Abstraction and Representation

This book deals with the development of thinking under different cultural conditions, focusing on the evolution of mathematical thinking in the history of science and education. Starting from Piaget's genetic epistemology, it provides a conceptual framework for describing and explaining the development of cognition by reflective abstractions from systems of actions.

Contenu

Introduction. Part 1: On action and cognition. 1. Action and cognition in Piaget's genetic epistemology and in Hegel's logic. 2. Representation and meaning. Part 2: Education in context. 3. Philosphical and pedagogical remarks on the concept `Abstract'. 4. What is mathematical ability and how do ability differences emerge in mathematics education? 5. Mathematics education and society. 6. Preliminary remarks on the relationship of the principles of teaching arithmetic to the early history of mathematics. Part 3: Cultural evolution of arithmetical thinking. 7. The development of arithmetical thinking: on the role of calculating aids in ancient Egyptian and Babylonian arithmetic. 8. The first representations of numbers and the development of the number concept. 9. On the relationship between ontogenesis and historiogenesis of the number concept. Part 4: On historical epistemology. 10. Abstraction and representation. 11. The concept of labor in historical materialism and the theory of socio-historical development. 12. Tools of science. Name index. Subject index.