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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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- Analysis of the Framework Educational Program from the point of view of mathematical concepts. - Binary relations, properties of binary relations in a set. Equivalence relations and set decomposition. - Complementary relation, inverse relation, properties of binary relations in a set. - Equivalence relations and their use for organizing and sorting sets. - Display as a special type of binary session. Types of display (injective, subjective, bijective). - Bijective display. Inverse display. Special case of display - mathematical function - Display, examples of display in student activities focused on the development of mathematical concepts. - Concepts related to natural number and methods of their development. The concept of cardinal number. Finite and infinite sets. Inequality between cardinal numbers. - Addition and multiplication of cardinal numbers. Properties of addition and multiplication of cardinal numbers. - The concept of a natural number as a cardinal number of non-empty sets. Operations in the set of natural numbers. Natural arrangement of the set of natural numbers. - Algebraic structures. Binary operations. Properties of binary operations. - Development of spatial imagination in primary education, spatial orientation and wayfinding. Common and different properties of spatial formations, determining the position of objects in space using simple expressions. - 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. - Plane shapes in primary education (point, line, semi-line, line segment, square, rectangle, quadrilaterals, circle, circle), their observation, naming. Differentiation of planar structures from three-dimensional ones, network of bodies, cutting and folding, representation of three-dimensional structures in a plane.
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Methods for working with texts (Textbook, book), Practice exercises, Analysis of a presentation
- Participation in classes
- 28 hours per semester
- Term paper
- 30 hours per semester
- Preparation for course credit
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| unspecified |
| unspecified |
| learning outcomes |
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| analysis of the framework of educational program from the point of view of mathematical ideas |
| analysis of the framework of educational program from the point of view of mathematical ideas |
| binary relations position in learning tasks |
| binary relations position in learning tasks |
| concept of numbers and its historical development |
| concept of numbers and its historical development |
| methods leading to the development of geometric ideas |
| methods leading to the development of geometric ideas |
| operations with natural numbers and their properties |
| operations with natural numbers and their properties |
| Skills |
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| describe the position of the field of mathematics and its application in the national curriculums |
| describe the position of the field of mathematics and its application in the national curriculums |
| use knowledge about statements and binary relations in solving learning tasks |
| use knowledge about statements and binary relations in solving learning tasks |
| use knowledge about natural numbers in the creation of mathematical ideas among first-grade elementary school students |
| use knowledge about natural numbers in the creation of mathematical ideas among first-grade elementary school students |
| describe the methods of introducing the concept of natural number |
| describe the methods of introducing the concept of natural number |
| introduce non-traditional methods of solving arithmetic and geometric mathematical problems |
| introduce non-traditional methods of solving arithmetic and geometric mathematical problems |
| teaching methods |
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| Knowledge |
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| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Analysis of a presentation |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Practice exercises |
| Analysis of a presentation |
| Practice exercises |
| assessment methods |
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| Written examination |
| Written examination |
| Analysis of seminar paper |
| Analysis of seminar paper |
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Recommended literature
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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, 2001.
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Hejný, M. Vyučování matematice orientované na budování schémat: aritmetika 1. stupně. Praha: UK., 2014.
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Kaslová, M. Předmatematické činnosti v předškolním vzdělávání.. Praha: Raabe., 2010.
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Markechová, D., & Tirpáková, A. Rozvoj matematických predstáv o číslach. Nitra.
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Partová, E., & Židek, O. Príručka k príprave na súbornú skúšku z matematiky.. Bratislava, 1993.
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Pavelková, M. Pohled učitelů prvního stupně základních škol na žákovskou otázku. e- Pedagogium, 3, 53-64..
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