Epistemological Foundations of Mathematical Experience

Paperback (Softcover reprint of the original 1st ed. 1991)
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Editorial Reviews

Twelve papers by psychologists, educationists, and mathematicians address issues connected with understanding, analyzing, expressing, and enhancing the mathematical experiences of children. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387976006
  • Publisher: Springer New York
  • Publication date: 10/4/1991
  • Series: Recent Research in Psychology Series
  • Edition description: Softcover reprint of the original 1st ed. 1991
  • Edition number: 1
  • Pages: 312
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.69 (d)

Table of Contents

1 Philosophical and Psychological Aspects of Constructivism.- Foundationalism and Constructivism.- Psychological Constructivism.- Foundations Revisited.- Overview of Chapters.- 2 The Import of Fodor’s Anti-Constructivist Argument.- Fodor’s Argument.- Reconstructing the Argument.- What’s Wrong with Contemporary Models of Representation?.- Why Should We Care?.- Interactivism: Outline of a Solution.- Conclusions.- 3 The Learning Paradox: A Plausible Counterexample.- A Guiding Analogy.- An Example of the Learning Paradox.- A Weak Form of the Innatist Hypothesis.- Learning the Initial Number Sequence.- A More General Reformulation of Learning.- Final Comments.- 4 Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and Piaget’s Approach.- Reflection.- Abstraction.- Re-Presentation.- The Power of Symbols.- Piaget’s Theory of Abstraction.- Form and Content.- Scheme Theory.- Four kinds of Abstraction.- The Question of Awareness.- Conclusion.- Philosophical Postscript.- 5 A Pre-Logical Model of Rationality.- Rationality as Logic.- Some Thoughts About Thought.- The Nature of Rationality.- The Necessity of Rationality.- The Rationality of Rationality.- The Rationality of Necessity.- The Nurturance of Rationality.- Conclusion.- 6 Recursion and the Mathematical Experience.- What is Recursion?.- What Contributes to Children’s Mathematical Experience?.- Mathematical Knowledge Building as a Recursive Activity.- Summary.- 7 The Role Mathematical Transformations and Practice in Mathematical Development.- Transfer Problem Illustration.- Plan of Chapter.- Acquiring Mental Maps as a Metaphor for Interactive Knowing.- Infant Number Skills.- Addition and Subtraction.- Preschoolers’ Understanding of One-to-One Correspondence.- Children’s Acquisition of Some Algebraic Manipulations.- Summary and Conclusions.- 8 The Concept of Exponential Functions: A Student’s Perspective.- The Traditional Account of Exponential Expressions and Exponential Functions.- Method.- Results.- Conclusions.- Discussion: Implications of Findings for Mathematics Education.- 9 Constructive Aspects of Reflective Abstraction in Advanced Mathematics.- Mathematical Knowledge and its Acquisition.- The Constructive Aspect of the Reflective Abstraction.- My Research Program.- Specific Mathematics Topics.- 10 Reflective Abstraction in Humanities Education: Thematic Images and Personal Schemas.- Piaget, Education, and Hermeneutics.- Reflective Abstraction of “Being Romantic”.- Equilibration and the Cognitive Compensations.- An Integrated Guiding Image.- 11 Enhancing School Mathematical Experience Through Constructive Computing Activity.- Aspects of Significant School Mathematics Experiences.- Experiential Aspects of Constructive Computing Activities.- Summary.- 12 To Experience is to Conceptualize: A Discussion of Epistemology and Mathematical Experience.- Construction of Mathematical Thought.- Curriculum and Pedagogy.- Methodology.- Mathematics Education as Paideia.- Postscript.- References.- Author Index.

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