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This book focuses on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The volume is intended for researchers in the field, as well as for mathematics educators teaching the next generation of students.
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BELIEFS: A HIDDEN VARIABLE IN MATHEMATICS EDUCATION? Mathematics Education Library VOLUME 31 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. BELIEFS: A HIDDEN VARIABLE IN MATHEMATICS EDUCATION? Edited by GILAH C. LEDER La Trobe University, Australia ERKKI PEHKONEN University of Turku, Finland and GÜNTER TÖRNER University of Duisburg, Germany KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: Print ISBN: 0-306-47958-3 1-4020-1057-5 ©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 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 TABLE OF CONTENTS vii xi xiii Tables and Figures Acknowledgements Contributors 1 Chapter 1: Setting the Scene Gilah C. Leder, Erkki Pehkonen, and Günter Törner PART 1 BELIEFS: CONCEPTUALIZATION AND MEASUREMENT Chapter 2: Framing Students’ Mathematics-Related Beliefs. A Quest for Conceptual Clarity and a Comprehensive Categorization 13 Peter Op’t Eynde, Erik de Corte, and Lieven Verschaffel Chapter 3: Rethinking Characterizations of Beliefs 39 Fulvia Furinghetti and Erkki Pehkonen Chapter 4: Affect, Meta-Affect, and Mathematical Belief Structures 59 Gerald A. Goldin Chapter 5: Mathematical Beliefs – A Search for a Common Ground: Some Theoretical Considerations on Structuring Beliefs, Some Research Questions, and Some Phenomenological Observations 73 Günter Törner Chapter 6: Measuring Mathematical Beliefs and Their Impact on the Learning of Mathematics: A New Approach 95 Gilah C. Leder and Helen J. Forgasz Chapter 7: Synthesis - Beliefs and Mathematics Education: Implications For Learning, Teaching, and Research 115 Douglas B. McLeod and Susan H. McLeod PART 2 TEACHERS’ BELIEFS Chapter 8: Mathematics Teacher Change and Development. The Role of Beliefs 127 Melvin (Skip) Wilson and Thomas J. Cooney Chapter 9: Mathematics Teachers’ Beliefs and Experiences with Innovative Curriculum Materials. The Role of Curriculum in Teacher Development Gwendolyn M. Lloyd v 149 vi CONTENTS Chapter 10: A Four Year Follow-up Study of Teachers' Beliefs after Participating in a Teacher Enhancement Project 161 Lynn C. Hart Chapter 11: Belief Structure and Inservice High School Mathematics Teacher Growth 177 Olive Chapman Chapter 12: Participation and Reification in Learning to Teach: The Role of Knowledge and Beliefs 195 Salvador Llinares Chapter 13: A Study of the Mathematics Teaching Efficacy Beliefs of Primary Teachers 211 George Philippou and Constantinos Christou