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Lecturer(s)
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Sedláček Lubomír, Mgr. Ph.D.
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Pavelková Marie, Mgr. Ph.D.
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Tirpáková Anna, prof. RNDr. CSc.
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Course content
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1. Mathematical language and symbolism, basics of propositional logic. 2. Statements, operations with statements, propositional formulas. 3. Quantification of statements. 4. Compound statements, negation of compound statements. 5. Simple mathematical proofs and their meaning. 6. Basics of set theory, set element, set equality and set inclusion relations. 7. Set operations (unification, intersection, addition) and properties of operations with sets. 8. Graphic representation of set operations, examples. 9. Importance of sets and set operations for primary mathematical education. 10. Development of initial ideas about relations - Cartesian product, binary relation, determination of binary relation 11. Graphic representation of binary relations. 12. Properties of binary relations (reflexivity, symmetry, transitivity, etc.) 13. Solving word problems with a focus on statements, sets and relations. 14. Verification of properties of relations and representations with emphasis on use in primary mathematics education.
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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), Activating (Simulation, games, dramatization), Practice exercises
- Participation in classes
- 42 hours per semester
- Preparation for course credit
- 30 hours per semester
- Preparation for examination
- 40 hours per semester
- Home preparation for classes
- 8 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| unspecified |
| unspecified |
| learning outcomes |
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| basic concepts of propositional logic, operations with propositions |
| basic concepts of propositional logic, operations with propositions |
| simple mathematical proofs and their meaning |
| simple mathematical proofs and their meaning |
| basics of set theory |
| basics of set theory |
| binary session |
| binary session |
| basic concepts of mathematical logic and set theory at the 1st grade of elementary school |
| basic concepts of mathematical logic and set theory at the 1st grade of elementary school |
| Skills |
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| define the basic concepts of propositional logic |
| define the basic concepts of propositional logic |
| analyze and solve problems from propositional logic |
| analyze and solve problems from propositional logic |
| analyze and solve set theory problems |
| analyze and solve set theory problems |
| apply theoretical knowledge from mathematics needed for teaching activities and for managing pupils' learning activities in Mathematics |
| apply theoretical knowledge from mathematics needed for teaching activities and for managing pupils' learning activities in Mathematics |
| teaching methods |
|---|
| Knowledge |
|---|
| Activating (Simulation, games, dramatization) |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Practice exercises |
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Activating (Simulation, games, dramatization) |
| Practice exercises |
| assessment methods |
|---|
| Written examination |
| Written examination |
| Didactic test |
| Didactic test |
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Recommended literature
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Bělík, M. Binární relace [online]. Ústí nad Labem: Univerzita Jana Evangelisty Purkyně., 2005.
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Eberová, J., & Stopenová, A. Matematika 1. Olomouc: Vydavatelství UP., 1997.
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Hejný, M. Vyučování matematice orientované na budování schémat: aritmetika 1. stupně. Praha: UK., 2014.
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Jirotková, D. Cesty ke zkvalitňování výuky geometrie. Praha: UK., 2010.
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Kuřina, F., & Půlpán, Z. Podivuhodný svět elementární matematiky. Praha: Akademia., 2006.
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Kuřina, F. Deset pohledů na geometrii. Praha: Albra., 1996.
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Kuřina, F. Matematika a porozumění světu. Praha: Akademie., 2009.
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Partová, K. Prirodzené čísla. Bratislava: ASCO Art&Science., 2002.
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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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Polášek, V., Sedláček, l. & Kozáková, L. Matematický seminář. Zlín: Nakladatelství UTB., 2018.
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