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Lecturer(s)
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Fajkus Martin, RNDr. Ph.D.
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Tirpáková Anna, prof. RNDr. CSc.
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Course content
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- Basic concepts of Euclidean geometry. Point, line segment, ray, line, polyline. Incidence of points a straight lines. - Arrangement of points. Mutual position of points and lines. - Triangle and its properties, plane, half-plane, mutual position of lines and planes. - Geometric relations - incidence, arrangement, similarity, parallelism. - Convex and non-convex sets. Convex and non-convex angle. Circle, round, sphere, spherical surface, arc, n-angle, quadrangle, parallelogram. - Solids. Free parallel projection. Developing spatial imagination. Meshes. - Conformity. Segment line comparison, segment line operations. Equality of angles and triangles. - Angle comparison and angle operations. Identical representations in the plane - identity, axial symmetry, central symmetry, displacement, rotation. Composing identical representations in a plane, group of similarities. - Segment line and angle measure. Units for measuring segment lines and angles. Measure of a planar formation. - Areas of some planar formations. Circumference and areas of rectangle, square. - The length of the circle. Use of mesh. Measure of spatial unit. - Cubic capacity of solids. Metric relations between geometric shapes - distances of point sets, divergences of segment lines and planes. - Construction tasks. Sets of points of a given property. - Axiomatic system. Models of Euclidean and non-Euclidean geometry. Historical notes
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Dialogic (Discussion, conversation, brainstorming), Methods for working with texts (Textbook, book), Activating (Simulation, games, dramatization)
- Home preparation for classes
- 10 hours per semester
- Term paper
- 22 hours per semester
- Preparation for course credit
- 30 hours per semester
- Participation in classes
- 28 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| unspecified |
| unspecified |
| learning outcomes |
|---|
| basic concepts of Euclidean geometry |
| basic concepts of Euclidean geometry |
| basic geometric relations |
| basic geometric relations |
| comparing convex and non-convex angles |
| comparing convex and non-convex angles |
| basic concepts of plane geometry |
| basic concepts of plane geometry |
| models of Euclidean and non-Euclidean geometry |
| models of Euclidean and non-Euclidean geometry |
| Skills |
|---|
| explain Euclid's theorems |
| explain Euclid's theorems |
| compare geometric relationships - incidence, arrangement, congruence, parallelism |
| compare geometric relationships - incidence, arrangement, congruence, parallelism |
| compare the angles of planar shapes and solids |
| compare the angles of planar shapes and solids |
| determine the measure of planar and spatial formations |
| determine the measure of planar and spatial formations |
| describe the importance of Euclidean models for the development of geometric ideas |
| describe the importance of Euclidean models for the development of geometric ideas |
| teaching methods |
|---|
| Knowledge |
|---|
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Activating (Simulation, games, dramatization) |
| Monologic (Exposition, lecture, briefing) |
| Activating (Simulation, games, dramatization) |
| Monologic (Exposition, lecture, briefing) |
| assessment methods |
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| Didactic test |
| Didactic test |
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Recommended literature
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Divíšek, F. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, 1989.
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Jirotková, D. Cesty ke zkvalitňování výuky geometrie. Praha: UK., 2010.
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Kouřim, J. et al. Základy elementární geometrie pro učitelství 1. stupně ZŠ. Praha: SPN, 1985.
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Kuřina, F. Deset pohledů na geometrii. Praha: Albra., 1996.
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Kuřina, F. 10 geometrickýcvh transformací. Praha: Prometheus., 2002.
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Stopenová, A. Matematika II. Geometrie s didaktikou. Olomouc: UPOL, 1999.
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Stopenová, A. Vybrané úlohy z elementární geometrie pro studenty učitelství 1. stupně ZŠ. Olomouc: UPOL, 1996.
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Žilková, K., & Židek, O. Manipulačná geometria. Bratislava, 2013.
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Žilková, K. Geometria [online]. Trnava: PF Trnavská univerzita, 2013.
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