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Combinatorics in mathematics competitions
Kadeřábek, Václav ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
This work analyzes the possibilities of division of combinatorial problems that occur in mathematical competitions. It contains presentation of Combinatorics taught at secondary schools. It shows the differences between solving problems in schools and math competitions. Using graphs and tables, it demonstrates an unbalanced distribution of combinatorial problems. In conclusion, it offers some types of examples that are missing in competitions, or are there in insufficient numbers.
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Mathematical problems from real life for secondary schools using an interactive white board
Hyánek, Martin ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Mathematical problems from real life for secondary schools using an interactive white board. (Diploma thesis.) ABSTRACT The diploma thesis deals with the possibility of IWB application in the teaching of mathematics at a secondary school. The aim was to examine its didactical potential for the teaching of mathematical functions. For this purpose, I created and described three interactive presentations in programs Smart Notebook and Math Tools focused on elementary mathematical functions that are illustrated on examples from real life and interconnect knowledge from diverse subjects. Namely it is a quadratic function and its application in sport, exponential function and its application in geography and goniometric function sinus and its application in music. One of the presentations was applied in practice. The thesis reflects the experience from teaching and also looks into how students perceive using the IWB during teaching. It was confirmed that the teacher's role is in the use of IWB is indispensable. The theoretical part of the thesis contextualizes the IWB application from historical, technical and didactical points of view. The thesis can serve as an inspiration for the practical use of IWB in mathematics teaching. Key words: interactive white board (IWB), interactive teaching, Smart Notebook, Math...
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GeoGebra in mathematics education
Havelková, Veronika ; Zhouf, Jaroslav (advisor) ; Jančařík, Antonín (referee)
The aim of this work is to introduce and assess the potential of using GeoGebra software on multiple levels of mathematical education process and to analyze the expectation of pupils and students using this program. A reader is introduced to GeoGebra program itself and to various researches and articles sharing this common topic - usage of dynamic geometry educational programs and GeoGebra in mathematical education. This work is supported by two field researches that were carried out at the second stage of an elementary school and by another reseach made with students of mathematical education at the Charles University, the Faculty of Education. Next part of this work presents and covers more possibilities of using this program in the educational process of the second stage of elementary schools, and it also shows various options the program offers not just for teaching of mathematics, but also for other fields.
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Tandemat - didactic game for the teaching of mathematics at the secondary school
Šilhánová, Lucie ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Tandemat - didactic game for the teaching of mathematics at the secondary school The thesis concerns a didactic game called Tandemat which I have created as a complement for the teaching of mathematics at secondary schools. The goal of the thesis is to find out and describe the potential of this game for the teaching of mathematics at this school level. First, the importance of games in our lives and also in teaching is mentioned. Next, some resources concerning games in the teaching of mathematics are described. The core of the thesis consists of the game Tandemat which I have elaborated and which is inspired by the popular game Activity. The results of the pilot studies of the game with the preliminary name Aktivity which were realized at elementary school and university helped to improve the game into its present version Tandemat. This has been tested by five groups of pupils in four classes of a secondary grammar school. The experiments were recorded and the acquired data were analyzed using the method based on the grounded theory approach. Moreover, a questionnaire was administered to pupils, concerning their grades in mathematics and the Czech language and their remarks on the game itself. The results of the analyses, observations and questionnaires show the potential and the limits of...
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Use of Japanese Puzzles in Teaching Mathematics at Primary School
Pěničková, Barbora ; Kloboučková, Jaroslava (advisor) ; Jančařík, Antonín (referee)
This diploma thesis deals with Japanese puzzles and their use in teaching mathematics at primary school. Its main aim is to verify if it is possible for the pupils to achieve comparable results with older pupils and adult Sudoku solvers supposing that these learners are systematically guided through an escalating set of Sudoku puzzles. The theoretical part of the thesis is focused on the history of Sudoku, several strategies of its solving, other examples of Japanese puzzles and also on Sudoku in the context of its use at school. The practical part describes a series of experiments with pupils of the first, later second grade of a primary school, which were conducted in order to verify the hypothesis of this thesis.
