL PERSPECTIVE IN MATHEMATICS
EDUCATION
8. CONCLUSION: CRITIQUE INWARD AND OUTWARD 104
Chapter 4: CRUCIAL DESCRIPTIONS: TOWARD CRITIQUE OF 107
THEORY, PRACTICE AND RESEARCH
1. INTRODUCTION 107
2. CRUCIAL DESCRIPTIONS AND THEORY-PRACTICE 108
RELATIONS
3. CRUCIAL DESCRIPTIONS AND RESEARCH 112
3.1. Transparency 113
3.2. Transformacy 114
3.3. Generativity 116
3.4. Exemplarity 117
4. CONCLUSION 118
Chapter 5: CRUCIAL DESCRIPTION OF A SOCIAL, CULTURAL, 121
POLITICAL APPROACH: Part I – Sumaiya and the
Imagined Hypothetical Situation
1. INTRODUCTION 121
2. ABOUT SUMAIYA 122
CONTENTS VII
3. SUMAIYA IN HER THIRD YEAR: INTRODUCTION TO 124
A NEW CURRICULUM APPROACH
4. SUMAIYA IN HER FOURTH YEAR: PREPARING FOR 130
TEACHING PRACTICE
4.1. An imagined hypothetical teacher 130
4.2. Imagined hypothetical pupils 132
4.3. Imagined hypothetical project ideas 132
4.4. Imagined hypothetical project work issues 134
5. SUMAIYA IN THE ACTUAL CURRENT SITUATION: 138
THE SCHOOL, THE TEACHER, AND THE CLASS
Chapter 6: CRUCIAL DESCRIPTION OF A SOCIAL, CULTURAL, 149
POLITICAL APPROACH: PART 2 – Sumaiya and the
Arranged Situation
1. INTRODUCTION 149
2. PROJECT WORK BEGINS 150
2.1. Reflections of Day 3: Project work issues 156
2.2. Reflections of Day 3: Group work issues 163
2.3. Reflections of Day 3: Teaching and learning 164
mathematics issues
3. GROUP 1: TIME SPENT AFTER SCHOOL 166
3.1. Reflections on Group 1: Group work issues 180
3.2. Reflections on Group 1: Project work issues 183
3.3. Reflections on Group 1: Teaching and learning 185
mathematics issues
4. GROUP 2: DEVELOPING A MATHEMATICS 187
NEWSLETTER
4.1. Reflections on Group 2: Group work issues 195
4.2. Reflection on Group 2: Project work and mathematics 198
teaching and learning issues
5. GROUP 4: THE SPORTS SURVEY 201
5.1. Reflection on Group 4: Group work issues 211
5.2. Reflection on Group 4: Project work and mathematics 213
teaching and learning issues
6. GROUPS 3 AND 5: MONEY SPENT ON MY 217
EDUCATION
6.1. Group 3: Money spent on my education 218
6.2. Group 5: Money spent on my education 227
6.3. Reflections on Group 3 and 5: Group work issues 235
6.4. Reflections on Group 3 and Group 5: Project work 243
issues
6.5. Reflections on Group 3 and Group 5: Mathematics 246
teaching and learning issues
Chapter 7: FROM DESCRIPTION TO THEMES 253
1. INTRODUCTION 253
2. STRUCTURE AND FREEDOM 254
VIII CONTENTS
3. AUTHORITY AND DEMOCRACY 260
4. MATHEMATICS AND CONTEXT 270
5. DIFFERENTIATION AND EQUITY 281
6. ACTUALITY AND POTENTIALITY 290
Chapter 8: FROM THEMES TO THEORETICAL LANDSCAPE 301
1. INTRODUCTION 301
2. COMPLEMENTARITY 302
3. FREEDOM AND STRUCTURE 306
4. DEMOCRACY AND AUTHORITY 310
5. CONTEXT AND MATHEMATICS 316
6. EQUITY AND DIFFERENTIATION 324
7. POTENTIALITY AND ACTUALITY 332
Chapter 9: A PEDAGOGY OF CONFLICT AND DIALOGUE 337
1. INTRODUCTION 337
2. PEDAGOGY, THEORY AND PRACTICE 338
3. CONFLICT IN A MATHEMATICS PEDAGOGY 342
4. DIALOGUE IN A MATHEMATICS PEDAGOGY 347
5. COMPLEMENTARITY IN A PEDAGOGY OF CONFLICT 353
AND DIALOGUE
6. STRENGTHS AND WEAKNESSES; LIMITATIONS AND 358
DREAMS
References 361
Index 371
Appendices 375
APPENDIX A – GROUP 1: TIME SPENT AFTER 376
SCHOOL
APPENDIX B – GROUP 2: DEVELOPING A 381
NEWSLETTER
APPENDIX C – GROUP 3: MONEY SPENT ON MY 388
EDUCATION
APPENDIX D – GROUP 4: THE SPORTS SURVEY 393
APPENDIX E – GROUP 5: MONEY SPENT ON MY 396
EDUCATION
ACKNOWLEDGEMENTS
This book is based on a dissertation by the same title, awarded for a Doctoral Degree
in Natural Science, Aalborg University, Denmark (2000).
This study was part of a mathematics education Ph.D. project funded by the
Foundation for Research Development (South Africa) and the Danish Government. It
involved Aalborg University, and the Royal Danish School of Educational Studies in
Denmark; and the Centre for the Advancement of Science and Mathematics Education
(University of Natal), and the Centre for Educational Research, Evaluation and Policy
(University of Durban-Westville) in South Africa. These linkages were coordinated and
managed largely through the efforts and commitment of Ole Skovsmose.
