Stephen I. Brown e Marion I. Walter
Psychology Press |1993 |355 páginas | rar – pdf | 14,88 Mb
link (password : matav)
Based in part upon that work and also upon a number of articles by its authors, other members of the mathematics education community began to apply and expand upon their ideas. This collection of thirty readings is a testimony to the power of the ideas that originally appeared. In addition to reproducing relevant materials, the editors of this book of readings have included a considerable amount of interpretive text which places the articles in the context of problem solving. While the preponderance of essays focus upon mathematics and mathematics education, some of them point to the relevance of problem posing to other fields such as biology or psychology. In the interpretive text that accompanies each chapter, they indicate how ideas expressed for one audience may be revisited or transformed in order to ready them for a variety of audiences.
Contents
PREFACE ix
INTRODUCTION xili
Reflections on the Power of Problem Posing xiv
On the Audience for the Book xv
A Note on Reading the Collection xvi
A Caveat of Sorts xvii
CHAPTER I. REFLECTIONS INTRODUCTORY COMMENTS 1
SECTION 1: PEDAGOGICAL FOCUS: THE DESIGN OF A COURSE
EDITORS’ COMMENTS 3
ESSAYS
1. In the Classroom: Student as Author and Critic Stephen I. Brown and Marion I. Walter 7
2. Problem Posing in Mathematics Education Stephen I. Brown and Marion I. Walter 16
SECTION 2: ELABORATIONS AND APPLICATIONS OF PROBLEM POSING SCHEMES
EDITORS’ COMMENTS 28
ESSAYS:
3. On Building Curriculum Materials That Foster Problem Posing, E. Paul Goldenberg 31
4. Removing the Shackles of Euclid: 8: “Strategies”, David S. Fielker 39
5. “What if Not?” A Technique for Involving and Motivating Students in Psychology Courses, Werner Feibel 52
SECTION 3: RATIONALE: TOWARDS A MULTIPLISTIC VIEW OF THE WORLD
EDITORS’ COMMENTS 59
ESSAYS:
6. A Problem Posing Approach to Biology Education, John R. Jungck 64
7. An Experience with Some Able Women Who Avoid Mathematics, Dorothy Buerk 70
8. The Invisible Hand Operating in Mathematics Instruction: Student’s Conceptions and Expectations, Raffaella Borasi 83
9. The Logic of Problem Generation: From Morality and Solving to De-Posing and Rebellion, Stephen I. Brown 92
10. Vice into Virtue, or Seven Deadly Sins of Education Redeemed, Israel Scheffler 104
CHAPTER II. ALGEBRA AND ARITHMETIC 117
INTRODUCTORY COMMENTS
SECTION 1: ASKING WHY
EDITORS’ COMMENTS 118
ESSAYS:
11. Number Sense and the Importance of Asking “Why?” David J. Whitin 121
12. Creating Number Problems, Marian Small 130
13. Making Your Own Rules, Dan Brutlag 134
14. 1089: An Example of Generating Problems, Rick N. Blake 141
SECTION 2: MISTAKES
EDITORS’ COMMENTS 152
ESSAYS:
15. Mathematical Mistakes, Lawrence Nils Meyerson 153
16. Algebraic Explorations of the Error Raffaella Borasi
SECTION 3: TINKERING WITH WHAT HAS BEEN TAKEN FOR GRANTED
EDITORS’ COMMENTS 164
ESSAYS:
17. Problem Stories: A New Twist on Problem Posing, William S. Bush and Ann Fiala 167
18. How to Create Problems, Stephen I. Brown 174
19. Beyond Problem Solving: Problem Posing, Barbara M. Moses, Elizabeth Bjork, and E. Paul Goldenberg 178
20. Mathematical Investigations: Description, Rationale, and Example, Barry V. Kissane 189
21. Curriculum Topics Through Problem Posing, Marion Walter 204
22. Is the Graph of y = cx Straight? Alex Friedlander and Tommy Dreyfus 204
SECTION 4: YOUR TURN
EDITORS’ COMMENTS 220
ESSAY:
23. Because a Door Has To Be Open or Closed, An Intriguing Problem Solved by Some Inductive Exploration, Charles Cassidy and Bernard R. Hodgson 222
CHAPTER III. GEOMETRY: EDITORS’ COMMENTS 229
INTRODUCTORY COMMENTS
SECTION 1: LOOKING BACK
EDITORS’ COMMENTS 231
ESSAYS:
24. The Looking-Back Step in Problem Solving, Larry Sowder 235
25. Reopening the Equilateral Triangle Problem: What Happens If . . . , Douglas L Jones and Kenneth L Shaw 240
26. Mathematics and Humanistic Themes: Sum Considerations, Stephen I. Brown 249
SECTION 2: THE INTERTWINE OF PROBLEM POSING AND PROBLEM SOLVING
EDITORS’ COMMENTS 279
ESSAYS:
27. Problem Posing in Geometry, Larry Hoehn 281
28. Students Microcomputer-Aided Exploration in Geometry, Daniel Chazan 289
SECTION 3: SOMETHING COMES FROM NOTHING
EDITORS’ COMMENTS
ESSAY:
29. Generating Problems From Almost Anything, Marion Walter
SECTION 4: YOUR TURN
EDITORS’ COMMENTS
ESSAY:
30. A Non-Simply Connected Geoboard-Based on the Not” Idea, Philip A. Schmidt
AUTHOR INDEX
SUBJECT INDEX
NOTES ON CONTRIBUTORS