
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


Web application for teaching of complex numbers
Kneblík, Radovan ; Robová, Jarmila (advisor) ; Staněk, Jakub (referee)
This thesis deals with complex numbers and teaching of them in high school mathematics. The thesis is a web page, it includes the definition of complex numbers in various forms (form of ordered pair, algebraic, polar and exponential form) and operations and also conversions between forms. The lecture is enhanced with interactive applets, which demonstrate given topic. Solved exercises, exercises leading to set of points satisfying a condition and an overall test are also parts of the thesis. Web page created within the thesis can be used by high school students as well as by teachers. 1


Circumferences and areas of plane figures
Šrámek, Martin ; Robová, Jarmila (advisor) ; Šarounová, Alena (referee)
Title: Circumferences and areas of plane figures Author: Martin Šrámek Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This diploma thesis Circumferences and areas of plane figures is designed for teachers and high school students. Teachers might find some interesting tasks including various metric problems from the field of synthetic geometry as well as inference of mathematic equations for calculation circumferences and areas of plane figures which are taught at elementary schools and high schools. Pupils can appreciate solved tasks and their knowledge can be applied to other similar tasks. The ninth chapter includes more difficult tasks. There are many drawings exported from GeoGebra which can help students to understand the task better. Keywords: circumference, area, length, teaching of mathematics


Binary relations and their use in teaching of mathematics
Muzikářová, Zdena ; Robová, Jarmila (advisor) ; Odvárko, Oldřich (referee)
The bachelor thesis presents a collection of exercises where binary relations are used to solve equations, inequalities and their systems. It is a teaching text designated for a mathematics seminar at the high school. The collection is pri marily intended for high school students, but it can also serve as a source of exercises for teachers. The work focuses on graphical representation of binary re lations and their use in solving problems. The thesis also includes an introduction of new concepts which are supplemented by relevant definitions and illustrative examples. 1


Analytical representation of congruent transformations at high schools
Ptáčková, Tereza ; Robová, Jarmila (advisor) ; Hromadová, Jana (referee)
This work deals with analytical representation of congruent transforma tion in a plane at high schools. The work is a web page, it contains several interactive components which help student to understand the problem like hyperlinks, stepping of the construction, applets, etc. The work contains several solved problems. Main emphasis is placed on the connection of the synthetic and the analytic approach to congruent transformation. The work uses knowledge of analytic geometry students learn at high school. The web page is aimed at talented students of high school and for teaching at mathematical class. 1


Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools
Dohnalová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.


Geometric transformation in secondary school mathematics with the support of internet
Ptáčková, Tereza ; Robová, Jarmila (advisor) ; Štěpánová, Martina (referee)
This work deals with geometric transformation in a plane in high school mathematics. The work is a web page, it contains several interactive components which help student to understand the problem like hyperlinks or stepping of the construction. The work contains several solved problems. Main emphasis is placed on illustration of problems in the form of drawings and construction. The illustration is better by using of applets. The applets show the steps of the construction one after another as the students proceed with the con struction on a sheet of paper. Together with each step of construction its symbolic description is showed. Created web page could be used by highschool students as well as tea chers to demonstrate the problem.


Web application: Basic knowledge of mathematics at secondary school
Pavlicová, Vladimíra ; Robová, Jarmila (advisor) ; Karger, Adolf (referee)
The presented work is intended to serve as a teaching material in particular for pupils of the first year of secondary school, focusing on the basic knowledge of mathematics. The first part of the thesis is devoted to an analysis of existing web page, which corresponds to the theme of the diploma thesis. The evaluation takes into account the expertise as well as the scope of use of interactive elements. In the next part, the created teaching material in a form of web page is presented. It deals with the subject matter of powers, roots, polynomials and rational expressions. In accordance with current trend, the emphasis is put on both visualisation of curriculum (charts, use of graphics) and interactivity. All exercises to practise involve solution, therefore users are allowed to gain immediate feedback and thus to study individually. Web page is free available.


Divisibility for talented students of secondary schools
Živčáková, Andrea ; Robová, Jarmila (advisor) ; Bečvář, Jindřich (referee)
This thesis is an educational text for high school students. It aims to teach them how to solve typical problems concerning divisibility found in mathematical correspondence seminars and mathematical olympiad. Basic notions from the theory of divisibility are recalled (e.g. prime numbers, divisors, multiples). Criteria of divisibility by 2 to 20 are introduced, as well as diophantine equations and practical applications of prime numbers in real life. One whole chapter is dedicated to problems and exercises. Powered by TCPDF (www.tcpdf.org)


Regular polyhedra and their properties
Pavlovičová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
This work is intended for all people from the general public especially for all people interested in regular polyhedra geometry. The work can be also used as didactic aid by education of regular polyhedra. It is an comprehensive text which summarizes description, history, classification of this five regular polyhedra. We will also focus on their properties and occurence. Basic calculations of surfaces, volumes and radii of the circles circumscribed and inscribed are in the work too. The text is supplemented with illustrative pictures made in GeoGebra and Cabri3D. Some chapters are supplemented with photos.
