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Lecturer(s)
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Bártková Eva, Mgr. Ph.D.
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Bártek Květoslav, Mgr. Ph.D.
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Dofková Radka, doc. PhDr. Ph.D.
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Course content
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- Point, line segment, half- line, line, polygonal line. Incidence between points and lines. Ordered points. Relative position of points and lines. - Triangle (and its properties), plane, half-plane, relative position of lines and planes. Parallelism. Convex set, angle, circle, sphere, spherical surface, arc of a circle, n-gon, quadrangular, parallelogram. - Solids. Parallel projection. Development of spatial imagination. Shape grids. - Identity (sameness). Comparison of line segments, line segment operations (intersections). Corresponding angles and triangles. Comparing angles and angular operations. - Congruent planar mappings ?identity, axial symmetry, central symmetry, translation, rotation, translational symmetry. Composition of congruent mappings and properties of composition. Group of congruent mappings. Congruent linear and spatial mappings. Homothety and similarity of geometric figures. Basic concepts of topology. Overlapping geometric figures. - Line segment measurement and measure of a set. Units of measurement with respect to line segments and angles. Measuring line segments at lower primary schools. Measuring planar shapes. Areas of certain planar shapes. Perimeter and area of a rectangle and a square at the primary school. Length of a circle. Use of square grids. Measuring spatial figures. Volumes of certain solids. Metric relations between geometric figures ? distances between sets of points, angles between lines and planes. Construction tasks. Sets of points with given properties. - Axiomatic system, axiom requirements. Deductive proof in geometry. Euclidean and Non-Euclidean geometry models. Historical notes and their use at primary schools.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 26 hours per semester
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Learning outcomes
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The purpose of the subject is to provide future teachers with the necessary level of knowledge and skills (drawing, measuring, solving of geometry tasks) that they will need when teaching geometry at primary schools. The subject matter comprises the whole system of plane and space geometry concepts, geometry mappings, and the measure theory
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Prerequisites
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Foundation mathematics in extent basic and central school
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Assessment methods and criteria
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Mark, Oral exam, Written exam
Active participation in the lessons, passing continuous tests (60%), elaboration and submitting of a seminar paper. Written and oral exam.
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Recommended literature
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KOUŘIM, J. a kol. (1985). Základy elementární geometrie. Praha.
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OPAVA, Z. (1989). Matematika kolem nás. Praha: Albatros.
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STOPENOVÁ, A. (1999). Matematika II. Geometrie s didaktikou. Olomouc.
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STOPENOVÁ, A. (1996). Vybrané úlohy z elementární geometrie pro studenty učitelství 1. stupně ZŠ. Olomouc.
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STOPENOVÁ, A. (2005). Základy matematiky 3. Olomouc.
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STOPENOVÁ, A. (2006). Základy matematiky 5. Olomouc.
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