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Lecturer(s)
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Chytrý Vlastimil, doc. PhDr. Ph.D.
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Course content
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1. Constructivist conception of teaching (mechanism of cognitive process). 2. Deductive construction of geometry (axioms, definitions, theorems). Axiomatic concepts of Euclidean geometry (point, line, plane, incidence of point and line, ternary relation "between" for points, ....), intuitive introduction of these concepts in school. (Eukleides, Hilbert). 3. Basic symbolism associated with geometry. Working with symbols. 4. Geometric shapes as sets of points. Problems of using set concepts in teaching geometry, various didactic approaches. Definition of the terms half-line, opposite half-line, half-plane, opposite half-plane, half-space, opposite half-space and their introduction in the teaching of geometry at the first grade school. 5. Problems on constructions of geometric shapes. Different cases of intersection or unification of geometric shapes, definitions of terms: angle (convex and non-convex), triangle, planar strip, tetrahedron, circular segment, circular segment, etc. 6. Classification of the mutual position of two geometric shapes according to their intersection. Parallelism, divergence, non-parallelism of lines as a binary relation in the set of all lines in the plane and in space. Definition of these terms, properties, use in the curriculum at the first grade school. 7. Relation in geometry. The issue of anchoring relations in the curriculum of the first stage of primary school. 8. Operations in geometry. The issue of anchoring operations in the curriculum of the first stage of primary school. 9. Representation (definition, properties, representation between sets, definition field, domain of values, simple representation). Concordance of lines, concepts introduced on the basis of similarity of lines. Congruence of angles and concepts introduced on the basis of congruence of angles. 10. Convexity of geometric shapes, definition of convex shape, examples of convex and non-convex shapes in the plane and in space, or use of the theorem on the intersection of convex formations. 11. The use of a practical manipulative approach in the teaching of geometry at the first stage of elementary school (POP UP geometry, kits, etc.). 12. Identical representations in the plane and in space. 13. Dynamic geometry? basic principles of working with the relevant program. 14. Possibilities of using dynamic geometry at the first stage of primary school.
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Learning activities and teaching methods
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unspecified, unspecified, unspecified
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Learning outcomes
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In the subject Geometry with Didactics, a system of geometric concepts necessary for teaching geometry at the first stage of primary school is creatively developed. Increased attention is paid to geometric, especially spatial imagination, the quality of graphic communication and modern elements that penetrate the teaching of geometry in terms of supporting material and applications / programs. The student will get acquainted, for example, with the program Geogebra, or the possibilities of working with interfaces enabling video calls and video conferencing. Emphasis will be placed on the use of non-traditional teaching methods and forms for the maximum possibility of involving students with SPU or gifted students during teaching. These methods include the black box method, the confrontation method, the ship meeting method, the Gordon method, the Philips 66 method, the Hobo method, paper folding and more. All these methods will be supplemented by work with a textbook and test sets and interspersed with practical examples.
The student can: - describe the constructivist concept of teaching geometry, - work with basic geometric objects and define them, - analyze relations, operations and representations in geometry (describe the occurrence of these elements in textbooks for primary schools), - describe the use of a practical manipulative approach in the teaching of geometry in the first stage, - Work with software and dynamic geometry.
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Prerequisites
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The subject requires no specific prerequisites.
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Assessment methods and criteria
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unspecified
1. 80% participation in seminars. 2. Successful completion of the credit test. 3. Activity in seminars.
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Recommended literature
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HEJNÝ, M., KUŘINA, F. Dítě, škola a matematika, Portál, Praha, 2001.
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CHYTRÝ, Vlastimil, PRCHALOVÁ, Jana. Geometrie s didaktikou II. I. Vyd. Ústí nad Labem: Univerzita J. E. Purkyně, 2013, 82s..
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Jirotková, D. Cesty ke zkvalitňování výuky geometrie. Praha, 2010.
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PERNÝ, Jaroslav. Kapitoly z elementární geometrie I. Vyd. 2., upr. Liberec: Technická univerzita v Liberci, 2009, 58 s. ISBN 978-80-7372-539-6..
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PERNÝ, Jaroslav. Kapitoly z elementární geometrie II. Vyd. 1. Liberec: Technická univerzita v Liberci, 2005, 57 s. ISBN 80-7372-025-6..
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