Problem Posing: Reflections and Applications

By Stephen I. Brown; Marion I. Walter | Go to book overview

PROBLEM POSING: REFLECTIONS AND APPLICATIONS

Edited by Stephen I. Brown University at Buffalo

Marion I. Walter University of Oregon

LEA LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS 1993 Hillsdale, New Jersey Hove and London

-iii-

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Problem Posing: Reflections and Applications
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Preface ix
  • Reflective Essays xi
  • Algebra and Arithmetic xi
  • Algebra and Arithmetic xii
  • Algebra and Arithmetic xii
  • Reference xii
  • Introduction xiii
  • References xvii
  • I Reflective Essays: Editors' Comments 1
  • References 5
  • 1: In the Classroom: Student as Author and Critic 7
  • 2: Problem Posing in Mathematics Education 16
  • Conclusion 26
  • References 30
  • 3: On Building Curriculum Materials That Foster Problem Posing 31
  • References 38
  • 4: Removing the Shackles of Euclid: 8: Strategies 39
  • 5: "What If Not?" 52
  • References 57
  • References 63
  • 6: A Problem Posing Approach to Biology Education 64
  • References 69
  • 7: An Experience with Some Able Women Who Avoid Mathematics 70
  • Summary 81
  • 8: The Invisible Hand Operating in Mathematics Instruction: Students' Conceptions and Expectations 83
  • Conclusions 90
  • 9: The Logic of Problem Generation: From Morality and Solving to De-Posing and Rebellion 92
  • References 102
  • 10: Vice into Virtue, or Seven Deadly Sins of Education Redeemed 104
  • Conclusion 116
  • II Algebra and Arithmetic Editors' Comments 117
  • References 120
  • 11: Number Sense and the Importance of Asking "Why?" 121
  • Reference 129
  • 12: Creating Number Problems 130
  • References 133
  • 13: Making Your Own Rules 134
  • Conclusion 139
  • 14: 1089: An Example of Generating Problems 141
  • References 151
  • 15: Mathematical Mistakes 153
  • Reference 158
  • 16: Algebraic Explorations of the Error 12+̸/2+̸4=1/4 159
  • References 163
  • 17: Problem Stories: A New Twist on Problem Posing 167
  • References 173
  • 18: How to Create Problems 174
  • Summary 177
  • 19: Beyond Problem Solving: Problem Posing1 178
  • References 187
  • Footnote 187
  • 20: Mathematical Investigation: Description, Rationale, and Example 189
  • Conclusion 202
  • References 203
  • 21: Curriculum Topics Through Problem Posing 204
  • References 210
  • 22: Is the Graph of y = kx Straight? 211
  • References 219
  • 23: Because a Door Has to Be Open or Closed: An Intriguing Problem Solved By Some Inductive Exploration 222
  • Conclusion 227
  • References 228
  • III Geometry Editors' Comment 229
  • References 234
  • 24: The Looking-Back Step in Problem Solving 235
  • Summary 238
  • References 239
  • 25: Reopening the Equilateral Triangle Problem: What Happens If . . . 240
  • References 248
  • 26: Mathematics and Humanistic Themes 249
  • Summary 276
  • Being Present 276
  • 27: Problem Posing in Geometry 281
  • References 288
  • 28: Students' Microcomputer- Aided Exploration in Geometry 289
  • Conclusion 298
  • References 299
  • 29: Generating Problems From Almost Anything 302
  • References 316
  • 30: A Non-Simply Connected Geoboard -- Based on the "What If Not" Idea 319
  • Summary 325
  • References 326
  • Author Index 327
  • Subject Index 330
  • Notes on Contributors 332
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