Philosophical Dimensions in Mathematics Education
Philosophical Dimensions in Mathematics Education brings together diverse recent developments exploring philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a
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Mathematics Education Library VOLUME 42 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board J.P. Becker, Illinois, U.S.A. C. Keitel, Berlin, Germany F. Leung, Hong Kong, China G. Leder, Melbourne, Australia D. Pimm, Edmonton, Canada A. Sfard, Haifa, Israel O. Skovsmose, Aalborg, Denmark
The titles published in this series are listed at the end of this volume.
Karen François Jean Paul Van Bendegem (Editors)
Philosophical Dimensions in Mathematics Education
Karen François Free University of Brussels B-1050 Brussels Belgium [email protected]
Jean Paul Van Bendegem Free University of Brussels B-1050 Brussels Belgium [email protected]
Series Editor: Alan Bishop Monash University Melboure 3800 Australia [email protected]
Library of Congress Control Number: 2007926609 ISBN-13: 978-0-387-71571-1
e-ISBN-13: 978-0-387-71575-9
Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com
Contents
Editors and Contributing Authors Prelude JEAN PAUL VAN BENDEGEM AND KAREN FRANÇOIS
vii 1
Interlude 1
11
The Untouchable and Frightening Status of Mathematics KAREN FRANÇOIS
13
Interlude 2
41
Philosophical Reflections in Mathematics Classrooms SUSANNE PREDIGER
43
Interlude 3
59
Integrating the Philosophy of Mathematics in Teacher Training Courses DIMITRIS CHASSAPIS
61
Interlude 4
81
Learning Concepts Through the History of Mathematics ALBRECHT HEEFFER
83
vi
Contents
Interlude 5
105
The Meaning and Understanding of Mathematics
107
Interlude 6
129
The Formalist Mathematical Tradition as an Obstacle to Stochastical Reasoning MARIA MELETIOU-MAVROTHERIS
131
Interlude 7
157
Logic and Intuition in Mathematics and Mathematical Education ARD VAN MOER
159
Interlude 8
181
A Place for Education in the Contemporary Philosophy of Mathematics BART VAN KERKHOVE
183
Interlude 9
211
Ethnomathematics in Practice RIK PINXTEN AND KAREN FRANÇOIS
213
Postlude ALAN J. BISHOP
229
Name Index
233
Subject Index
237
CARMEN BATANERO AND CARMEN DÍAZ
Editors and Contributing Authors EDITORS Karen François has a Masters Degree in Moral Sciences, a Bachelors of Philosophy from the University of Ghent, and an advanced Masters Degree in Women’s Studies from the University of Antwerp. She is c
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