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Lecturer(s)
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Honzík Lukáš, PhDr. Ph.D.
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Pěchoučková Šárka, PhDr. Ph.D.
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Huclová Miroslava, PhDr. Ph.D.
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Course content
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1. Triangle and its properties - angles in a triangle, sorting triangles, triangle inequality. Výšky, těžnice, těžiště, middle příčky triangle. Typografie. Geometric symbols. The basic rules of correct alignment of rovinných údárů, druhy čar. The basic rules of creating a sketch. 2. Construction of triangles - similarity of triangles, theorems about similarity of triangles and their use, construction tasks. Methodology for solving design tasks. Suitable pomůcky for teaching, use of dynamic mathematical software. 3. Similar view - similar shapes, axis alignment, center alignment, displacement, rotation. Soumérnosti kolem nás. Use in elementary school teaching. Basic rules of rýsování. Suitable pomůcky for teaching, use of dynamic mathematical software. 4. Advanced application problems and problems, solving basic problems of mathematical competitions on a given topic. 5. Čtyřúhelníky - classification, basic drawing rules, mathematická symbolika. Metodika solution of practical problematicy. Organizational forms of teaching suitable for thematic areas of mathematics education. 6. Circle, circle - the relative position of a circle and a straight line, the relative position of a straight line and a plane, the relative position of two circles. Metodika solution of practical problematicy. Thalet's theorem and its practical application. 7. Right-angled triangle - Pythagorean theorem and its practical application, relations between sides and angles. Similar shapes, similar triangles. Activation methods for use at elementary schools. 8. Multiple points of a given property - multiple points in a plane. Practical examples, solution methodology, proper rýsování. 9. Free horizontal projection, vertical projection, 3D modeling and 3D printing using digital skills. 10. Creating geometric ideas in children of preschool age, creating geometric ideas in children of younger school age.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Collaborative instruction, Cooperative instruction, Discussion, Instruction based on dialogue, Multimedia supported teaching, Students' portfolio, Individual study
- Contact hours
- 39 hours per semester
- Preparation for an examination (30-60)
- 55 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
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| master the elementary geometric concepts and their relationships at the level of KMT/MSD4 |
| define the elementary concepts of geometry (point, line, broken line, semi-line, line, half-line, plane, triangle, angle, tetrahedron) in terms of mathematical theory |
| define the concept of congruent representation |
| specify manipulative activities that develop children's concept of symmetry |
| Skills |
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| distinguish the relative position of two lines in the plane and space, the relative position of a line and a plane and the relative position of two planes |
| apply some principles of free parallel projection and activities related to it to the 1st grade mathematics curriculum |
| analyze activities with building blocks in terms of the development of spatial intelligence |
| demonstrate the basic properties of axial symmetry, central symmetry and plane symmetry |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| define the concept of similarity representation |
| analyze sets of points in terms of their properties |
| draw general conclusions about given sets |
| decide what geometric figure is formed by points satisfying a given property |
| categorize the different stages of the process of measuring a line segment in primary school |
| distinguish the different levels of development of pre-school children's geometric thinking |
| specify manipulative activities and other activities that lead to the development of geometric imagination of children of younger school age |
| Skills |
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| differentiate between congruent and similar representations |
| demonstrate the basic properties of congruence |
| analyze the assignment of a construction problem, defend the procedure of their own solution |
| propose activities leading to the concept of the content of a square and a rectangle and to the definition of the concept of volume |
| apply the knowledge of the Pythagorean Theorem and Euclidean Theorems in solving concrete practical problems |
| on the basis of video recordings, practical examples and study of textbooks, analyse different approaches to introducing elementary concepts of geometry (point, line, line segment, broken line, semi-line, line, triangle) on primary school |
| compare the different mathematics textbooks of the 1st grade in terms of integration of mathematics and science |
| to propose and test specific activities for children that avoid formalism in the cognitive process of the pupil |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Interactive lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Collaborative instruction |
| Cooperative instruction |
| Students' portfolio |
| Discussion |
| Skills |
|---|
| Interactive lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Collaborative instruction |
| Cooperative instruction |
| Individual study |
| Students' portfolio |
| Competences |
|---|
| Lecture supplemented with a discussion |
| Collaborative instruction |
| Cooperative instruction |
| Students' portfolio |
| assessment methods |
|---|
| Knowledge |
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| Combined exam |
| Oral exam |
| Group presentation at a seminar |
| Skills |
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| Combined exam |
| Skills demonstration during practicum |
| Group presentation at a seminar |
| Continuous assessment |
| Oral exam |
| Competences |
|---|
| Combined exam |
| Group presentation at a seminar |
| Continuous assessment |
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Recommended literature
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Cvičení z elementární aritmetiky a elementární geometrie : Určeno stud. denního studia, studia při zaměstnání a postgrad. studia. Část 2.. 1. vyd. Ostrava : Pedagogická fakulta, 1991. ISBN 80-7042-039-1.
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učebnice, pracovní sešity a metodické příručky matematiky pro 1. st. ZŠ.
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Základy elementární geometrie pro učitelství 1. stupně ZŠ : Celost. vysokošk. učebnice pro stud. pedagog. fakult. 1. vyd. Praha : SPN, 1985.
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Bělík, Miroslav. Geometrie s didaktikou : učební text pro studium učitelství prvního stupně základní školy. Vyd. 1. V Ústí nad Labem : Univerzita J.E. Purkyně, 2007. ISBN 978-80-7044-875-5.
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Divíšek, J. a kol.:. Didaktika matematiky pro učitelství l.stupně ZŠ.
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FRANCOVÁ, M., LVOVSKÁ, L. Texty k základům elementární geometrie: pro studium učitelství 1. stupně základní školy. Brno: Masarykova univerzita, 2014. ISBN 978-80-210-7594-8.
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Frobisher, Anne, Frobisher, Len. Didaktika matematiky II: Porozumieť, riešiť, počítať. Bratislava, 2015. ISBN 978-80-8140-200-5.
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Hejný, Milan; Novotná, Jarmila; Stehlíková, Naďa. Dvacet pět kapitol z didaktiky matematiky. Praha : Pedagogická fakulta UK, 2004. ISBN 80-7290-189-3.
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Kuřina, František. Deset geometrických transformací. 1. vyd. Praha : Prometheus, 2002. ISBN 80-7196-231-7.
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