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Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)
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Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)
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Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)
Freudenthal, H. (1972): Mathematics as an Educational Task, Springer. Klein, F. (1908): Elementary Mathematics from an Advanced Standpoint. Lakatos, I. (1972): Proofs and Refutations. Cambridge University Press. Polya, G. Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. |
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Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (03.02.2022)
Every student will present an exposition of the fundamental ideas of a particular chapter of the discussed books. The chapters will be agreed upon on the first seminar. The final evaluation will take into consideration this exposition as well as his activity during the discussion of the presentations of other students. Students, who for some reasons will not be able to have their presentations in person will send in a written essay in English, having 5 to 10 pages. |
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Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)
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 |