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Lecturer(s)
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Fajkus Martin, RNDr. Ph.D.
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Pavelková Marie, Mgr. Ph.D.
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Course content
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1) Axiomatic system. Models of Euclidean and non-Euclidean geometry. Historical notes. 2) Basic concepts of Euclidean geometry. Point, line segment, ray, straight line, polyline. Incidence of points and lines. Axioms of incidence. 3) Mutual position of points and lines; plane, half-plane, mutual position of lines and planes. 4) Geometric relations - incidence, arrangement, congruence, parallelism. 5) Triangle and its properties. Congruence of triangles. 6) Convex and non-convex sets: angle, circle, circle, arc, triangle, quadrilateral, n-gon; sphere, spherical surface. 7) Angle, types of angles. Circle and circle. 8) Congruence. Comparison of lines, operations with lines. Comparison of angles and operations with angles. 9). Congruent projections in the plane - identity, axial symmetry, central symmetry, translation, rotation. Composition of congruent projections in the plane, congruence group. 10) Measure of a line segment and angle. Units of measurement of lines and angles. Perimeter of a plane figure. 11) Contents of some plane figures. Use of square grids. 12) Solids. Free parallel projection. Development of spatial imagination. Grids of solids. 13) Volumes and surfaces of solids. Metric relations between geometric figures - distances of point sets, deviations of lines and planes. 14) Construction problems. Sets of points of given properties.
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Learning activities and teaching methods
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- Participation in classes
- 42 hours per semester
- Home preparation for classes
- 70 hours per semester
- Preparation for examination
- 68 hours per semester
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| prerequisite |
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| Knowledge |
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| basic concepts of geometry in the plane and in space, |
| basic concepts of geometry in the plane and in space, |
| basic geometric representations and measure theory, |
| properties of a triangle with application in solving problems, |
| properties of a triangle with application in solving problems, |
| basic geometric representations and measure theory, |
| perimeters and areas of selected plane figures, volumes of solids, |
| metric relations between geometric figures. |
| metric relations between geometric figures. |
| perimeters and areas of selected plane figures, volumes of solids, |
| Skills |
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| apply knowledge about a triangle and its properties, knowledge about a plane, a half-plane, the relative position of lines and planes |
| apply knowledge about a triangle and its properties, knowledge about a plane, a half-plane, the relative position of lines and planes |
| apply knowledge about spatial imagination, |
| apply knowledge about spatial imagination, |
| apply knowledge and skills in the field of geometry for teaching at the first level of primary school |
| apply knowledge and skills in the field of geometry for teaching at the first level of primary school |
| can handle construction tasks from elementary geometry, |
| can handle construction tasks from elementary geometry, |
| apply theoretical knowledge from elementary geometry. |
| apply theoretical knowledge from elementary geometry. |
| learning outcomes |
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| Knowledge |
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| define basic concepts of elementary geometry |
| define basic concepts of elementary geometry |
| explain basic concepts of geometry in the plane and in space |
| explain basic concepts of geometry in the plane and in space |
| characterize basic geometric representations and measure theory |
| characterize basic geometric representations and measure theory |
| explain properties of a triangle with an application to problem solving |
| explain properties of a triangle with an application to problem solving |
| calculate perimeters and areas of selected plane figures |
| calculate perimeters and areas of selected plane figures |
| calculate perimeters and areas of selected plane figures |
| calculate perimeters and areas of selected plane figures |
| Skills |
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| apply knowledge about a triangle and its properties |
| apply knowledge about a triangle and its properties |
| argue their solutions when constructing problems in a plane, half-plane, and the relative position of lines and planes |
| argue their solutions when constructing problems in a plane, half-plane, and the relative position of lines and planes |
| apply knowledge about plane and spatial imagination |
| apply knowledge about plane and spatial imagination |
| justify the properties of triangles with an overlap in application when solving problems |
| justify the properties of triangles with an overlap in application when solving problems |
| defend their solutions when constructing problems from elementary geometry |
| defend their solutions when constructing problems from elementary geometry |
| apply metric relations between geometric figures |
| apply metric relations between geometric figures |
| teaching methods |
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| Knowledge |
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| Methods for written tasks (e.g. comprehensive exams, written tests) |
| Methods for written tasks (e.g. comprehensive exams, written tests) |
| Skills |
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| Activating (Simulation, games, dramatization) |
| Activating (Simulation, games, dramatization) |
| assessment methods |
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| Knowledge |
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| Analysis of educational material |
| Analysis of educational material |
| Analysis of another type of paper written by the student (Casuistry, diary, plan ...) |
| Analysis of another type of paper written by the student (Casuistry, diary, plan ...) |
| Analysis of the student's performance |
| Analysis of the student's performance |
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Recommended literature
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Francová, M., & Lvovská, L. Texty k základům elementární geometrie: Pro studium učitelství 1. stupni základní školy.. Masarykova univerzita, 2014.
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Francová M., Matoušková K., & Vaňurová, M. Sbírka úloh s elementární geometrie.. Masarykova univerzita, 2013.
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Molnár, J., Perný, J., & Stopenová, A. (2006). Prostorová představivost a prostředky k jejímu rozvoji. Praha: JČMF.??. 2006.
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Musser, G. L., Burger, B. E., & Peterson, B. E. Mathematics for elementary teacher. New York: John Wiley & Sons.?. 2001.
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Stopenová A. Matematika II. Geometrie s didaktikou.. Olomouc: Univerzita Palackého v?Olomouci., 1999.
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Stopenová A. Vybrané úlohy z elementární geometrie pro studenty učitelství 1. stupně ZŠ. Univerzita Palackého v?Olomouci.?. 1996.
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