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Relations and their applications
Čulíková, Markéta ; Novotná, Jarmila (advisor) ; Zamboj, Michal (referee)
The thesis deals with relations and their applications. The first chapter summarizes the introductory theoretical knowledge that is necessary for understanding the topic relations: an element, set, ordered pairs, Cartesian Product. The important definitions are introduced for all of these concepts and the related information is summarized within this chapter. The second chapter defines the concept of relations and operations on them. It includes various types of graphical representations of relations and their advantages and disadvantages. The concept of relation on a set and the properties of this relation alongside with some special types of relations derived from them are introduced in this chapter. The concepts of function are also defined in this part of the thesis. The third chapter indicates the relations that appear in real life - in relationships and games, in curriculum and puzzles. The properties of those relations are determined and the knowledge of relations and their properties is used to facilitate the solution of logical problems. It also supports gaining deeper understanding of those problems. The thesis includes two groups of tasks. The first one covers elementary tasks related to the topic of sets, ordered pairs, Cartesian Product and relations. The second part is concerned with...
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Venn diagrams - Teaching Mathematics using the CLIL method for upper secondary pupils
Vojířová, Barbora ; Novotná, Jarmila (advisor) ; Moraová, Hana (referee)
This thesis focuses on the teaching of mathematics using the CLIL method. The topic is Venn diagrams and learning how to solve problems using these diagrams. The language chosen for the CLIL method is English. First, the CLIL method is described, and later I introduce sets and Venn diagrams. The aim of the thesis is to prepare and implement two lessons using the CLIL method in English, and two lessons in Czech, followed by preparing a test in both languages for a third lesson. The thesis was realized by conducting a teaching experiment, which took place in two classes of multi- year grammar school (in the Quintas - the first year of secondary school). I have compiled and tested four worksheets - two with Czech tasks, two with English tasks, a presentation for the lesson using the CLIL method, and tests for both language versions. Both the tasks and solutions are part of the thesis. Before the preparation of the thesis, the following two research questions were identified: 1. What needs to be taken into consideration when preparing for the Venn diagrams lesson using the CLIL method, and what needs to be added to this lesson compared to the Czech lesson? 2. At what success rate will pupils learn using the CLIL method in English and pupils using Czech, with regard to equation building and answers to...
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Binary relations and mappings in teaching of mathematics
Muzikářová, Zdena ; Robová, Jarmila (advisor) ; Hromadová, Jana (referee)
The diploma thesis presents a collection of solved problems in binary relations. Students are familiarized with various applications of binary relations on high school mathematics and geometry. The work focuses on graphical representation of binary relations and their use in solving equations, inequalities and their sys- tems. It is a teaching text designated for a mathematics seminar at high school. In addition to exercises, it also includes an introduction of new concepts which are supplemented by relevant definitions and illustrative examples. 1
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