Syllabus
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
Annotation
The aim of the course is to get the students acquainted with some of the classical works in mathematics education. The course has the form of a seminar, where students will read and discuss selected passages from the works of George Polya, Imre Lakatos and Hans Freudenthal.
We will begin with the book of George Polya: Mathematical Discovery, On Understanding, Learning, and Teaching Problem Solving and we will discuss the concept of heuristics. Second will be the book of Imre Lakatos(1972): Proofs and Refutations and we will focus on creating concepts and definitions.
As a third work we will discuss Hans Freudenthal (1972): Mathematics as an Educational Task, in terms of the relationship between mathematics and the real world. Finally, we will return to the past of didactics of mathematics to the book of Felix Klein (1908): Elementary Mathematics from Advanced Standpoint.