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Lecturer(s)
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Pavelková Marie, Mgr. Ph.D.
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Course content
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1. Objectives of teaching mathematics at the 1st level of primary school. Basic curriculum documents for primary education. Didactics of mathematics. Currently existing paradigms in mathematics education. Constructivist approach versus transmissive approach in education. Epistemological formalism. 2. Teaching methods, organizational forms, pedagogical strategies and procedures in teaching mathematics 3. Basic concepts of set theory and mathematical logic in elementary mathematics. 4. Numeration and introductory knowledge of natural numbers. 5. Binary operations in arithmetic at the 1st level of primary school and their properties - addition, introduction of the concept, models and methods of representation. 6. Binary operations in arithmetic at the 1st level of primary school and their properties - subtraction, introduction of the concept, models and methods of representation. 7. Binary operations in arithmetic at the 1st level of primary school and their properties - multiplication, introduction of the concept, models and methods of representation. 8. Binary operations in arithmetic at the 1st grade of elementary school and their properties - division, introduction of the concept, models and methods of representation. 9. Concept-forming process in teaching mathematics. Stages of the cognitive process according to M. Hejný. 5 levels of understanding geometric concepts according to van Hiele. 10. Developing financial literacy - competencies for primary education and their application to teaching mathematics. 11. Mathematical learning tasks, their classification, didactic significance and solution procedures. Methods of solving mathematical tasks (methodof induction and deduction, analytical and synthetic methods, experimental methods, etc.). 12. Word problems in mathematics, types of word problems (simple and complex), solving word problems. Methods of solving word problems. 13. Whole and rational numbers. Introducing fractions, non-negative decimal numbers in mathematical theory. Methodological procedure for introducing fractions and the issue of introducing decimal numbers at the 1st level of primary school. 14. Assessment and classification in mathematics. Assessment methods and procedures. Verbal assessment.
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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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| describe the procedure for deriving basic mathematical operations |
| describe the procedure for deriving basic mathematical operations |
| classify mathematical problems with an emphasis on word problems in mathematics teaching |
| classify mathematical problems with an emphasis on word problems in mathematics teaching |
| creatively bring new solutions to the given task |
| creatively bring new solutions to the given task |
| describe the stages of the concept-forming process in arithmetic and geometry |
| describe the stages of the concept-forming process in arithmetic and geometry |
| list the currently existing paradigms in mathematics teaching |
| list the currently existing paradigms in mathematics teaching |
| 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 |
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| Knowledge |
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| 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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Kuřina, F. Matematika jako pedagogický problém. Gaudeámus, 2016.
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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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