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Solving problems from the domain of electrical circuits
Devera, Filip ; Novotná, Jarmila (advisor) ; Jančařík, Antonín (referee)
TITLE: Solving problems from the domain of electrical circuits AUTHOR: Filip Devera DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: The subject of this thesis is solving problem from the domain of electrical circuits. Because the theory of electrical circuits itself is a broad subject, this thesis is going to focus only on a small subcategory, mainly electrical circuits, where the power sources supply the current and voltage either at a constant direct flow or with a harmonic waveform. Furthermore these circuits will be discussed only in their stabilized state. This may seem as a gross simplification of the subject, but majority of electronic devices works with direct or harmonic power supply. The goal set for this thesis is to define relationships for the design of selected electrical circuits derived from the much broader theory of electromagnetic field. Various methodologies and procedures for the design of electronic ci- rcuits exist, that are based on these relationships. These methods will be illustrated on solved examples. Aside from the physical characterization of circuits a mathematical apparatus will be needed to solve equations and sys- tem of equations, derived from the physical relationships.
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Elementary functions and domain
Vitásek, Tomáš ; Pilous, Derek (advisor) ; Jančařík, Antonín (referee)
The aim of my bachelor thesis is to show the teachers and the students of educational mathematics the relation between the elementary functions and their domains and the methods of creating problems focused on finding the domain. In the chapter called "Zobrazení", I try to define and explain the terminology closely connected to elementary functions and their doma- ins which I use in the following parts. Crucial chapters are "Definiční obory elementárních funkcí" and "Návrhy úloh". In the first of those two chapters I thoroughly explain the algorithm of solving problems focused on finding the domain of elementary functions and I discuss what the domains of various elementary functions are like. In the second of those two chapters, I suggest functions fitting a concrete domain. The aim is to suggest functions in a way that a student taking their maturita exam in mathematics at high school would be able to solve the problem of finding the domain. Keywords: elementary function, domain, function composition.
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Mathematics on the chess board
Šperl, Jiří ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
TITTLE: Mathematics on the chessboard AUTHOR: Jiří Šperl DEPARTMENT: The Department of mathematics and the teaching of mathematics SUPERVISOR: RNDr. Antonín Jančařík, Ph.D. ABSTRACT: The main subject of my thesis is mathematical problems on the chessboard using chess pieces. The work aims to demonstrate how a secondary school student would approach and solve several typical mathematical tasks of this nature. Consequently, it outlines ways to incorporate chessboard mathematical problems and exercises in mathematical classes. Moreover, the thesis includes a compact collection of solved problems on the chessboard that can serve as an inspiring source of unconventional mathematical tasks in conventional mathematical education. My own mathematical research forms a major part of the thesis. The research was conducted as a series of tests in three school classes. In order to achieve a high de- gree of objectivity classes of students with different specializations were selected to take part in the tests. The participating classes were also of different age groups. The theoretical part of the thesis takes a look at the past of the subject and presents several interesting historical problems concerning the mathematics on the chess- board. Last but not least, the thesis contains a discussion of solutions of the...
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Language recognition based on the frequency analysis
Čadek, Jan ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
TITLE: Language recognition based on the frequency analysis SUMMARY: The aim of this bachelor thesis is to use the basic cryptoanalytic aid - frequency analysis - for the recognition of the language of a text (or of a cryptogram). The first chapter is devoted to the history of cryptology. Chapter 2 focuses on frequency analysis, its principle is explained on a simple example. In the third part, there is the description of three programs for language recognition. Last chapter compares the results, which I gained through my programs, with the affinity of European languages as described in linguistics. One of the conclusions of my work is that the real affinity of languages is well approximated using the program analysis. KEY WORDS: frequency analysis, cryptology, European languages, recognition, relationships of languages
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