Construction of Arithmetical Meanings and Strategies
The studies presented in this book should be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The 'eaching experiment· was carried out with half a dozen children entering first gr
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Leslie P. Steffe
Paul Cobb
With the Collaboration of Ernst von Glasersfeld
Construction of Arithmetical Meanings and Strategies Foreword by Hermine Sinclair
Springer-Verlag New York Berlin Heidelberg London Paris Tokyo
Leslie P. Steffe Department of Mathematics Education The University of Georgia Athens, GA 30601. USA Paul Cobb Department of Education Purdue University West Lafayette, IN 47907. USA Ernst von Glasersfcld Professor Emeritus Department of Psychology The University of Georgia Athens, GA 30601, USA
With 9 Figures
Library of Congress Cataloging-in-Publication Data Steffe, Leslie P. Construction of arithmetical meanings and strategies. (Recent research in psychology) Bibliography: p. I. Number concept in children~Case studies. I. Cobb, Paul. II. Glasersfeld, Ernst von. III. Title. IV. Series. 87-32297 BF723.N8S74 1988 153.1 '5 ISBN-13: 978-0-387-96688-5 001: 10.1007/978-1-4612-3844-7
e-ISBN -13: 978-1-4612-3844-7
© 1988 by Springer-Verlag New York 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-Verlag, 175 Fifth Avenue, New York. NY 10010. 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 of general description names. trade names, trademarks. etc. in this publication. even if the former are not especially identified. is not to be taken as a sign that such names. as understood by the Trade Marks and Merchandise Marks Act. may accordingly be used freely by anyone. Camera-ready copy prepared by the authors using Microsoftword.
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Foreword The studies presented in this book should be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The 'eaching experiment· was carried out with half a dozen children entering first grade over two years in biweekly sessions. Methodologically the authors' research is original. It is a longitudinal but not a naturalistic study, since the experimenter-teachers directed their interaction with each individual child with a view to his or her possible progress. It is experimental in the sense that two groups of subjects were selected according to criteria derived from an earlier study (Steffe, von Glasersfeld, Richards & Cobb, 1983) and that the problems proposed were comparable, though far from identical across the subjects; but unlike more rigid and shorter "learning" or ''training" studies it does not include pre- and posttests, or predetermined procedures. Theoretically, the authors subscribe to Piagefs constructivism: numbers are made by children, not found (as they may find some pretty rocks, for example) or accepted from adults (as they may accept and use a toy). The authors interpret changes in the children's counting behaviors in terms of constru
