Summary Mathematics is one of the great cultural achievements of humankind. Every schooled person understands the rudiments of number and measures and sees the world through this quantifying conceptual framework. By these means mathematics provides the file:///ho

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Social Constructivism as a Philosophy of Mathematics


title: Social Constructivism As a Philosophy
of Mathematics SUNY Series, Reform in
Mathematics Education
author: Ernest, Paul.
publisher: State University of New York Press
isbn10 | asin: 0791435881
print isbn13: 9780791435885
ebook isbn13: 9780585075587
language: English
subject Mathematics--Philosophy,
Constructivism (Philosophy)
publication date: 1998
lcc: QA8.4.E76 1998eb
ddc: 510/.1
subject: Mathematics--Philosophy,
Constructivism (Philosophy)

Page ii
SUNY SERIES IN SCIENCE, TECHNOLOGY, AND SOCIETY
SAL RESTIVO AND JENNIFER CROISSANT, EDITORS
AND
SUNY SERIES, REFORM IN MATHEMATICS EDUCATION
JUDITH SOWDER, EDITOR




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Page iii


Social Constructivism as a Philosophy of Mathematics

Paul Ernest

STATE UNIVERSITY OF NEW YORK PRESS




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Page iv
Published by
State University of New York Press, Albany
© 1998 State University of New York
All rights reserved
Printed in the United States of America
No part of this book may be used or reproduced in any manner whatsoever without
written permission. No part of this book may be stored in a retrieval system or transmitted
in any form or by any means including photocopying, recording, or otherwise without the
prior permission in writing of the publisher.
For information, address State University of New York
Press, State University Plaza, Albany, N.Y. 12246
Production by E. Moore
Marketing by Nancy Farrell
Library of Congress Cataloging-in-Publication Data
Ernest, Paul.
Social constructivism as a philosophy of mathematics / Paul
Ernest.
p. cm. (SUNY series in science, technology, and society)
(SUNY series, reform in mathematics education)
Includes bibliographical references and index.
ISBN 0-7914-3587-3 (hardcover : alk. paper). ISBN 0-7914-3588-1
(pbk. : alk. paper)
1. MathematicsPhilosophy. 2. Constructivism (Philosophy)
I. Title. II. Series. III. Series: SUNY series, reform in
mathematics education.
QA8.4.E76 1997
510´.1DC21 97-3515
CIP
10 9 8 7 6 5 4 3 2 1



Page v


Contents

List of Tables and Figures vii
Acknowledgments ix
Introduction xi



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1. A Critique of Absolutism in the Philosophy of Mathematics 1
2. Reconceptualizing the Philosophy of Mathematics 39
3. Wittgenstein's Philosophy of Mathematics 64
4. Lakatos's Philosophy of Mathematics 97
5. The Social Construction of Objective Knowledge 131
6. Conversation and Rhetoric 162
7. The Social Construction of Subjective Knowledge 206
8. Social Constructivism: Evaluation and Values 247
Bibliography 279
Index 305




Page vii


Tables and Figures

Table 4.1. A Comparison of Popper's LSD and Lakatos's LMD 100
Table 4.2. A Comparison of Lakatos's LMD with His MSRP 109
Table 4.3. Cyclic Form of Lakatos's Logic of Mathematical 117
Discovery
Table 5.1. Dialectical Form of the Generalized Logic of 151
Mathematical Discovery
Table 7.1. Harré's Model of 'Vygotskian Space' 209
Table 7.2. Dowling's Model of Contexts for Mathematical 236
Practices
Figure 7.1. The Creative/Reproductive Cycle of Mathematics 243




Page ix


Acknowledgments




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