Constructivist Views on the Teaching and Learning of Mathematics || Front Matter

Front MatterSource: Journal for Research in Mathematics Education. Monograph, Vol. 4, ConstructivistViews on the Teaching and Learning of Mathematics (1990), pp. i-193Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/749906 .

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JOURNAL FOR

RESEARCH IN

MATHEMATICS

EDUCATION MONOGRAPH NUMBER 4

^^^^fBtti^ll n II tBfAAm AI

National Council of Teachers of Mathematics



A Monograph Series of the National Council of Teachers of Mathematics

The JRME monograph series is published by the Editorial Panel as a sup- plement to the journal. Each monograph has a single theme related to the learning or teaching of 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 manuscript for consideration as a monograph should send four copies of the complete manuscript to the monograph series editor. Manuscripts should be no longer than 200 double-spaced typewritten pages. The name, affiliations, and qualifications of each contributing author should be included with the manuscript.

Series Editor FRANK K. LESTER, JR., Indiana Univer-

sity, Bloomington, IN 47405

Associate Editor DIANA LAMBDIN KROLL, Indiana Uni-

versity, Bloomington, IN 47405 Editorial Panel CATHERINE BROWN, Virginia Polytech-

nic Institute and State University; Chair MICHAEL T. BATTISTA, Kent State Uni-

versity, Ohio PAUL COBB, Purdue University MARY GRACE KANTOWSKI, Univer-

sity of Florida CAROL N. LARSON, University of Ari-

zona LARRY SOWDER, San Diego State Uni-

versity ALAN OSBORNE, Ohio State University;

Board Liaison

Manuscripts should be sent to Frank K. Lester, Jr. Room 309, Education Building Indiana University Bloomington, IN 47405



CONSTRUCTIVIST VIEWS ON THE

TEACHING AND LEARNING

OF MATHEMATICS



CONSTRUCTIVIST VIEWS ON THE

TEACHING AND LEARNING

OF MATHEMATICS

edited by

Robert B. Davis Carolyn A. Maher

Nel Noddings

NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS



Copyright ? 1990 by THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, INC.

1906 Association Drive, Reston, Virginia 20191-1593 All rights reserved

Fourth printing 1999

Library of Congress Cataloging-in-Publication Data

Printed in the United States of America Constructivist views on the teaching and learning of mathematics /

edited by Robert B. Davis, Carolyn A. Maher, Nel Noddings. p. cm. - (Journal for research in mathematics education.

Monograph; no. 4) Includes bibliographical references. ISBN 0-87353-300-3 1. Mathematics-Study and teaching. I. Davis, Robert B.

(Robert Benjamin), 1926- . II. Maher, Carolyn Alexander. II. Noddings, Nel. IV. Series. QA12.C654 1990 510'.71-dc20 90-45001

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 interpreted as official positions of the Council.

Printed in the United States of America



Table of Contents

Acknowledgments

Background:

Introduction:

Part One:

Chapter One:

Chapter Two:

Chapter Three:

Part Two:

Chapter Four:

Chapter Five:

Chapter Six:

vii

ix A Call to Action

Constructivist Views on the Teaching and Learning of Mathematics --------------------------------------

Constructivism: Promise and Problems

Constructivism in Mathematics Education

Nel Noddings ----------------------------------------

An Exposition of Constructivism: Why Some

Like It Radical

Ernst von Glasersfeld ----------------------------------------

Epistemology, Constructivism, and Discovery

Learning Mathematics

Gerald A. Goldin --------------------------------------

The Nature of Mathematics and How It Is Learned

Children's Learning: A Cognitive View

Arthur J. Baroody & Herbert P. Ginsburg ------------------

1

7

19

31

51

The Nature of Mathematics: What Do We Do When We

"Do Mathematics"?

Robert B. Davis & Carolyn A. Maher ---------------------- 65

Teacher's Learning: Building Representations of

Children's Meanings

Carolyn A. Maher & Robert B. Davis ----------------------- 79

v



Constructivism in the Classroom

Chapter Seven:

Chapter Eight:

Part Four:

Chapter Nine:

Chapter Ten:

Chapter Eleven:

Discovery Learning and Constructivism

Robert B. Davis -------------------------- 93

What Constructivism Implies for Teaching Jere Confrey ---------------------------------- 107

Children and the Education of Teachers

Classrooms as Learning Environments for

Teachers and Researchers

Paul Cobb, Terry Wood, & Era Yackel ------ ------- 125

Teacher Development in Mathematics in a

Constructivist Framework

Carolyn A. Maher & Alice Alston ------------

On the Knowledge of Mathematics Teachers

Leslie P. Steffe ---------------------------------

147

167

Conclusions

Chapter Twelve:

References

Suggestions for the Improvement of Mathematics

Education

Robert B. Davis, Carolyn A. Maher & Nel Noddings - 187

------------------------- 1195

vi

Part Three:



Acknowledgments

There are many who made possible the completion of this monograph and to whom we wish to

express our appreciation. First, to the sponsors of the initial 1986 working conference: Martin

Friedman, Director of the Office of Teacher Education, New Jersey Department of Higher Education, and Gerald A. Goldin, Director of the Rutgers University Center for Mathematics, Science and Computer Education. Their support and vision made possible the forum that initiated

this work. Second, to the colleagues who presented position papers at the working conference and

stimulated discussion and thought on timely issues. Third, to the graduate students who read and

commented on the first draft of the manuscript; and fourth, to the many support staff who assisted in the technical preparation of the manuscript: Lynda Smith Deming for her attention to the many details in the copy editing and organization and for her illustrations in Chapters 5, 6, 7 and 11; Barbara Smith, for her typing, organizing and generally invaluable assistance.

Special thanks are expressed to the anonymous reviewers of drafts of this manuscript. Their suggestions were very helpful to us in preparing the final version.

Lastly, but most importantly, we wish to thank both the teachers with whom we work and

our students. They continue to help us learn about learning and teaching.

vii Vll



PART ONE

CONSTRUCTIVISM: PROMISE AND PROBLEMS



PART TWO

THE NATURE OF MATHEMATICS

AND HOW IT IS LEARNED



PART THREE

CONSTRUCTIVISM IN THE CLASSROOM



PART FOUR

CHILDREN AND THE EDUCATION OF TEACHERS



CONCLUSIONS



REFERENCES



Documents

Constructivist Views on the Teaching and Learning of Mathematics || Front Matter