Studies in Reflecting Abstraction

ISBN-13: 9781841691572 / Angielski / Twarda / 2001 / 352 str.

Jean Jean Piaget; Robert L. Campbell; Robert L. Campbell

Opis

This translation of the French Recherches sur l'abstraction reflechissante (1977), make available in English, Piaget's only treatise on reflecting abstraction - a process he came to attribute considerable importance to in his later thinking and which he believed to be responsible for many of the advances that take place in human development, especially our understanding of mathematics.

Spis treści

Introduction: Reflecting Abstraction in Context (Robert L. Campbell) Part 1: The Abstraction of Logico-arithmetic Relations. Preface: Logico-arithmetical or Algebraic Abstraction. 1. Abstraction, Differentiation, and Integration in the Use of Elementary Arithmetic Operations. 2. The Construction of Common Multiples. 3. The Inversion of Arithmetic Operations. 4. Abstraction Generalization During Transfers of Units. 5. Problems of Class Inclusion and Logical Implication. 7. The Form and Logical Implication. 8. The Formation of Analogies. 9. From Concrete Forms of the Klein Group to the INRC Group. Part 2: The Abstraction of Order. 9. Additive and Exponential Series. 10. Conditions on Reading off Complex Additive Series. 11. Ordering Practical Activity. 12. Changes in Ordering or Necessary Backtracking. Conclusion of Part Two. Part 3: The Abstraction of Spatial Relationships. 13. Relations Between the Surface Area and the Perimeter of Rectangles. 14. The Movements of a Suspended Projectile. 15. Diagonals. 16. The Displacement of a Reference Point in a System of Cyclic Movements. 17. Abstraction from Displacements and from their Coordinates. 18. Rotations and Translations. 19. The Rotation of a Bar Around a Pivot During the Sensorimotor Period. Conclusion of Part 3. General Conclusions: I. Projection. II. The Creation of Novelties Specific to Reflecting Abstraction. III. Equilibration, the Source of Noveltles, and Relationships Between the Intentions and Extensions of Structures. IV. Empirical and Reflecting Abstraction.

O autorze

Jean Piaget, Robert L. Campell