Classic works of mathematics education - OPNM3M015A

• Title: Classic works of mathematics education
• Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
• Faculty: Faculty of Education
• Actual: from 2023
• Semester: winter
• E-Credits: 5
• Examination process: winter s.:
• Hours per week, examination: winter s.:1/2, C [HT]
• Extent per academic year: 0 [hours]
• Capacity: unknown / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Is provided by: OKNM3M015A
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; priority enrollment if the course is part of the study plan
• Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
• Is interchangeable with: OKNM3M015A

Annotation

English

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.

Czech

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

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