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Lecturer(s)
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Tirpáková Anna, prof. RNDr. CSc.
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Pavelková Marie, Mgr. Ph.D.
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Course content
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1. Development of initial ideas about propositions - mathematical language and symbolism, basics of propositional logic. 2. Truth value of a statement, operations with statements. 3. Compound statements, negation of compound statements. 4. Development of initial ideas about sets - set element, relationships between sets. The importance of sets and set operations for pre-primary and primary mathematics education. 5. Set operations (unification, intersection, addition) and properties of operations with sets. 6. Graphic representation of set operations, examples. 7. Development of initial ideas about relations - binary relation, determination of binary relation. 8. Properties of binary relations in a set. Equivalence relations and their use for organizing and sorting sets. 9. Display as a special type of binary session, display properties. 10. Special case of display - mathematical function. 11. Solving word problems with a focus on statements, sets and relations. 12. Concepts related to natural number and methods of their development. Propedeutics of numerical operations in contextual tasks. A natural number as a cardinal number of non-empty sets. 13. Addition and multiplication operations in a set of natural numbers. Natural arrangement of the set of natural numbers. 14. Properties of addition and multiplication of natural numbers. 15. Development of spatial imagination in primary education, orientation in space and wayfinding. Common and different properties of spatial formations, determining the position of objects in space using simple expressions. 16. Activities related to measurement, work in the field and orientation in space. Differentiation of planar structures from three-dimensional ones, network of bodies, cutting and folding, representation of three-dimensional structures in a plane. 17. Planar and spatial formations (point, line, line, square, rectangle, quadrilaterals, circle, circle), their observation and naming.
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Dialogic (Discussion, conversation, brainstorming), Projection (static, dynamic), Practice exercises, Individual work of students, Dealing with situational issues - learning in situations
- Educational trip
- 16 hours per semester
- Preparation for examination
- 28 hours per semester
- Preparation for course credit
- 20 hours per semester
- Participation in classes
- 56 hours per semester
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| prerequisite |
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| Knowledge |
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| not specified |
| not specified |
| learning outcomes |
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| comprehensively explain the importance of pre-mathematical preparation for preschool children |
| comprehensively explain the importance of pre-mathematical preparation for preschool children |
| describe basic areas of mathematical ideas |
| describe basic areas of mathematical ideas |
| define the methods used in the development of pre-mathematical concepts in children of preschool age |
| define the methods used in the development of pre-mathematical concepts in children of preschool age |
| characterize basic theoretical approaches for the development of pre-mathematical concepts |
| characterize basic theoretical approaches for the development of pre-mathematical concepts |
| define the meaning of orientation in plane and in space for preschool education |
| define the meaning of orientation in plane and in space for preschool education |
| Skills |
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| implement controlled activities based on appropriately set goals |
| implement controlled activities based on appropriately set goals |
| propose didactic activities for the development of pre-mathematical concepts in preschool children |
| propose didactic activities for the development of pre-mathematical concepts in preschool children |
| use appropriate didactic strategies in the implementation of pedagogical practice |
| use appropriate didactic strategies in the implementation of pedagogical practice |
| justify the chosen didactic approach in the implementation of the didactic activity |
| justify the chosen didactic approach in the implementation of the didactic activity |
| reflect a didactic approach |
| reflect a didactic approach |
| teaching methods |
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| Knowledge |
|---|
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Practice exercises |
| Practice exercises |
| Dealing with situational issues - learning in situations |
| Dealing with situational issues - learning in situations |
| Individual work of students |
| Individual work of students |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| assessment methods |
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| Oral examination |
| Analysis of the student's performance |
| Analysis of the student's performance |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Oral examination |
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Recommended literature
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Rámcový vzdělávací program pro předškolní vzdělávání..
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Ficová, L., & Žilková, K. Mentálne mapy ako prostriedok integrácie obsahu primárneho matematického vzdelávania.. Prešov: Vydavateľstvo PdF Prešov., 2012.
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Gerová, Ľ. Propedeutika matematiky a počiatočné matematické predstavy.. Banská Bystrica: PdF, Mateja Bela., 2007.
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Hejný, M., & Kuřina, F. Dítě, škola a matematika.. Praha: Portál, 2001.
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Kaslová, M. Předmatematické činnosti v předškolním vzdělávání.. Praha: Raabe., 2010.
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Pártová, E., & Židek, O. Príručka k príprave na súbornú skúšku z matematiky.. Bratislava: PdF UK., 1993.
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Polák, J. Didaktika matematiky: jak učit matematiku zajímavě a užitečně.. Plzeň: Fraus, 2016.
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Uherčíková, V., & Haverlík, I. K. Pracovné listy na rozvíjanie matematických predstáv u detí v MŠ a v ZŠ.. Bratislava: Dony., 2007.
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