Table Of ContentMfect and Mathematical Problem Solving
Douglas B. McLeod Verna M. Adams
Editors
Affect and Mathematical
Problem Solving
A New Perspective
With 16 Illustrations
Springer-Verlag New York Berlin Heidelberg
London Paris Tokyo
Douglas B. McLeod Verna M. Adams
Elementary and Secondary Education 105 Aderhold Hall
Washington State University University of Georgia
Pullman, Washington 99164-2122, USA Athens, Georgia 30602, USA
Library of Congress Cataloging-in-Publication Data
Affect and mathematical problem solving: a new perspective 1 Douglas
B. McLeod, Verna M. Adams, editors.
p. cm.
Includes bibliographies and index.
ISBN-13: 978-1-4612-8178-8 e-lSBN-13: 978-1-4612-3614-6
DOl: 10.1007/978-1-4612-3614-6
1. Problem solving-Study and teaching-Psychological aspects.
2. Mathematics-Study and teaching-Psychological aspects.
3. Mfect (Psychology) I. McLeod, Douglas B. II. Adams, Vema M.
QA63.A34 1989
153.4'3-dc 19 88-39063
Printed on acid-free paper.
© 1989 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1s t edition 1989
All rights reserved. This work may not be translated or copied in whole or in part without the written
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9 8 7 6 5 4 3 2 1
Preface
Research on mathematical problem solving has received considerable attention
in recent years, not only from those who do research on mathematics learning
and teaching, but also from psychologists and others who work in the cognitive
sciences. Although most of this research has focused on cognitive factors, there
has been a surge of interest in the role of affect in mathematical problem solving.
This book explores these affective factors and their relationships to the cognitive
processes involved in problem solving. The ideas are of particular interest to
those who work in mathematics education, psychology, and other fields that are
related to the cognitive sciences.
The origins of the book can be found in George Mandler's (1984) theory of
emotion and in Edward Silver's (1985) effort to integrate the multiple perspec
tives that influence research on mathematical problem solving. Therefore, the
interdisciplinary mix for this volume includes not only the usual perspectives of
mathematics education, cognitive psychology, and artificial intelligence, but also
cognitive approaches to clinical and counseling psychology.
The book is divided into five parts. The first introduces the basic ideas of Man
dler's theory and suggests how the theory can be applied in research on mathe
matical problem solving. Part II presents five studies of learning that test and
extend the theory, and the five chapters in Part III perform the same function in
the context of research on teaching. Part IV includes two responses to the theory,
one from the viewpoint of mathematics education, and the other from cognitive
psychology. Finally, following George Polya's recommendations, Part V is spent
"looking back" at the problem of how to build a theory of affective factors in
mathematical problem solving.
The development of an interdisciplinary volume like this one requires a sub
stantial amount of time both for interaction and reflection by the participants. In
this case we were fortunate to have the support of the National Science Founda
tion for two meetings where the chapter authors and other researchers had a
chance to debate the issues and report on their own research. The first meeting
was held in May 1986, in San Diego, and focused on presenting and discuss
ing Mandler's theory. Participants also outlined their plans for implementing
Mandler's ideas in their own research during the next year. In June 1987, the
vi Preface
participants met again in San Diego and reported on the results of their efforts to
incorporate affective factors in their research on mathematical problem solving.
This volume grew out of the papers that were presented at the second meeting.
In addition to these two meetings, subgroups of participants presented symposia
at the 1987 Annual Meetings of both the American Educational Research Associ
ation and the National Council of Teachers of Mathematics. Consequently, we
have here not the typical report of the proceedings of a conference, but the results
of two years of study, debate, and research by the participants.
The preparation of this volume was supported in part by National Science
Foundation Grant No. MDR-8696142, as well as by other grants from several
agencies to some of the individual authors. Any opinions, conclusions, or recom
mendations are those of the authors and do not necessarily reflect the views of
the funding agencies. We also want to acknowledge the cooperation of both of the
academic institutions that have served as the host for this project, San Diego
State University and Washington State University.
We want to thank all of the authors for their contributions and cooperation. We
are especially grateful to George Mandler of the University of California at San
Diego for his willingness to share his psychological theories and to see them
tested in the domain of mathematics classrooms. Special thanks are also due to
Elizabeth Fennema of the University of Wisconsin, who shared generously of her
experience in research on affect and mathematics education. Fennema and Man
dler both served on our interdisciplinary Project Advisory Board, along with
David Carlson, a research mathematician at San Diego State University, and FJ.
Crosswhite, Past-President of the National Council of Teachers of Mathematics.
The Advisory Board, along with Ray Hannapel of the National Science Founda
tion, played an important role in the development of the project, and we are
grateful for their help.
In addition, we want to thank the staff members in San Diego and Pullman who
have assisted us with this project, especially Kathie Duncan. We also want to
thank the people at Springer-Verlag for their help in producing this book. Finally,
we thank our families for their support throughout this project.
