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ISSN 0883-9530 JOURNAL FOR RESEARC IN MATHE EDUCA MONOGRAPHNUMBER6 is National Council of Teachers of Mathematics A Monograph Series of the National Council of Teachers of Mathematics series is The JRME monograph published by the Editorial Panel as a to the journal. Each supplement has a single theme related monograph of to the learning or teaching mathematics. To be considered for publication, a manuscript should be (a) a set of reports of coordinated studies, (b) a set of articles synthesizing a large body of research, (c) a single treatise that examines a major research issue, or (d) a report of a single research study that is too lengthy to be published as a journal article. Any person wishing to submit a as a manuscript for consideration send four should copies of monograph to the the complete manuscript monograph series editor. Manuscripts should be no longer than 200 doublespaced typewritten pages. The name, affiliations, and qualifications of each contributing author should be included with the manuscript. Series Editor DOUGLAS A. GROUWS, Universityof Iowa, Iowa City, IA 52242 Associate Editor DIANA V. LAMBDIN, Indiana University, Bloomington, IN 47405 Editorial Panel CATHERINEBROWN, Universityof Pittsburgh;Chair MICHAELT. BATTISTA, Kent State University,Ohio PAUL COBB, PurdueUniversity MARTIN L. JOHNSON, Universityof Marylandat College Park CAROL NOVILLISLARSON, University of Arizona PATRICIAS. WILSON, Universityof Georgia ALAN OSBORNE, Ohio State University; BoardL aison Manuscriptsshould be sent to Douglas A. Grouws Universityof Iowa N259 LindquistCenter Iowa City, IA 52242 RETHINKINGELEMENTARYSCHOOL MATHEMATICS: INSIGHTS AND ISSUES edited by TerryWood Paul Cobb Ema Yackel DeborahDillon commentaryby MartinSimon NATIONALCOUNCILOF TEACHERSOF MATHEMATICS Copyright ? 1993 by THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, INC. 1906 Association Drive, Reston, Virginia 22091-1593 All rights reserved Library of Congress Cataloging-in-Publication Data Rethinking elementary school mathematics : insights and issues / edited by Terry Wood ... [et al.]. cm. - (Journal for research in mathematics education. p. Monograph; no. 6) Includes bibliographical references. ISBN 0-87353-362-3 1. Mathematics-Study and teaching (Elementary)-United States. . II. Series. I. Wood, Terry Lee, 19421993 QA135.5.R485 372. 7'044-dc20 93-20649 CIP The publications of the National Council of Teachers of Mathematics present a variety of viewpoints. The views expressed or implied in this publication,unless otherwise noted, should not be interpretedas official positions of the council. Printedin the United States of America TABLE OF CONTENTS ACKNOWLEDGMENTS ......................................................... iv ABSTRACT.................................................................... AUTHORS .................................................... ................vi BACKGROUND OFTHERESEARCH ............................... INTRODUCTION: Paul Cobb, Terry Wood, Erna Yackel, and Grayson Wheatley 1 PART 1: Learning Mathematics: Multiple Perspectives 1. Second-Grade Classroom: Psychological Perspective....................7 Terry Wood (An overview of work by Cobb, Wood, Yackel, and Wheatley) 2. Creating an Environment For Learning Mathematics: Social Interaction Perspective.......................................... TerryWood (An overview of work by Cobb, Yackel, and Wood) 15 3. Theoretical Orientation ................................................21 Paul Cobb, ErnaYackel, and TerryWood 4. Developing a Basis for Mathematical Communication Within Small Groups ..................................................33 ErnaYackel, Paul Cobb, and Terry