Problem Posing

Contents: Preface. Introduction. Part I: Reflections.Section 1: Pedagogical Focus: The Design of a Course.S.I. Brown, M.I. Walter, In the Classroom: Student as Author and Critic. S.I. Brown, M.I. Walter, Problem Posing in Mathematics Education. Section 2: Elaborations and Applications of Problem Posing Schemes.E.P. Goldenberg, On Building Curriculum Materials That Foster Problem Posing. D.S. Fielker, Removing the Shackles of Euclid: 8 "Strategies". W. Feibel, "What if Not?" A Technique for Involving and Motivating Students in Psychology Courses. Section 3: Rationale: Towards a Multiplistic View of the World.J.R. Jungck, A Problem Posing Approach to Biology Education. D. Buerk, An Experience with Some Able Women Who Avoid Mathematics. R. Borasi, The Invisible Hand Operating in Mathematics Instruction: Student's Conceptions and Expectations. S.I. Brown, The Logic of Problem Generation: From Moraltiy and Solving to De-Posing and Rebellion. I. Scheffler, Vice into Virtue, or Seven Deadly Sins of Education Redeemed. Part II: Algebra and Arithmetic.Section 1: Asking Why.D.J. Whitin, Number Sense and the Importance of Asking "Why?" M. Small, Creating Number Problems. D. Brutlag, Making Your Own Rules. R.N. Blake, 1089: An Example of Generating Problems. Section 2: Mistakes.L.N. Meyerson, Mathematical Mistakes. R. Borasi, Algebraic Explorations of the Error 16/64 = 1/4. Section 3: Tinkering With What Has Been Taken For Granted.W.S. Bush, A. Fiala, Problem Stories: A New Twist on Problem Posing. S.I. Brown, How to Create Problems. B.M. Moses, E. Bjork, E.P. Goldenberg, Beyond Problem Solving: Problem Posing. B.V. Kissane, Mathematical Investigations: Description, Rationale, and Example. M. Walter, Curriculum Topics Through Problem Posing. A. Friedlander, T. Dreyfus, Is the Graph of y = kx Straight? Section 4: Your Turn.C. Cassidy, B.R. Hodgson, Because a Door Has To Be Open or Closed, An Intriguing Problem Solved by Some Inductive Exploration. Part III: Geometry: Editors' Comments.Section 1: Looking Back.L. Sowder, The Looking-Back Step in Problem Solving. D.L. Jones, K.L. Shaw, Reopening the Equilateral Triangle Problem: What Happens If... S.I. Brown, Mathematics and Humanistic Themes: Sum Considerations. Section 2: The Intertwine of Problem Posing and Problem Solving.L. Hoehn, Problem Posing in Geometry. D. Chazan, Students Microcomputer-Aided Exploration in Geometry. Section 3: Something Comes From Nothing.M. Walter, Generating Problems From Almost Anything. Section 4: Your Turn.P.A. Schmidt, A Non-Simply Connected Geoboard-Based on the "What If Not" Idea.