Epistemological Foundations of Mathematical Experience /

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 bo...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Steffe, Leslie P. (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York, 1991.
Colección:Recent research in psychology,
Temas:
Psychology.
Mathematics.
Psychology
Mathematics
Psychologie.
Mathématiques.
psychology.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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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