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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. Statements - truth value of statements, negation of statements. 2. Statements - propositional forms and formulas, tautologies. 3. Contradiction, satisfiable propositional formula. 4. Operations with statements, truth value tables. 5. Sets - set element, relations between sets. 6. Sets - representation of sets with Venn and other diagrams. 7. Operations with sets and their properties. 8. Relations on sets - properties of binary relations in a set. 9. Transitivity, connection and order relations. 10. Binary relation and its graph, complementary relation, inverse relation, composite relation. 11. Mapping - properties of mapping, inverse mapping, composite mapping, definition of mapping and equality. 12. Plane and spatial geometric figures and their properties and characteristics. 13. Distinguishing plane figures from spatial ones, network of bodies. 14. Orientation in a plane using concepts, orientation in space in relation to objects in space, orientation of various objects in space.
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Dialogic (Discussion, conversation, brainstorming), Demonstration, Individual work of students
- Preparation for course credit
- 30 hours per semester
- Term paper
- 23 hours per semester
- Participation in classes
- 7 hours per semester
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| prerequisite |
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| Knowledge |
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| position of propositional logic in preschool education |
| position of propositional logic in preschool education |
| truth values of statements in conjunction, disjunction, implication and equivalence |
| truth values of statements in conjunction, disjunction, implication and equivalence |
| determination of a set by enumeration of elements and a characteristic property |
| determination of a set by enumeration of elements and a characteristic property |
| operations with sets - intersection, union, difference and complement of sets |
| operations with sets - intersection, union, difference and complement of sets |
| binary relations in a set, determination of relations based on the Cartesian product |
| binary relations in a set, determination of relations based on the Cartesian product |
| Skills |
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| justify connections with compound statements |
| justify connections with compound statements |
| connect knowledge from propositional logic when creating learning tasks for preschool children |
| connect knowledge from propositional logic when creating learning tasks for preschool children |
| formulate findings from Cartesian and knot graphs |
| formulate findings from Cartesian and knot graphs |
| design a didactic activity for preschoolers using relationships in binary relations |
| design a didactic activity for preschoolers using relationships in binary relations |
| critically assess the importance of representation in creating ideas about quantity in preschool children |
| critically assess the importance of representation in creating ideas about quantity in preschool children |
| learning outcomes |
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| Knowledge |
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| describe the importance of propositional logic for preschool education |
| describe the importance of propositional logic for preschool education |
| analyze relationships between sets based on symbolic notations |
| analyze relationships between sets based on symbolic notations |
| characterize Cartesian products in set notation |
| characterize Cartesian products in set notation |
| explain the importance of equivalent sets for preschool education |
| explain the importance of equivalent sets for preschool education |
| list and evaluate individual types of depictions in relation to tasks for preschool children |
| list and evaluate individual types of depictions in relation to tasks for preschool children |
| Skills |
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| determine the truth value of a statement |
| determine the truth value of a statement |
| identify quantified statements |
| identify quantified statements |
| determine the intersection, union, difference, and complement of a set |
| determine the intersection, union, difference, and complement of a set |
| create learning tasks with statements and sets |
| create learning tasks with statements and sets |
| identify binary relations in a set based on node graphs |
| identify binary relations in a set based on node graphs |
| teaching methods |
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| Knowledge |
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| Demonstration |
| Demonstration |
| Dialogic (Discussion, conversation, brainstorming) |
| Individual work of students |
| Individual work of students |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Dialogic (Discussion, conversation, brainstorming) |
| assessment methods |
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| Written examination |
| Analysis of the student's performance |
| Analysis of the student's performance |
| Analysis of educational material |
| Grade (Using a grade system) |
| Written examination |
| Grade (Using a grade system) |
| Analysis of educational material |
| Analysis of seminar paper |
| Analysis of seminar paper |
| Analysis of another type of paper written by the student (Casuistry, diary, plan ...) |
| Analysis of another type of paper written by the student (Casuistry, diary, plan ...) |
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Recommended literature
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Francová, M., Lvovská L. Texty k základům elementární geometrie. Brno: Masarykova univerzita., 2014.
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GEROVÁ, Ľ. Propedeutika matematiky a počiatočné matematické predstavy. Banská Bystrica, 2007.
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HEJNÝ, M., KUŘINA, F. Dítě, škola a matematika. Praha, 2001.
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Kaslová, M. Předmatematické činnosti v předškolním vzdělávání. Praha: Raabe, 2010.
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Krajcarová, J., & Pavelková, M. Umělecké vzdělávání u dětí s matematickým nadáním. Kreatívne vzdelávanie. In CREA-AE 2014. Zohor, 2014.
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Panáčová, J., Beránek, J.. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ.. Brno: Masarykova univerzita, 2025.
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PARTOVÁ, E. Relácie a ich aplikácie v predškolskej matematike. Bratislava, 2004.
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Staudková, H., Tůmová, V., & Landová, V.. Matematika, Numerace, sčítání a odčítání do 6.. Všeň: Alter., 2019.
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