IMAk05 Geometry 1

Faculty of Education
Autumn 2019
Extent and Intensity
0/0/.7. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Leni Lvovská, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMAk05/01: Fri 20. 9. 9:00–11:50 učebna 32, Fri 1. 11. 9:00–11:50 učebna 32, Fri 13. 12. 10:00–11:50 učebna 32, L. Lvovská
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course students should be able to understand and explain the followed knowledge: Basic geometry terms, properties and relations between them, mainly terms included in subject matter of elementary school. Students will be acquainted with inter-subject connections, they will understand the possibilities of fostering the imagination and the possibilities of stimulating constructive thinking in geometry of elementary school. Weither at the end of the course students should be able to solved chosen constructive and proof exercises (mostly triangles, quadrangles and circles). During the course, the student will also be acquainted with some possibilities of digital support of teaching geometry, especially with the educational software GeoGebra.
Learning outcomes
At the end of the course students should be able to understand and explain the followed knowledge: Basic geometry terms, properties and relations between them, mainly terms included in subject matter of elementary school. Students will be acquainted with inter-subject connections, they will understand the possibilities of fostering the imagination and the possibilities of stimulating constructive thinking in geometry of elementary school. Weither at the end of the course students should be able to solved chosen constructive and proof exercises (mostly triangles, quadrangles and circles). During the course, the student will also be acquainted with some possibilities of digital support of teaching geometry, especially with the educational software GeoGebra.
Syllabus
  • History of geometry. Geometric imagination in plane. Context of geometry with the world around us. Basic concepts of Euclidean geometry, axioms, axiomatic concepts. Hilbert's axiomatic system. Symbols used in geometry. Line segment, half-line, half-line, half-plane, opposite half-line. Convex and non-convex set of points. Convex and non-convex angle. A polyline. A simple polyline, a closed polyline. Polygons. Triangle, basic properties, relations between sides and angles in a triangle. Theorem of sum of inner angles in a triangle and its proof, theorem about outer angle of a triangle - proof, triangular inequality - proof, theorems on opposite sides and angles of a triangle and its proof. Triangular partitions - center of gravity, middle partitions, heights, axes of sides and axes of inner and outer angles of the triangle (theorems on the basic properties of these partitions).. Chosen geometrical exercises - proofs and constructions Basic geometry terms, properties and relations between them, mainly terms included in subject matter of elementary school. Geometrical objects as a set of points. Solution of chosen proof exercises (mostly triangles, quadrangles and circles). Constructional and planimetric exercises and their solution.
Literature
  • FRANCOVÁ, Marta, Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Texty k základům elementární geometrie : pro studium učitelství 1. stupně základní školy. 2. opr. vyd. Brno: Masarykova univerzita, 1994, 107 s. ISBN 8021008806. info
  • FRANCOVÁ, Marta, Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Sbírka úloh z elementární geometrie. 2. vyd. Brno: Masarykova univerzita, 2004, 86 s. ISBN 8021035706. info
  • KOUŘIM, Jaroslav, Ondrej ŠEDIVÝ and František KUŘINA. Základy elementární geometrie : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985, 156 s. info
  • FRANCOVÁ, Marta and Leni LVOVSKÁ. Texty k základům ELEMENTÁRNÍ GEOMETRIE (Textbooks to the Basics of ELEMENTARY GEOMETRY). 1. vydání. Brno, 2014, 77 pp. ISBN 978-80-210-7594-8. info
Teaching methods
Seminar, consultation.
Assessment methods
Colloquium, written test, discussion.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on the extent and intensity of the course: 8 konzultací.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2018, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2019/IMAk05