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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. Basic concepts of set theory and mathematical logic in elementary mathematics. 2. Numeration and introductory knowledge about natural numbers. 3. Binary operations in arithmetic in the 1st stage of primary school and their properties - addition, introduction of the term, models and methods of representation. 4. Binary operations in arithmetic in the 1st stage of primary school and their properties - subtraction, introduction, concepts and methods of representation. 5. Binary operations in arithmetic in the 1st stage of primary school and their properties - multiplication, introduction of the concept, models and methods of representation. 6. Binary operations in arithmetic in the 1st stage of primary school and their properties - division, introduction of the concept, models and methods of representation. 7. Fractions and their modeling, comparison. 8. Typology of word problems, simple and complex word problems and methods of solution. 9. Levels of cognitive process in geometry, their characteristics and importance for the diagnosis of the student. 10. School geometry: overview of basic geometric concepts and modeling of geometric concepts. 11. Binary relations and operations in geometry at the 1st stage of primary school. Modeling methods. 12. Elementary knowledge of measure theory, methods of measuring geometric shapes. 13. Development of spatial imagination in primary mathematics education. Orientation in space. Solids and their properties. 14. Development of financial literacy - competencies for primary education and their application to teaching mathematics.
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Learning activities and teaching methods
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Dialogic (Discussion, conversation, brainstorming), Methods for working with texts (Textbook, book), Practice exercises, Educational trip
- Preparation for course credit
- 20 hours per semester
- Participation in classes
- 56 hours per semester
- Educational trip
- 4 hours per semester
- Home preparation for classes
- 10 hours per semester
- Preparation for examination
- 30 hours per semester
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| prerequisite |
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| Knowledge |
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| unspecified |
| unspecified |
| Students have basic mathematical skills. Students acquire the basic competences needed to teach mathematics. Students can work with pupils according to the needs, interests and abilities of pupils: work with pupils with specific developmental learning disabilities in mathematics and work with gifted pupils. |
| Students have basic mathematical skills. Students acquire the basic competences needed to teach mathematics. Students can work with pupils according to the needs, interests and abilities of pupils: work with pupils with specific developmental learning disabilities in mathematics and work with gifted pupils. |
| Skills |
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| Students have basic mathematical skills. Students acquire the basic competences needed to teach mathematics. Students can work with pupils according to the needs, interests and abilities of pupils: work with pupils with specific developmental learning disabilities in mathematics and work with gifted pupils. |
| Students have basic mathematical skills. Students acquire the basic competences needed to teach mathematics. Students can work with pupils according to the needs, interests and abilities of pupils: work with pupils with specific developmental learning disabilities in mathematics and work with gifted pupils. |
| learning outcomes |
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| Knowledge |
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| knowledge of the content of mathematics at the 1st grade of elementary school |
| knowledge of the content of mathematics at the 1st grade of elementary school |
| define and sort mathematical problems with an accent on word problems in teaching mathematics |
| define and sort mathematical problems with an accent on word problems in teaching mathematics |
| explain the methodology of teaching geometry at elementary school |
| explain the methodology of teaching geometry at elementary school |
| 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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| understand the mathematical reasoning of a child of younger school age and its characteristics |
| understand the mathematical reasoning of a child of younger school age and its characteristics |
| didactic representation of topics from mathematics and planning of teaching mathematics in primary education, which are integrated into primary education in RVP ZV |
| didactic representation of topics from mathematics and planning of teaching mathematics in primary education, which are integrated into primary education in RVP ZV |
| use mathematical terminology in professional communication |
| 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 |
|---|
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Practice exercises |
| Educational trip |
| Educational trip |
| Practice exercises |
| assessment methods |
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| Didactic test |
| Didactic test |
| 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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Coufalová, J. Matematika s didaktikou pro 1. ročník učitelství 1. stupně ZŠ. Plzeň: Západočeská univerzita, 2004.
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Divíšek, F., et al. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha: SPN, 1989.
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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: Univerzita Karlova v Praze, 2014.
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Jirotková, D. Cesty ke zkvalitňování výuky geometrie. Praha: Univerzita Karlova v Praze, 2010.
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Musser, G. L., Burger, W. F., & Peterson, B. E. Mathematics for Elementary Teachers.. New York: John Wiley, 2001.
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Polášek, V., Sedláček, l. & Kozáková, L. Matematický seminář. Zlín: Nakladatelství UTB., 2018.
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Žilková, K., & Židek, O. Manipulačná geometria. Bratislava, 2013.
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