Epistemological Foundations of Mathematical Experience

1. Front Matter

   Pages i-xvii

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2. Philosophical and Psychological Aspects of Constructivism

   • Clifford Konold, David K. Johnson

   Pages 1-13

3. The Import of Fodor’s Anti-Constructivist Argument

   • Mark H. Bickhard

   Pages 14-25

4. The Learning Paradox: A Plausible Counterexample

   • Leslie P. Steffe

   Pages 26-44

5. Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and Piaget’s Approach

   • Ernst von Glasersfeld

   Pages 45-67

6. A Pre-Logical Model of Rationality

   • Mark H. Bickhard

   Pages 68-77

7. Recursion and the Mathematical Experience

   • Thomas E. Kieren, Susan E. B. Pirie

   Pages 78-101

8. The Role Mathematical Transformations and Practice in Mathematical Development

   • Robert G. Cooper Jr.

   Pages 102-123

9. The Concept of Exponential Functions: A Student’s Perspective

   • Jere Confrey

   Pages 124-159

10. Constructive Aspects of Reflective Abstraction in Advanced Mathematics

    • Ed Dubinsky

    Pages 160-202

11. Reflective Abstraction in Humanities Education: Thematic Images and Personal Schemas

    • Philip Lewin

    Pages 203-237

12. Enhancing School Mathematical Experience Through Constructive Computing Activity

    • Larry L. Hatfield

    Pages 238-259

13. To Experience is to Conceptualize: A Discussion of Epistemology and Mathematical Experience

    • Patrick W. Thompson

    Pages 260-281

14. Back Matter

    Pages 283-312

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On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.

• Lernen
• Mathematica
• Mathematik/Lernmethoden
• algebra
• arithmetic
• awareness
• epistemology
• experience
• function
• knowledge
• learning
• logic
• mathematics
• psychology
• recursion

• College of Education, Mathematics Education Department, The University of Georgia, Athens, USA

  Leslie P. Steffe

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