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Lecturer(s)
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Tirpáková Anna, prof. RNDr. CSc.
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Pavelková Marie, Mgr. Ph.D.
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Course content
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- Didactics of mathematics as a scientific discipline, personalities of didactics of mathematics. - Objectives of teaching mathematics, national and school documents. - Pedagogical, philosophical and psychological theories and trends in the context of mathematics didactics. Stages of concept-forming process. - Evaluation and classification in mathematics lessons. Diagnostics of understanding mathematical concepts, cognitive formalism. - J. Marzano: 5 dimensions of learning. Examples of processing the preparation for a mathematics lesson in the spirit of Marzan's theory. - G. Polya: 4 steps in solving a problem task. Discovering mathematics - mathematics as a method of solving problems. - Van Hiele: 5 levels of understanding geometric concepts. Illustration of diagnostics of geometric thinking of pupils and methods of removing misconceptions. - Theory of creating mathematical problems and tests. Solutions and evaluations. - Mathematical competitions and other standards for gaining and developing students' interest in mathematics. - Teaching mathematics according to the needs, interests and abilities of students. Model situations of educational activities in teaching mathematics. - Methods of developing functional and combinatorial thinking in elementary mathematics. - The importance of illustration in teaching elementary mathematics. Use of cognitive technologies in teaching mathematics (CAS systems, dynamic geometry environment, etc.). - Criteria for selecting quality pedagogical software for teaching elementary mathematics. - Basic stages of the history of mathematics as a science. History of mathematics teaching.
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Dialogic (Discussion, conversation, brainstorming), Methods for working with texts (Textbook, book), Educational trip
- Participation in classes
- 56 hours per semester
- Educational trip
- 8 hours per semester
- Home preparation for classes
- 5 hours per semester
- Preparation for course credit
- 10 hours per semester
- Preparation for examination
- 30 hours per semester
- Term paper
- 11 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| unspecified |
| unspecified |
| learning outcomes |
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| interpret the theoretical starting points and practical aspects of mathematics didactics |
| interpret the theoretical starting points and practical aspects of mathematics didactics |
| define and sort mathematical problems with an emphasis on word problems in teaching mathematics |
| define and sort mathematical problems with an emphasis on word problems in teaching mathematics |
| explain the methodology of teaching geometry at primary and secondary schools |
| explain the methodology of teaching geometry at primary and secondary schools |
| creatively bring new solutions to the given task |
| creatively bring new solutions to the given task |
| analyze and present selected mathematics curriculum within school practice |
| analyze and present selected mathematics curriculum within school practice |
| Skills |
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| to evaluate and justify the results of mathematical problems, to evaluate different methods of students' solutions |
| to evaluate and justify the results of mathematical problems, to evaluate different methods of students' solutions |
| interpret and apply the basic principles of evaluating the performance of pupils in mathematics |
| interpret and apply the basic principles of evaluating the performance of pupils in mathematics |
| adequately use mathematical terminology in professional communication |
| adequately use mathematical terminology in professional communication |
| mathematize real situations and create mathematical models |
| mathematize real situations and create mathematical models |
| work with pupils according to the pupils' needs, interests and abilities |
| work with pupils according to the pupils' needs, interests and abilities |
| teaching methods |
|---|
| Knowledge |
|---|
| Methods for working with texts (Textbook, book) |
| Monologic (Exposition, lecture, briefing) |
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Educational trip |
| Methods for working with texts (Textbook, book) |
| Educational trip |
| Monologic (Exposition, lecture, briefing) |
| assessment methods |
|---|
| Oral examination |
| Oral examination |
| Analysis of seminar paper |
| Analysis of seminar paper |
| Analysis of educational material |
| Analysis of educational material |
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Recommended literature
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Blažková, R. Dyskalkulie a další specifické poruchy učení v matematice. Brno: Masarykova univerzita, 2009.
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Hejný, M., & Kuřina, F. Dítě, škola, matematika: konstruktivistické přístupy k vyučování. Praha: Portál, 2009.
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Hejný, M., Novotná, J., & Stehlíková, N. Dvacet pět kapitol z didaktiky matematiky. Praha: PedF UK, 2004.
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Hejný, M. Vyučování matematice orientované na budování schémat: aritmetika 1. stupně. Praha: UK., 2014.
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Jitková D. at al. Cesty ku skvalitňovaniu výučby geometrie. Praha: Univerzita Karlova v Praze, 2010.
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Kopka, J. Hrozny problémů ve školské matematice. Ústí nad Labem: UJEP, 1999.
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Molnár, J. Učebnice matematiky a klíčové kompetence. Olomouc: UPOL, 2007.
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Novák, B. Vybrané kapitoly z didaktiky matematiky. Olomouc: UPOL, 2004.
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Polášek, V., & Sedláček, L. Dynamic Geometry Environments As Cognitive Tool In Mathematic Education. Journal of Technology and Information Education, 7(2), 45-54. 2015.
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Van Hiele, P. M. Structure and Insight: A Theory of Mathematics Education.. Orlando: Academic Press, 1986.
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Žilková, K. Teória a prax geometrických manipulácií v primárnom vzdelávaní. Praha: Powerprint, 2013.
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