Cognitive Science and Mathematics Education

311 Pages·1987·4.165 MB·English

by  Alan H. Schoenfeld

COGNITIVE SCIENCE
and
MATHEMATICS EDUCATION

COGNITIVE SCIENCE
and
MATHEMATICS EDUCATION
edited by
Alan H. Schoenfeld
University of California
I~ ~~o~1!~~~:up
NEW YORK AND LONDON
First Published by
Lawrence Erlbaum Associates, Inc., Publishers
365 Broadway
Hillsdale, New Jersey 07642
Transferred to Digital Printing 2009 by Routledge
270 Madison Ave, New York NY 10016
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Copyright © 1987 by Lawrence Erlbaum Associates, Inc.
All rights reserved. No part of this book may be reproduced in
any form, by photostat, microform, retrieval system, or any other
means, without the prior written permission of the publisher.
Library of Congress Cataloging-in-Publication Data
Cognitive science and mathematics education.
Bibliography: p.
Includes index.
1. Mathematics-Study and teaching. 2. Cognition.
I. Schoenfeld, Alan H.
QA11.C54 1987 510'.7 87-5362
ISBN 0-89859-791-9 (hc)
0-8058-0057-3 (Pbk)
Publisher's Note
The publisher has gone to great lengths to ensure the quality of this reprint
but points out that some imperfections in the original may be apparent.
For Anna Louise
with love and hope

Contents
1 Cognitive Science and Mathematics Education: 1
An Overview
Alan H. Schoenfeld
2 Foundations of Cognitive Theory and Research for 33
Mathematics Problem-Solving
Edward A. Silver
3 Instructional Representations Based on Research about 61
Understanding
James G. Greeno
4 Cognitive Technologies for Mathematics Education 89
RoyD. Pea
5 Problem Formulating: 123
Where Do Good Problems Come From?
Jeremy Kilpatrick
6 From the Teacher's Side of the Desk 149
Anna Henderson
7 New Knowledge about Errors and New Views about 165
Learners: What They Mean to Educators and More
Educators Would Like to Know
Stephen B. Maurer
8 What's All the Fuss about Metacognition? 189
Alan H. Schoenfeld
vii
viii PREFACE
9 Cognitive Science and Algebra Learning 217
Ronald H. Wenger
10 Cognitive Science and Mathematics Education: 253
A Mathematician's Perspective
H. O. Pollak
11 Cognitive Science and Mathematics Education: 265
A Mathematics Educator's Perspective
F. Joe Crosswhite
Author Index 279
Subject Index 285
Contributors
Dr. F. Joe Crosswhite
Mathematics, Northern Arizona University
Flagstaff, Arizona 86011
Dr. James Greeno
Education and Psychology, University of California
Berkeley, CA 94720
Mrs. Anna Henderson
Maury High School
Norfolk, VA 23517
Dr. Jeremy Kilpatrick
Mathematics Education, University of Georgia
Athens, GA 30602
Dr. Steven B. Maurer
Mathematics Swarthmore College
Swarthmore, P A 19081
Dr. Roy Pea
Education, New York University
New York, NY ~OO03
ix