Mathematics Education and Language Interpreting Hermeneutics and Pos
Contemporary thinking on philosophy and the social sciences has primarily focused on the centrality of language in understanding societies and individuals; important developments which have been under-utilised by researchers in mathematics education. In t
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Mathematics Education Library VOLUME 20
Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board H. Bauersfeld, Bielefeld, Germany 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.
MATHEMATICS EDUCATION AND LANGUAGE Interpreting Hermeneutics and Post-Structuralism Revised Second Edition
by
TONY BROWN Institute of Education. The Manchester Metropolitan University. u.K.
KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
A C.I.P. Catalogue record for this book is available from the Library of Congress.
Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
ISBN 978-94-010-0726-9 (eBook) ISBN 978-0-7923-6969-1 DOI 10.1007/978-94-010-0726-9
All Rights Reserved © 200 I Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
CONTENTS
Acknowledgements About the author
vii lX
INTRODUCTION
1
SHORT REVIEW OF RECENT RESEARCH
7
CHAPTER 1. HERMENEUTICS AND MATHEMATICS EDUCATION
21
Action and Meaning Phenomenology Hermeneutics Hermeneutics and Education Towards an Hermeneutical Understanding of Mathematics
25 28 36 47 49
CHAPTER 2. THE PRODUCTION OF MATHEMATICAL MEANING: 57 A POST-STRUCTURALIST PERSPECTIVE Post-Structuralism: A Radical Form of Hermeneutics Post-Structuralism, Education and Mathematics Saussurian Linguistics and Mathematics Self-Reflexivity in Mathematical Engagement Creating and Inheriting Mathematics CHAPTER 3. SHARING MATHEMATICAL PERSPECTIVES Discourse or Reality? Locating Mathematical Knowledge Assessing Mathematical Activity Combining Language and Experience CHAPTER 4. SOME LESSONS
58 60 63 71 77 80 81 83 86 88 101
CONTENTS
vi
CHAPTER 5.
THE PHENEMENOLOGY OF THE MATHEMATICS CLASSROOM
Personal Space Appresentational Association Acting in the Supposed World
134 136 148 156
CHAPTER 6. TEACHER-STUDENT INTERACTIONS
159
CHAPTER 7 . NARRATIVES OF LEARNING MATHEMATICS
173
Multiple Accounts The Transition from Arithmetical to Algebraic Thinking Storying Transition Semantic Innovation Concluding Comments
174 177 180 182 189
CHAPTER 8. MATHEMATICS AND LANGUAGE
192
CHAPTER 9. DEVELOPING TEACHER PRACTICE
210
Writing as a Mechanism for Professional Development Building a Professional Discourse of Mathematics Teaching within an Initial Training Course Building an Understanding of the Teacher's Task through Practitioner
