In the course we will read and discuss three books:

George Polya: How to solve it?

1. Polya's general approach to mathematics education as problem solving

2. Polya's set of questions, which a teacher should ask a student in order to help him

3. Polya's concept of analogy and of heuristics in mathematics education

Imre Lakatos: Proofs and Refutations.

4. Lakatos' approach to mathematics education as conceptual development

5. Lakatos' fundamental notions as monster barring, lemma incorporation

6. The possibility to transfer these notions to other areas than theory of polyhedra

Hans Freudenthal: China Lectures

7. Freudenthal's approach to mathematics education as exploratory activity

8. The basic notions of Freudenthal's realistic mathematics

9. Discussion of basic mathematical notions as introduced by Freudenthal

10. A comparison of the three approaches - their differences and common features