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Lecturer(s)
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Charvátová Lenka, PhDr.
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Bímová Daniela, Mgr. Ph.D.
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Příhonská Jana, doc. RNDr. Ph.D.
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Course content
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Lectures: In the lectures, a brief theoretical introduction to the mentioned topics and an introduction to basic concepts from the didactic point of view are done. All concepts will be interpreted from the point of view of their application in the teaching of mathematics at the primary school level, while the accuracy of the interpretation is subordinate to this aspect. The seminars are taught based on the previous lectures, including practical applications of the primary school level of mathematics. 1. Axiomatic construction of geometry - groups of axioms, models of non-euclidean geometries. 2. - 3. Planimetry - basic geometric terms (point, line, plane), derived terms (semi-line, line-segment, angle, half-plane), circle. 4. - 5. Plane figures and their properties. 6. Stereometry - basic terms (point, line, plane) 7. - 8. Basic solids, their properties and nets. Platonic solids. Paper models of solids. 9. - 10. Representation of geometric objects in space. Mapping methods - Free parallel projection (solving spatial problems in the FPP, planar cuts of a cube). 11. Monge's projection (basic principles, orthogonal views on the solids). 12. - 13. A measure of geometric objects, their properties. Length of the line segment, area of a plane figure, the volume of a basic solid, size of an angle. Units of the measurements. 14. Sets of points of the given properties.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Demonstration of student skills, Seminár, Students' portfolio
- Class attendance
- 28 hours per semester
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Learning outcomes
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Axiomatic construction of geometry. A brief theoretical introduction to the topics of planimetry and stereometry, introduction to basic concepts from a didactic point of view. Simple planimetric constructions of planar geometric objects. Mapping methods - Free parallel projection, Monge's projection - their basic principles and displaying of the basic bodies in them. Measurement of geometrical objects and its properties. Equipping with elementary habits and skills needed in teaching geometry at primary school - explanation of the curriculum, methodical procedures, a creation of teaching aids and work with them.
Theoretical knowledge and practical skills from the required area.
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Prerequisites
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Knowledge of elementary and secondary school geometry.
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Assessment methods and criteria
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Presentation of artistic and creative activities, Test
Active participation in seminars, successful passing of 2 tests, successful submission of seminar work (preparation of given teaching aids for independent work of pupils, their presentation or interpretation of the curriculum - preparation and presentation of a sample explanatory lesson).
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Recommended literature
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Osnovy a metodické příručky k těmto učebnicím..
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Rámcový vzdělávací program pro ZV..
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Učebnice matematiky pro 1.-5. ročník základní školy..
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Vzdělávací program Základní škola. Praha, Fortuna 1996..
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Bartlová, E. Míra geometrických útvarů v učivu matematiky druhého stupně základní školy. Brno, 2011.
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Divíšek, J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, SPN 1989.. &, &.
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Etzold, H. - Petzschler, I. Nápadník aktivit a her do hodin matematiky pro 2. stupeň ZŠ, SŠ a gymnázia. Brno, 2013. ISBN 978-80-266-0174-6.
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Chytrý, V. - Prchalová, J. Geometrie s didaktikou II. Ústí nad Labem, 2013.
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Kouřim, J. a kol. Základy elementární geometrie pro učitelství l. st. ZŠ. Praha, SPN, 1985.
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