Pullman, Washington Douglas B. McLeod
Athens, Georgia Verna M. Adams
Contents
Preface .......................... , . . . .. . .. . . . . . . .. . .. . . .. . . . v
Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Part I A Theory of Affect for Mathematical Problem Solving
Chapter 1 Mfect and Learning: Causes and Consequences
of Emotional Interactions
GEORGE MANDLER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 The Role of Affect in Mathematical Problem Solving
DOUGLAS B. McLEOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 3 Describing the Affective Domain: Saying What We Mean
LAURIE E. HART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Part II Studies of Learning
Chapter 4 Affect in Schema Knowledge: Source and Impact
SANDRA P. MARSHALL .............................. 49
Chapter 5 Aesthetic Influences on Expert Mathematical
Problem Solving
EDWARD A. SILVER and WENDY METZGER ..... . . . . . . . . . 59
Chapter 6 Self-Confidence, Interest, Beliefs, and Metacognition:
Key Influences on Problem-Solving Behavior
FRANK K. LESTER, JOE GAROFALO,
and DIANA LAMBDIN KROLL. . . . . . . . . . . . . . .. . . . . . . . . . 75
Chapter 7 Information Technologies and Affect in
Mathematical Experiences
JAMES J. KAPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
viii Contents
Chapter 8 Searching for Affect in the Solution of Story Problems
in Mathematics
LARRY SOWDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 104
Part III Studies of Teaching
Chapter 9 Young Children's Emotional Acts While Engaged
in Mathematical Problem Solving
PAUL COBB, ERN A YACKEL, and TERRY WOOD. . . . . . . . . . .. 117
Chapter 10 Teaching Practices and Student Mfect in Problem-Solving
Lessons of Select Junior-High Mathematics Teachers
DOUGLAS A. GROUWS and KATHLEEN CRAMER. . . . . . . . . .. 149
Chapter 11 Mfect and Problem Solving in an Elementary School
Mathematics Classroom
ALBA G. THOMPSON and PATRICK W. THOMPSON ......... 162
Chapter 12 Mfective Factors and Computational Estimation Ability
JUDITH THREADGILL SOWDER. . . . . . . . . . . . . . . . . . . . . . . .. 177
Chapter 13 Mfective Issues in Teaching Problem Solving:
A Teacher's Perspective
VERNA M. ADAMS .. '" .... " . . .. . . .. . . . . . . . . . . .. . .. 192
Part IV Responses to the Theory
Chapter 14 The Study of Mfect and Mathematics: A Proposed
Generic Model for Research
ELIZABETH FENNEMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 205
Chapter 15 Psychological Conceptions of Mathematics and Emotion
BARBARA A. McDoNALD . . . . . . . . . . . . . . . . . . . . . . . . . . .. 220
Part V Looking Back
Chapter 16 Mfect and Learning: Reflections and Prospects
GEORGE MANDLER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 237
Chapter 17 Beliefs, Attitudes, and Emotions: New Views of Mfect
in Mathematics Education
DOUGLAS B. McLEOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 245
Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 259
Subject Index ................................................ 265
Contributors
VERNA M. ADAMS
Department of Mathematics Education, University of Georgia, Athens,
Georgia 30602, USA
PAUL COBB
Department of Education, Purdue University, West Lafayette, Indiana 47907,
USA
KATHLEEN CRAMER
Department of Elementary Education, University of Wisconsin-River Falls,
River Falls, Wisconsin 54022, USA
ELIZABETH FENNEMA
Wisconsin Center for Education Research, University of Wisconsin-Madison,
Madison, Wisconsin 53706, USA
JOE GAROFAW
Department of Curriculum Instruction and Special Education, University of
Virginia, Charlottesville, Virginia 22903, USA
DOUGLAS A. GROUWS
Department of Curriculum and Instruction; Center for Research in Social
Behavior, University of Missouri, Columbia, Missouri 65211, USA
LAURIE E. HART
Department of Elementary Education, University of Georgia, Athens, Georgia
30602, USA
JAMES 1. KAPUT
Department of Mathematics, Southeastern Massachusetts University, North
Dartmouth, Massachusetts 02747; Educational Technology Center, Harvard
University, Cambridge, Massachusetts 02138, USA
DIANA LAMBDIN KROLL
School of Education, Indiana University, Bloomington, Indiana 47405, USA
x Contributors
FRANK K. LESTER
School of Education, Indiana University, Bloomington, Indiana 47405, USA
GEORGE MANDLER
Center for Human Information Processing, University of California-San
Diego, La Jolla, California 92093, USA
SANDRA P. MARSHALL
Department of Psychology; Center for Research in Mathematics and Science
Education, San Diego State University, San Diego, California 92182, USA
BARBARA A. McDONALD
Navy Personnel Research and Development Center, San Diego, California
92107, USA
DOUGLAS B. McLEOD
Elementary and Secondary Education, Washington State University, Pullman,
Washington 99164-2122; Department of Mathematical Sciences, San Diego
State University, San Diego, California 92182, USA
WENDY METZGER
Department of Mathematics, Palomar College, San Marcos, California 92069,
USA
EDWARD A. SILVER
School of Education; Learning Research and Development Center, University
of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
JUDITH THREADGILL SOWDER
Department of Mathematical Sciences, San Diego State University, San Diego,
California 92182, USA
LARRY SOWDER
Department of Mathematical Sciences, San Diego State University, San Diego,
California 92182, USA
ALBA G. THOMPSON
Department of Mathematics, Illinois State University, Normal, Illinois 61761,
USA
PATRICK W. THOMPSON
Department of Mathematics, Illinois State University, Normal, Illinois 61761,
USA
TERRY WOOD
Department of Education, Purdue University, West Lafayette, Indiana 47907,
USA
ERNA YACKEL
Department of Mathematical Sciences, Purdue University Calumet, Calumet,
Indiana 46323, USA
Part I A Theory of Affect
for Mathematical
Problem Solving