I thank Ole for the months he spent here in South Africa and the many roles he took
as main supervisor in the project, mentor, colleague and friend. I acknowledge him for
many of the ideas he inspired and jointly developed in this research and his
encouragement for continuing it into a book. But I appreciated most of all the strong
democratic ethos and relations he brought to the project. The project was sustained
equally through the contribution of several key supervisors who gave generously of their
time and expertise. It was the vision and initiative of John Volmink that shaped the
project in the early stages; and his critique and comments on reading my first complete
draft were affirming and thought provoking. Jonathan Jansen supported the group and
contributed a great deal in planning the research design and in general research training
through the many workshops and seminars he conducted. His critique on several draft
chapters was invaluable for conceptual clarification and shifts. Jill Adler’s participation
during the struggle with analysis and writing were important in addressing gaps and
silences in the research. Iben Christiansen read several draft chapters and her warm and
sensitive critique helped in reorganising and making critical refinements to ideas. I must
mention also Michael Otte for the many email conversations and his support and
encouragement for exploring some of the theoretical ideas in the study.
The ‘Ph.D. group’, as all those in the project came to call themselves, offered
tremendous support through the network of peer supervision. Herbert Khuzwayo, Maga
Moodley, Nomsa Dlamini, Bunny Naidoo, Cassius Lubisi, Mathume Bopape, and others
who joined our monthly seminars over the years were crucial to the completion of this
project, serving as a research reference group, and keeping my research programme on
track. Colleagues in Denmark are also remembered with gratitude for seminars and
many discussions, and for their warm hospitality: Allan Tarp, Jebbe Scott and others, but
especially Paola Valero for her sharp and strong comments. Elin Emborg must be
thanked for making my stays in Denmark easier and enjoyable.
The research could not have taken place without the generosity of the many research
participants – the student teachers; and the staff and pupils at the schools. In particular, I
thank the student teachers who put in an additional effort to collect data and share their
reflections - Sumaiya Desai; Jasmin Paras; Zwelabantu Elphus Zuma; Jabulani
Gcabashe; Anita Samsukal; Ramona Ramdas; Deborah-Ann Naidoo; Sashni Chetty;
IX
X ACKNOWLEDGEMENTS
Swasthi Mistry; Betty Rambaros; Tracy Ganasen; Noklunga Nxumalo. I must, however,
single out the school which is the main site for this research and the principal and class
teacher who allowed us into their school and classroom and participated so willingly in
the study. I appreciate very much the opportunity to have worked with Sumaiya Desai
and the pupils who spoke and acted so freely, openly and trustingly.
I also thank my colleagues and friends in the Faculty of Education at the University
of Durban-Westville who provide the space for talking about my ideas, and take the time
to read my work and interact with me. I am especially grateful to Michael Samuel, Sue
Singh, Betty Govinden, Vijay Reddy, and Rookaya Bawa for their friendship during the
many years that studies such as these are endured.
Reworking a thesis into a book takes a special perseverance. For helping me to
sustain this effort I must thank those who took the time and energy to read, discuss, and
comment on the work: Alan Bishop, Nyna Amin, Cliff Malcolm, Steve Lerman, Rubby
Dhunpath, Jill Adler; and Michael Samuel. The many research students that I have the
privilege to work with are also greatly appreciated.
To all the members of my family who provided support and encouragement, and to
Kishore, I express my gratitude. Most of all to my sons, Nishay and Hashil, who put up
with my many and varied absences, I thank them for their unconditional love, their
honesty, for their sense of humour, and for the joy and meaning they bring to my life.
Warm appreciation goes to Nomosa Mtshali for her help in keeping our home going
through these many years.
This book, and the dissertation from which it was made possible came about through
the support, encouragement and input of many people, whose lives intersected with mine
in so many different ways in the time it has taken to complete such endeavours, many of
whom I have not mention here, I thank them too.
For permission to reprint many of the ideas, I thank the following editors and
publishers:
“Democracy and authority. A complementarity in mathematics education?”, in
Zentralblatt für Didaktik der Mathematik/International Reviews on Mathematics
Education, 98(6), 27-36, 1999, in Chapters 7 and 8;
“A Pedagogy of conflict and dialogue for a mathematics education from a critical
perspective”, in For the Learning of Mathematics, 22(1), 29-41, 2002, in Chapter 9;
“Differentiation, in contradiction and co-operation, with equity in mathematics
education”, in the African Journal of Mathematics, Science and Technology Education,
Vol 6, 1-20, 2002, in Chapters 7 and 8;
“Methodological challenges for mathematics education research from a critical
perspective”, in P. Valero & R. Zevenbergen (eds.) Researching the Socio-political
Dimensions of Mathematics Education: Issues of Power in Theory and Methodology,
Dordrecht, Kluwer Academic Publishers, in press, in Chapter 3
“Researching mathematics education in situations of social and political conflict” in
A. J. Bishop, M. A. Clements, F. K. S. Leung, C. Keitel, & J Kilpatrick (Eds.) The
Second International Handbook of Mathematics Education, Dordrecht, Kluwer
Academic Publishers, co-author P. Valero, in press, in Chapter 3.
Renuka Vithal
