Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)

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: prof. RNDr. Naďa Vondrová, Ph.D. (02.02.2022)

The aim of the course is to get the students acquainted with some of the classical works in mathematics education. During the course, the 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. The second will be the book of Imre Lakatos(1972): Proofs and Refutations and we will focus on creating concepts and definitions. As the 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.

Descriptors - Czech

Last update: prof. RNDr. Ladislav Kvasz, DSc., Dr. (28.01.2022)

Celková časová zátěž studenta

135,0

Přidělené kredity

5

Zakončení

Z

Přímá výuka

Cvičení:

15 hod

Příprava na výuku

Doba očekávané přípravy na 1 cvičení

60 minut

Samostudium literatury (za semestr)

45 hodin

Práce se studijními materiály (za semestr)

20 hodin

Plnění průběžných úkolů (za semestr)

20 hodin

Plnění předmětu

Seminární práce

20 hodin

Příprava na zápočet

6 hodin

Literature

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.

Requirements to the exam

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.

Syllabus

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