Mathematical Thinking and Problem Solving

By: Alan H. Schoenfeld (Editor), Alan H. Sloane (Editor)

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Paperback | 1 September 1994 | Edition Number 1

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362 Pages

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In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives.

As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.*

A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

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Non-Fiction Medicine Other Branches of Medicine Clinical Psychology Psychotherapy Psychology Cognition & Cognitive Psychology Education Philosophy & Theory of Education Mathematics Teaching of a Specific Subject Higher & Further Education

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Contributors	p. xi
Acknowledgments	p. xv
Preface	p. xvii
The Role of Research in Reforming Mathematics Education: A Different Approach	p. 1
A Discussion of Judah Schwartz's Chapter	p. 8
Some Thoughts on Writing for the Putnam	p. 19
References	p. 29
Comments on Bruce Reznick's Chapter	p. 30
References	p. 38
A Discussion of Bruce Reznick's Chapter	p. 39
References	p. 51
Reflections on Doing and Teaching Mathematics	p. 53
References	p. 69
A Discussion of Alan Schoenfeld's Chapter	p. 71
References	p. 75
Democratizing Access to Calculus: New Routes to Old Roots	p. 77
References	p. 152
Comments on James Kaput's Chapter	p. 157
References	p. 170
Comments on James Kaput's Chapter	p. 172
References	p. 191
Making Calculus Students Think with Research Projects	p. 193
References	p. 208
A Discussion of Cohen, Knoebel, Kurtz, and Pengelley's Chapter	p. 209
A Theory and Practice of Learning College Mathematics	p. 221
References	p. 242
Comments on Ed Dubinsky's Chapter	p. 244
References	p. 246
Comments on Ed Dubinsky's Chapter	p. 248
Acknowledgments	p. 256
References	p. 256
The Role of Proof in Problem Solving	p. 257
References	p. 268
Comments on Susanna Epp's Chapter	p. 270
Acknowledgments	p. 277
References	p. 277
A Discussion of Susanna Epp's Chapter	p. 279
Classroom Instruction That Fosters Mathematical Thinking and Problem Solving: Connections Between Theory and Practice	p. 287
Acknowledgments	p. 302
Acknowledgments	p. 303
Comments on Thomas Romberg's Chapter	p. 305
References	p. 311
Comments on Thomas Romberg's Chapter	p. 312
References	p. 321
Epilogue	p. 323
Author Index	p. 327
Subject Index	p. 333
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Mathematical Thinking and Problem Solving

At a Glance

Paperback

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