# Didactical phenomenology

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* Didactische_fenomenologie (dutch)

## General

It is not uncommon to view mathematics as an abstraction of reality, or to characterize important mathematical ideas as representing the commonalities inherent in a wide variety of situations. In either case, we simplify or idealize the world, and take that simplified or idealized picture as the basis for what we do. Sometimes we even forget that original world.

In the concept of didactical phenomenology Hans Freudenthal returns us to the world from which we have abstracted. This world is part outside mathematics, part within mathematics; part abstract, part concrete; part rigorous thinking, part intuition and visual perception. This phenomenology focuses on the connections between a mathematical concept (the Nooumenons) and the complex world which relates to it (Phenomenons). These connections form the phenomenology of the mathematical structure. The implications of that world for the instruction of students is the didactical phenomenology.

Didactical phenomenology is one of the key concepts used in the theory behind Realistic Mathematics Education

## References

- Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: Reidel.
- Phenomenon
- Realistic Mathematics Education
- Treffers, A. (1987). Three dimensions: a model of goal and theory description in mathematics instruction - The Wiskobas project. Dordrecht: Kluwer Academic Publishers.

## Versions of this document

- 20080520, wikiteam