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PERSPECTIVES ON PRACTICE AND MEANING IN MATHEMATICS AND SCIENCE CLASSROOMS Mathematics Education Library VOLUME 25 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia Editorial Board H. Bauersfeld, Bielefeld, Germany I.P. Becker, Illinois, U.S.A. G. Leder, Melbourne, Australia A. Sfard, Haifa, Israel O. Stovsmose, Aalborg, Denmark S. Turnau, Krakow, Poland The titles published in this series are listed at the end of this volume. PERSPECTIVES ON PRACTICE AND MEANING IN MATHEMATICS AND SCIENCE CLASSROOMS Edited by DAVID CLARKE University of Melbourne, Victoria, Australia KLUWER ACADEMIC PUBLISHERS NEW YORK / BOSTON / DORDRECHT / LONDON / MOSCOW eBook ISBN: Print ISBN: 0-306-47228-7 0-792-36938-6 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com Editor’s Dedication To Sharon This page intentionally left blank. TABLE OF CONTENTS Preface Acknowledgements Chapter 1: Negotiating Meanings - An Introduction ix xi 1 David Clarke Chapter 2: Complementary Accounts Methodology 13 David Clarke Chapter 3: Untangling Uncertainty, Negotiation, and Intersubjectivity 33 David Clarke Chapter 4: Accounting for Accounts of Learning Mathematics: Reading the ZPD in Videos and Transcripts 53 Stephen Lerman Chapter 5: Mathematical Interactions and Their Influence on Learning 75 Derek Holton and Gill Thomas Chapter 6: Interest in Learning and Classroom Interaction 105 Mary Ainley Chapter 7: Cognitive Engagement in the Mathematics Classroom 131 Sue Helme and David Clarke Chapter 8: Measuring Values in Classroom Teaching and Learning 155 Carol Lewis-Shaw Chapter 9: Opportunities to Learn Science? Multiple Contexts at Work in a Science Classroom 197 Susan Rodrigues Chapter 10: The Role of Gesture in Co-constructing Mathematical Understanding 231 Robert Reeve and Fiona Reynolds Chapter 11 : Learning and Teaching from Ignorance to Understanding 255 John Baird Chapter 12: Teaching/Learning 2 91 David Clarke Appendices: A. Summary of Lessons Analysed B. Sample Integrated Text Author Index Subject Index 321 331 339 347 This page intentionally left blank. PREFACE This book represents the culmination of an unusual process of interpretation, negotiation and synthesis. It is the realisation of a vision of an integrated description of classroom practice and learning that motivated the research team members, who are also the chapter authors, during their analysis and in the subsequent integration of their results into the kaleidoscope that is this book. It is not complete. We would be the first to assert that any portrayal of a social setting as complex as a classroom is inevitably incomplete. But not, we think, without value. In part, it was our perception of the inadequacies of previous descriptions of classroom teaching and learning that initiated the complex process leading to the book you now hold in your hands. It is not our intention to reveal to you what mathematics and science classrooms are “really like”. Such a goal would be in contradiction of the theoretical and methodological