Abstraction and Representation
Essays on the Cultural Evolution of Thinking

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

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.

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.