The Construction of New Mathematical Knowledge in Classroom Interaction
The Construction of New Mathematical Knowledge in Classroom Interaction deals with the very specific characteristics of mathematical communication in the classroom. The general research question of this book is: How can everyday mathematics teaching be de
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Mathematics Education Library VOLUME 38 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board J.P. Becker, Illinois, U.S.A. C. Keitel, Berlin, Germany G. Leder, Melbourne, Australia A. Sfard, Haifa, Israel O. Skovsmose, Aalborg, Denmark S. Tumau, Rzeszow, Poland
The titles published in this series are listed at the end of this volume.
Heinz Steinbring (Author)
The Construction of New Mathematical Knowledge in Classroom Interaction An Epistemological Perspective
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Heinz Steinbring, Universität Duisburg-Essen, Essen Germany
Library of Congress Cataloging-in-Publication Data Steinbring, Heinz. The construction of new mathematical knowledge in classroom interaction: an epistemological perspective / Heinz Steinbring. p. cm.—(Mathematics education library; v. 38) Includes bibliographical references and indexes. ISBN 0-387-24251-1 (acid-free paper) -- ISBN 0-387-24253-8 (E-Book) 1. Mathematics—Study and teaching. 2. Teacher-student relationships. 3. Interaction analysis in education. I. Title. II. Series. QA11.2.S84 2005 510’.71—dc22
2004061914
© 2005 Springer Science+Business Media, Inc. 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, Inc., 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 know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the 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. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
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Dedication
This book is dedicated to Christely Kristin andHanna
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
ix
PREFACE
xi
GENERAL OVERVIEW OF THE BOOK OVERVIEW OF THE FIRST CHAPTER CHAPTER 1 Theoretical Background and Starting Point 1 Between Unity and Variety - Conceptions of the Epistemological Nature of Mathematical Knowledge 2 Theoretical Foundations and Methods of Epistemologically-oriented Analysis of Mathematical Interaction 3 Mathematical Knowledge and Communication - Communicative Systems Necessary Living Spaces for Processes of Mathematical Cognition OVERVIEW OF THE SECOND CHAPTER CHAPTER 2 The Theoretical Research Question 1 The Epistemological Problem of Old and New Mathematical Knowledge in the Social Classroom Interaction 2 The Relation between „Classroom Communication" and „Mathematical Interaction" 3 Social Construction of New Mathematical Knowledge Structures from an Interactive and Epistemological Perspective OVERVIEW OF THE THIRD CHAPTER CHAPTER 3 Epistemology-oriented Analyses of Mathematical Interactions 1 Development of Mathematical Knowledge in the Frame
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