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Lecturer(s)
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Tirpáková Anna, prof. RNDr. CSc.
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Sedláček Lubomír, Mgr. Ph.D.
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Pavelková Marie, Mgr. Ph.D.
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Course content
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1. Mathematical language and symbolism, basics of propositional logic. 2. Statement, operations with statements, statement formulas. 3. Quantification of statements. 4. Simple mathematical proofs and their meaning. 5. Basics of set theory, operations with sets. 6. Relationships between sets, representation of sets. 7. Importance of sets and set operations for primary mathematical education. 8. Binary relation in a set. 9. Properties of binary relations (reflexivity, symmetry, transitivity, etc.). 10. Equivalence relations and arrangement relations and their practical significance, good arrangement. 11. Solving word problems focusing on statements. 12. Proofs and sets (sets with non-empty intersection). 13. Verification of properties of relations and representations with emphasis on use in primary mathematics education. 14. Basic concepts of mathematical logic and set theory in the 1st grade of elementary school as a means of building knowledge about natural numbers.
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Learning activities and teaching methods
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- Preparation for examination
- 60 hours per semester
- Participation in classes
- 42 hours per semester
- Home preparation for classes
- 78 hours per semester
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| prerequisite |
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| Knowledge |
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| Students have knowledge at the level of high school mathematics. |
| Students have knowledge at the level of high school mathematics. |
| learning outcomes |
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| from propositional logic in primary education from evaluating the truth value of statements about basic concepts, marking and symbolism in set theory about set operations on binary relations in a set, determination of relations based on the Cartesian product |
| from propositional logic in primary education from evaluating the truth value of statements about basic concepts, marking and symbolism in set theory about set operations on binary relations in a set, determination of relations based on the Cartesian product |
| Skills |
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| determine the truth value of a statement identify quantified statements, negate quantified statements determine the intersection, union, difference, and complement of a set create learning tasks with statements and sets identify binary relations in a set based on node graphs and Cartesian graph |
| determine the truth value of a statement identify quantified statements, negate quantified statements determine the intersection, union, difference, and complement of a set create learning tasks with statements and sets identify binary relations in a set based on node graphs and Cartesian graph |
| teaching methods |
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| Knowledge |
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| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Skills |
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| Analysis of a presentation |
| Analysis of a presentation |
| Activating (Simulation, games, dramatization) |
| Activating (Simulation, games, dramatization) |
| assessment methods |
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| Knowledge |
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| Analysis of a presentation given by the student |
| Analysis of a presentation given by the student |
| 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: Univerzita Palackého v Olomouci. 1997.
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Igrah, G. The universal history of numbers. New York: John Wiley & Sons. 2001.
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Kuřina, F. Matematika a porozumění světu. Praha: Akademie. 2009.
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Markechová, D., Švecová, V., Tirpáková, A., & Stehlíková, B. Základy matematiky a matematickej logiky. Nitra: Univerzita Konštantína Filozofa v Nitre. 2011.
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Musser, G. L., Burger, B. E., & Peterson, B. E. Mathematics for elementary teacher. New York: John Wiley & Sons. 2001.
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Panáčová, J. & Beránek, J. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ. MU Brno. 2020.
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Polášek, V., Sedláček, L., & Kozáková, L. Matematický seminář. Zlín: Univerzita Tomáše Bati. 2018.
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