The art of problem posing

Stephen I. Brown, Marion I. Walter9780805849769, 9780805849776, 9781410611833, 0805849769, 0805849777

The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem posing (such as where problems come from, what to do with them, and the like) from the “other” to themselves and offers a broader conception of what can be done with problems. Special features include: an exploration of the logical relationship between problem posing and problem solving; sketches, drawings, and diagrams that illustrate the schemes proposed; and a special section on writing in mathematics.
In the updated third edition, the authors specifically: *address the role of problem posing in the NCTM Standards; *elaborate on the concept of student as author and critic; *include discussion of computer applications to illustrate the potential of technology to enhance problem posing in the classroom; *expand the section on diversity/multiculturalism; and *broaden discussion of discipline/classroom management methods.
This book offers present and future teachers at the middle school, secondary school, and higher education levels ideas to enrich their teaching and suggestions for how to incorporate problem posing into a standard mathematics curriculum.

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Table of contents :
Cover……Page 1
Title page……Page 3
Date-line……Page 4
Contents……Page 5
Acknowledgments: Third Edition……Page 7
1 Introduction……Page 11
Origins of the Book……Page 16
Ways of Reading the Book……Page 17
Contextualizing the Third Edition……Page 18
A First Look; What Are Some Answers?……Page 22
A Second Look at $x^2 + y^2 = z^2$……Page 24
A New Perspective……Page 27
Sticking to the Given: Some Examples……Page 29
Some Reflections on Phenomena to Investigate……Page 35
Strategies for Phase-One Problem Generation……Page 36
Seeing What Is in Front of You……Page 43
Attribute Listing for a New Problem Posing Strategy……Page 45
Now What? A Look at Three Attributes of Geoboards……Page 48
What Have We Done?……Page 54
A Return to the Pythagorean Theorem……Page 56
Summary……Page 74
Two Sample “What-If-Nots” in Some Detail……Page 76
Other Beginnings: Some Snippets……Page 89
Summary……Page 119
One Example in Detail……Page 121
Problem Solving Yields Problem Posing……Page 126
Reflections on Natural Links……Page 130
Summary……Page 136
7 Writing for Journals of Editorial Boards: Student as Author and Critic……Page 138
Course Description……Page 139
Organization of the Course……Page 141
A Word of Caution……Page 145
“Snippets” of Journal Materials……Page 147
Some “Moore” Reflections on the Editorial Board Scheme……Page 157
Variation of Editorial Board Experience: A Secular Talmud……Page 163
T.A.L.M.U.D.ic Course Description……Page 164
Organization of The T.A.L.M.U.D.ic Course……Page 166
A T.A.L.M.U.D.ic “Snippet”……Page 169
Other T.A.L.M.U.D.ic Beginnings……Page 172
Summary……Page 174
A Look Back……Page 175
Problem Posing and Math Anxiety……Page 176
Problem Posing and Cooperation……Page 177
A Research Agenda……Page 178
Bibliography……Page 182
Author Index……Page 187
Subject Index……Page 189