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Drozd rings
Nytra, Jan ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
This thesis focuses on Drozd rings. In the beginning, we mention important parts of algebraic theory for the definition of these rings. In the next chapter we describe an example of Drozd ring. In the following, we concentrate on Weil algebras - it shows up, that Drozd algebras over field of real numbers are specific examples of Weil algebras. We also construct groups of algebra automorphisms for these algebras. In the last part of the thesis, we mention Lie groups, because groups of algebra automorphisms of Weil algebras are examples of Lie groups.
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Transfer between verbal and algebraic descriptions. Pupils' strategies and problems
Novotná, Anežka ; Vondrová, Naďa (advisor) ; Roubíček, Filip (referee)
The aim of this thesis is to gain insight into the problems that pupils have when switching between verbal and algebraic expressions, through the analysis of their problem-solving processes. The work is divided into theoretical and experimental parts. The theoretical part of the paper contains three sections. The first describes the analysis of three selected Czech textbooks series for primary schools in terms of teaching the concept of variables and algebraic expressions. The next section deals with international comparative research TIMSS and the success of Czech pupils of year 8 in algebra. In the third section, results of international research concerning the issue of transition between verbal and algebraic expressions are described. The main part of the work is the experimental part, it aims to describe the difficulties encountered by pupils in algebra and to identify their likely sources. The basis for the own research was a set of 9 problems based on released TIMSS problems. The target group of pupils was year 9 of primary school, with whom the investigation was carried out via think-aloud interviews. First, a pilot study was conducted on a sample of 3 pupils, during which a set of test problems was checked. The main study involved 8 pupils. The think-aloud interviews were recorded and later...
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Mathematics in Ancient India
Sýkorová, Irena ; Bečvář, Jindřich (advisor) ; Veselý, Jiří (referee) ; Hykšová, Magdalena (referee)
The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.
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How pupils solve generalising tasks
Nováková, Aneta ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The diploma thesis focuses on generalization tasks. Its aim is to gain insight into the solving strategies that pupils use and to determine whether the chosen approach depends on the acquired knowledge about the variable. The work is divided into theoretical and research part. The theoretical chapter contains three parts. The first is devoted to letters in mathematics and generalization problems as one of the ways of introducing a variable. The next part presents the results of Czech pupils in the international comparative research TIMSS in the problems on generalisation. The last part is devoted to curricular documents and the analysis of selected textbooks in terms of the occurrence of generalization problems. More attention was devoted to the only textbook series which includes generalization tasks. The research part is the core of the work. Its aim is to describe the solution strategies of selected pupils. Four tasks were the basis of the research. They were selected by the author from various research sources and graded according to their difficulty. Pupils who had already encountered the term variable were the target group as well as pupils for whom it was a new term. Eight pupils participated in the research. They were interviewed about their solutions of the assigned tasks. Next, the...
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Solving algebraic problems in history and in the classroom
Vojáček, Josef ; Kvasz, Ladislav (advisor) ; Zamboj, Michal (referee)
This diploma thesis deals with the comparison of historical solutions of word problems with student solutions. Its aim was to describe how students solve historical word problems, while looking for analogies between student and historical solutions. This intention led me to a better understanding of student solutions. The theoretical part of the thesis describes important concepts for algebraic word problems, such as a variable, algebraic expression or algebraic word problem. In the historical part I describe chronologically the development of algebra from antiquity through the Middle Ages and the Renaissance to the Baroque. In each period, I mention important mathematicians of the time and present several solved word problems. In most cases, I analyze these solutions from the perspective of today's mathematics. The theoretical part describes the research that took place at the eight-year grammar school. As part of the research, I gave students 6 historical tasks across historical periods and then analyzed the ways in which students solved problems. I found that for most of the tasks, there were solutions similar to the historical solutions among the student's solutions. Some historical methods appeared very often. An example is the use of addition instead of multiplication, or division, as used by the...
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Expressions with variables in primary mathematics
Pokorný, Antonín ; Vondrová, Naďa (advisor) ; Pilous, Derek (referee)
The thesis is focused on the teaching of variable expressions at the eighth grade of elementary school and is divided into the theoretical, preparatory and experimental part. The theoretical part contains a short description of the objectives of the teaching of variable expressions. This section is complemented by the selected results of international comparative research and the classification of mistakes which pupils make in connection with the topic. An important part is the analysis of selected textbooks according them the teaching of variable expressions at the primary schools takes place. In the preparatory part there are presented the selected tasks of generalization which are recommended by the curriculum materials, but are not included in the textbooks. Component of the preparatory part is the presentation of algebra tiles environment. The core of the thesis is the experimental part aiming to compare the results of teaching of variable expressions in two differently taught groups. The first group was taught according to the textbook. In the second group the teaching was based on patterns of algebra tiles. The research of teaching results is focused on pupils' difficulties and the most frequent mistakes. The results indicated that the environment of algebra tiles helps to reduce number of...
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Use of applications of algebra in sciences at secondary schools
Novotný, Tomáš ; Novotná, Jarmila (advisor) ; Jančařík, Antonín (referee)
The MA thesis focuses on the strategies pupils use when solving mathematical problems involving systems of linear equations in other subjects, namely in physics and chemistry. Drawing on the results of the experiment, the aim of the thesis is to propose ways in which these problems can be used in math lessons. The first part of the thesis is dedicated to those branches of physics and chemistry in which systems of linear equations are used. In the following part, the experiment itself is described. Divided into two parts, the first part of the experiment focuses on pupils at lower secondary schools, the other on pupils at upper secondary schools. The final part of the thesis is dedicated to suggesting how problems from physics and chemistry can be used in math lessons when introducing and practising systems of linear equations. Powered by TCPDF (www.tcpdf.org)
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Mathematics in Ancient India
Sýkorová, Irena ; Bečvář, Jindřich (advisor) ; Veselý, Jiří (referee) ; Hykšová, Magdalena (referee)
The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.
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