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Lecturer(s)
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Sedláček Lubomír, Mgr. Ph.D.
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Course content
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- Mathematical language and symbols, basics of propositional logic (proposition, operations with propositions, propositional formulas, propositional quantification). - Simple mathematical proofs and their meaning. - Basics of set theory, operations with sets and relationships between sets, representation of sets. - Importance of sets and set operations for primary mathematical education. - Binary relations in a set, properties of binary relations (reflexivity, symmetry, transitivity etc.). - Equivalence relation, relations of arrangement and their practical meaning, good arrangement. - Solving of word problems focused on propositions, proving propositions and sets (sets with non-empty intersection). - Verification of relations properties and display relations with emphasis on use in primary mathematical education. - Basic concepts of mathematical logic and set theory in lower primary education as means of getting knowledge of natural numbers.
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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), Practice exercises
- Participation in classes
- 42 hours per semester
- Home preparation for classes
- 40 hours per semester
- Preparation for examination
- 38 hours per semester
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| prerequisite |
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| Knowledge |
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| nespecifikováno |
| nespecifikováno |
| learning outcomes |
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| The student will gain knowledge of theoretical bases in mathematics necessary for teaching and managing learning activities of pupils in lower primary mathematical education. |
| The student will gain knowledge of theoretical bases in mathematics necessary for teaching and managing learning activities of pupils in lower primary mathematical education. |
| teaching methods |
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| Practice exercises |
| Practice exercises |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| assessment methods |
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| Didactic test |
| Didactic test |
| Analysis of seminar paper |
| Analysis of seminar paper |
| Analysis of a presentation given by the student |
| Analysis of a presentation given by the student |
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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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DIVÍŠEK, F. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha: SPN, 1989.
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EBEROVÁ, J., STOPENOVÁ, A. Matematika 1. Olomouc: Vydavatelství UP, 1997.
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KRIŽALKOVIČ, K., CUNINKA, A., ŠEDIVÝ, O. Riešené úlohy z modernej matematiky. Bratislava: Alfa, 1974.
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KUŘINA, F. a kol. Matematika a porozumění světu. Praha: Akademia, 2009.
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KUŘINA, F., PŮLPÁN, Z. Podivuhodný svět elementární matematiky. Praha: Akademia, 2006.
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KUŘINA, F. Umění vidět v matematice. Praha: SPN, 1989.
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NOVOTNÁ, V., PISKLÁK, B. Matematika. [online]. Ostrava: Ostravská univerzita, 2003.
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ŠEDIVÝ, J. Úlohy o výrocích a množinách pro I. ročník gymnázia. Praha: Státní pedagogické nakladatelství, 1971.
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