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Lecturer(s)
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Břehovský Jiří, Mgr. Ph.D.
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Příhonská Jana, doc. RNDr. Ph.D.
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Bímová Daniela, Mgr. Ph.D.
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Pirklová Petra, RNDr. Ph.D.
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Course content
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Thematic areas 1. Axiomatic construction of planimetry - systems, and groups of axioms. 2. Planimetry - basic concepts of geometry (point, line, plane), derived concepts (semi-line, line segment, angle, half-plane, etc.), circle. 3. Planar figures and their properties. 4. Stereometry - basic concepts (point, line, plane, space). 5. Basic solids, their properties, and nets. 6. Representation of shapes - free parallel projection (basic rules and usage). 7. Representation of shapes - Monge's projection (basic principles, perpendicular views onto solids). 8. Measure of geometric shapes, its properties. The length of the line segment, the area of the planar figure, the volume of the solid, and the size of the angle. Units of measures. 9. Construction tasks, phases, and methods of solving construction tasks. Sets of all points of a given property - examples. 10. Congruent geometric mappings in the plane (central and axial symmetry, translation, rotation, identity) - properties and basic principles, usage. 11. Congruent geometric mappings in space (central, axial, and planar symmetry, translation, rotation, identity) - properties and basic principles, usage. 12. Similar geometric mappings in a plane and space (similarity, homothety) - properties and basic principles, usage. 13. Binary operations in geometry. 14. Binary relations in geometry.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Dialogue metods(conversation,discussion,brainstorming), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Lecture, Practicum, E-learning
- Class attendance
- 16 hours per semester
- Preparation for credit
- 14 hours per semester
- Home preparation for classes
- 18 hours per semester
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Learning outcomes
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In the lectures, a brief theoretical introduction to the mentioned topics is outlined and an introduction to the basic terms from a didactic point of view is made. All concepts will be presented from the point of view of their application in the teaching of mathematics at the 1st grade of elementary school, while the accuracy of the interpretation will be subject to this point of view. In the exercises, the material explained in the lecture is practiced, supplemented with practical applications related to the contents of the geometry and arithmetic curriculum of the 1st grade of elementary school.
Acquisition of basic theoretical knowledge and acquisition of practical skills in the areas of plane and three-dimensional geometry. Understanding of basic geometric concepts and connections between them.
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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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Combined examination, Student's performance analysis
Knowledge of the geometry topics determined for primary and secondary school. Requirements for successful credit completion: - active participation in exercises, - successful presentation of a paper on a selected topic assigned by the teacher. Requirements for passing the exam: - completion of credit, - the range of knowledge is defined by the subject syllabus.
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Recommended literature
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Učebnice a pracovní sešity matematiky a geometrie pro 1. st. ZŠ - různé řady.
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Francová, M. - Lvovská, L. Texty k základům elementární geometrie: Pro studium učitelství 1. stupně základní školy. Brno, Munipress, 2014. ISBN 978-80-210-7.
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Križalkovič, K. a kol. Didaktika matematiky na 1. stupni ZŠ. Bratislava, SPN, 1990.
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Palková, M. Průvodce matematikou 2 aneb co byste měli znát z geometrie ze základní školy. Brno, Didaktis, 2007. ISBN 978-80-7358-275-3.
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Zehnalová, J. Cvičení z elementární aritmetiky a elementární geometrie II. Ostrava, Ostravská univerzita, 2005. ISBN 80-7042-123-1.
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