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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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1. School geometry: overview of basic geometric concepts and modeling of geometric concepts. Anchoring geometry in the RVP ZV. 2. Introducing construction problems in first-level education. Phases of solving construction problems. 3. Determining and measuring angles in first-level education of primary school. 4. Symmetry - axis and plane of symmetry, symmetrical figures in the curriculum of the first level of primary school. Methods of modeling. 5. Elementary knowledge of measure theory, methods of measuring geometric figures. 6. Basic positional and metric properties of geometric figures. Mutual position of two lines according to their common points: parallelism, divergentity, eccentricity of lines as a binary relation in the set of all lines in the plane and in space. Definition of these concepts, properties, use in the curriculum of the first level of primary school. 7. Development of spatial imagination in primary mathematics education. Orientation in space. Solids and their properties. 8. Van Hiele: 5 levels of understanding geometric concepts. Illustrations of diagnostics of geometric reasoning of pupils and methods of eliminating misconceptions. 9. Education of pupils with special educational needs in mathematics (gifted pupils, pupils with learning disabilities). Creation of graded tasks. 10. Basic stages of the history of mathematics as a science. History of mathematics teaching. Motivation in teaching mathematics. Personality of a mathematics teacher, key competencies of a mathematics teacher. 11. Methods of developing functional and combinatorial thinking in elementary mathematics. 12. The importance of visualization in teaching elementary mathematics. Use of cognitive technologies in teaching mathematics (CAS systems, dynamic geometry environment, etc.). 13. Methods of developing functional and combinatorial thinking in elementary mathematics. 14. G. Polya: 4 stages in solving a problem. Discovering mathematics - mathematics as a method of solving problems.
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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 |
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| 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 |
|---|
| 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 |
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| 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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