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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.
Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Studující bude mít základní představu o klasických dílech autorů George Polya, Imre Lakatos a Hans Freudenthal a bude schopen vysvětlit rozdíly mezi něma. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (17.09.2024)
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Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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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. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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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. Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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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 Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (10.09.2024)
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Studující vysvětlí hlavní principy vybraných konstruktivistických přístupů k vyučování matematice. Studující s porozuměním a pomocí konkrétních příkladů bude schopen ilustrovat vyučování chápané jako řešení problémů (GP), jako osvojování si pojmů (IL) a jako řízené znovuobjevování (HF). Last update: Kvasz Ladislav, prof. RNDr., DSc., Dr. (17.09.2024)
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