Studies in Reflecting Abstraction
By Jean Piaget
Edited by Robert L. Campell
Translated by Robert L. Campell
Psychology Press – 2000 – 352 pages
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.
Rich with empirical research on reflecting abstraction at work in the thinking of 4 to 12 year olds, the studies in this volume examine its role in many contexts of cognitive development such as: reasoning about mathematics; forming analogies; putting objects in order by size and comparing the resulting series; and navigating through a wire maze. His theoretical discussions explore the relationships between reflecting abstraction and other central processes in his later theory, such as generalization, becoming conscious, and equilibration, as the differentiation of possibilities and their integration into necessities. These discussions indicate which aspects of his later theorizing were settled and which require further thought and investigation.
Studies in Reflecting Abstraction will be of interest to developmental and cognitive psychologists, educationalists, philosophers and anyone who seeks to understand human knowledge and its development.
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.