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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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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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| define the meaning of propositional logic in primary education |
| define the meaning of propositional logic in primary education |
| determine the truth values of propositions and quantified propositions |
| determine the truth values of propositions and quantified propositions |
| explain basic concepts, notation, and symbolism in set theory |
| explain basic concepts, notation, and symbolism in set theory |
| solve set operations |
| solve set operations |
| distinguish binary relations in a set, determine a relation based on the Cartesian product |
| distinguish binary relations in a set, determine a relation based on the Cartesian product |
| Skills |
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| justify the truth value of a statement |
| justify the truth value of a statement |
| justify the difference between statements and quantified statements |
| justify the difference between statements and quantified statements |
| explain the negation of quantified statements |
| explain the negation of quantified statements |
| connect intersection, union, difference and complement of a set with the creation of a learning task with statements and sets |
| connect intersection, union, difference and complement of a set with the creation of a learning task with statements and sets |
| critically evaluate the determination of a binary relation in a set based on knot graphs and a Cartesian graph |
| critically evaluate the determination of a binary relation in a set based on knot graphs and a 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) |
| Activating (Simulation, games, dramatization) |
| Activating (Simulation, games, dramatization) |
| 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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