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The effect of Singapore mathematics on the mathematical self-efficacy of elementary school pupils
Šulcová, Pavla ; Jančařík, Antonín (advisor) ; Jirotková, Darina (referee)
This diploma thesis partly follows from the research of Smetáčková and Vozková who developed a Czech mathematical self-efficacy questionnaire. It examines the student's mathematical self-efficacy, i.e. the student's belief about his ability to successfully work on solving mathematical problems, depending on gender, year and the type of word problems used. It is also dedicated to teaching, describing solutions and student strategies for solving word problems in the form of two types of Singaporean problems - What number makes sense and What question can you answer. It describes the mathematics teaching in Singapore, which is repeatedly placed in the top ranks in international testing. 53 pupils in the 4th and 5th year of elementary school participated in the research lasting 5 weeks. The students filled out a mathematical self-efficacy questionnaire at the beginning and end of the research. During the research, the 4th graders were presented with 8 Singapore- type problems What question can you answer, and the 5th graders were presented with 10 traditional-type or Singapore-type problems What number makes sense. Hypotheses were tested with a two-sample F-test. No difference in mathematical self- efficacy was demonstrated for boys and girls. The 4th -grade students rated as more mathematically...
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The use of 3D printers in mathematics education
Rohelová, Jitka ; Jančařík, Antonín (advisor) ; Janda, David (referee)
The aim of this thesis is to design, implement, and evaluate an educational model that integrates 3D printing into the teaching process, linking computer science and mathematics education with the goal of increasing student engagement and understanding. Furthermore, it explores the challenges associated with the use of 3D printing and 3D printers in mathematics teaching and subsequently proposes recommendations and creates materials that would allow the effective use of this technology in mathematics education. The collected data was analyzed using both quantitative and qualitative methods. The educational model was designed around the topic of stereometry and was implemented through an educational experiment involving 5 classes of a vocational high school. The conclusions drawn from the data analysis are consistent with theoretical assumptions about increased motivation and success of students when using 3D printers in education. A meeting was organized for teachers to share best practices on the topic of using 3D printing and 3D printers in mathematics teaching. Following group discussions with teachers, challenges faced by teachers (or schools) when integrating 3D printing into their curriculum were identified and described in two separate chapters. Additionally, a set of 3D models of...
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Pell's equation, continued fractions and Diophantine approximations of irrational numbers
Kodýtek, Jakub ; Beran, Filip (advisor) ; Jančařík, Antonín (referee)
This bachelor's thesis deals with Pell's equation, while clearly presenting structured information from studied domestic and foreign books, articles, and other sources. The goal of this thesis is to create study material primarily for university students but also for inquisitive high school students, and thus explain as intuitively as possible what Pell's equation is, how to find its solutions, and how it is related, for example, to continued fractions, approximations of irrational numbers, and invertible elements in Z[√n ]. The main motivation for solving Pell's equation throughout the work is specifically that its solutions give best approximations of irrational square roots. Pell's equation is presented in a brief historical context. Further, it is proved that there is a non-trivial integer solution for every Pell equation, and the theory of continued fractions is used to find it. To make the creation of continued fractions easier, the so-called Tenner's algorithm is introduced. Specifically, the search for a solution to Pell's equation is derived using convergents and the periodicity of continued fractions of irrational roots. Subsequently, the structure of the solution is described: it is proved that there is a so-called minimal solution that generates all positive solutions, and a set of...
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Algebraisation in problems with a geometric context - pupils' difficulties and mistakes
Benešová, Štěpánka ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
The aim of this thesis are problems in which pupils demonstrate the ability to switch between geometric and algebraic representation. The task of the thesis is to correctly identify the difficulties and mistakes of pupils in the algebraisation of problems with geometric context before the teaching of algebra and after the teaching of algebra. The thesis consists of theoretical and experimental parts. The theoretical part defines the necessary concepts, summarizes selected results of research and studies related to the algebraisation of problems with geometric context and contains an analysis of five selected textbooks for the eighth year of elementary school, which are used by pupils participating in the research. The analysis of textbooks is focused on chapters dealing with the topics of Algebraic expressions with variables and Powers. The experimental part focuses on research identifying difficulties and mistakes of pupils in solving problems in which pupils try to algebraically model geometric relations. The basis of the research was two sets of test problems followed by an individual conversation with the pupils. The first set of problems was made for sixth-graders, seventh-graders and eight- graders. The second set of problems was made for ninth-graders. The tests were used in two primary...
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Financial literacy of pupils and teachers of primary school
Novotný, Ondřej ; Jančařík, Antonín (advisor) ; Novotná, Jarmila (referee)
The presented diploma thesis is focused on financial literacy at basic school, with the focus on the integration of financial skills into the education on the secondary school. The main aim of the thesis is to compare several selected methods for education of financial literacy at basic school with the intention to select a optimal way for developing the financial literacy of students and solutions of their various economical situations, problems and decisions that expect them in their future life. The theoretical part contains introduction into the topic, introductory theoretical basis, basic definitions of important terms and a description of the educational system. Reasons for introduction of financial literacy education into basic education system are explained. Further, the strategic documents influencing the education of financial literacy at basic school, which are the base for creation of frame school programs for the education of financial literacy, are introduced. The situation is described in more detail and it is explained, how it is possible to introduce the financial literacy education in the school education programs in agreement with the frame education programs. In the end of the theoretical part, the selected methods for evaluation of the financial literacy education at the basic...
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Linear Diophantine equations and congruences
Kaňáková, Natálie ; Beran, Filip (advisor) ; Jančařík, Antonín (referee)
This bachelor's thesis summarizes and systematizes knowledge about congruences and linear Diophantine equations. This work is divided into two parts. The first part is dedicated to congruences. At first, it shows where we can find congruences in real life, congruence as a relation, its properties, and applications in calculating the last ciphers of large numbers, proofs of divisibility rules, or calculating the date of Easter. Afterward, we look into congruences containing unknowns - linear congruence equations. It looks into methods of solving linear congruences and illustrates them in exercises. The last topic of the first part is oriented on systems of linear congruences and the Chinese remainder theorem, both for non-coprime and coprime moduli, the algebraic version, applications in various types of problems, and modular representation of numbers. The second part of this thesis is dedicated to linear Diophantine equations - equations with integer solutions. It shows various methods of solving linear Diophantine equations with two, three, or more unknowns - the extended Euclidean algorithm, reduction method, substitution method, and others. This part also describes the relationship between linear congruences and linear Diophantine equations and the use of this relationship in solving both linear...
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A 3D geometric game in Unity
Trejbal, Tomáš ; Zamboj, Michal (advisor) ; Jančařík, Antonín (referee)
In this thesis, I am working on the creation of a 3D computer game with Unity engine. The game is called "Cubeidea" and focuses on geometry topics and spatial imagination. In the introduction of the thesis, I describe the motivation that led me to create this game. In the following chapters, I introduce the reader to the software tools used in the creation process, the characteristics of the game, and a description of the game space. The largest part of this thesis is then devoted to describing the algorithms that are implemented in the game to provide the various game functionalities and mechanisms, such as player movement in the game space, verification of level completion, etc. The reader will find examples of the game's source code in the thesis, which are used to supplement the description of the individual algorithms. If interested, the reader can look into the full source code of the game, which is included in the appendices of this thesis.
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