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Acceleration of numerical computation of heat conduction in solids in inverse tasks
Ondruch, Tomáš ; Komínek, Jan (referee) ; Pohanka, Michal (advisor)
The master's thesis deals with possible ways of accelerating numerical computations, which are present in problems related to heat conduction in solids. The thesis summarizes basic characteristics of heat transfer phenomena with emphasis on heat conduction. Theoretical principles of control volume method are utilized to convert a direct heat conduction problem into a sparse linear system. Relevant fundamentals from the field of inverse heat conduction problems are presented with reference to intensive computations of direct problems of such kind. Numerical methods which are well-suited to find a solution of direct heat conduction problems are described. Remarks on practical implementation of time-efficient computations are made in relation with a two-dimensional heat conduction model. The results are compared and discussed with respect to obtained computational time for several tested methods.
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Critical areas of mathematics at the primary school - analysis of teachers' didactic practices (linear equations)
Nováková, Anežka ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Kritická místa matematiky na základní škole (Analýza didaktických praktik učitelů - lineární rovnice) Critical Areas of Mathematics at the Primary School (Analysis of Teachers' Didactic Practices - Linear Equations) Abstract The goal of the diploma thesis is to describe didactic practices used by primary teachers when teaching linear equations, seen as one of the critical moments of primary school mathematics. First, semantic and structural models of linear equations and ways of teaching linear equations as suggested by selected textbooks for primary schools are described. Next, on the basis of literature review, pupil' problems and types of mistakes they make in this area are given. My research consisted of semistructured interviews with five experienced mathematics teachers and observations of their lessons. The interviews and observations were transcribed and the transcriptions were analysed by techniques of grounded theory. It was found out that the teachers use common didactic practices as well as their own which they develop. The practices, models which the teachers use when teaching linear equations, approaches to introducing equivalent operations, as well as a list of critical places within linear equations are the main results of the work. Keywords: Linear equations, models, pupils' problems,...
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Websites in teaching mathematics focused on linear equations and functions
Kloučková, Jana ; Mošna, František (advisor) ; Vondrová, Naďa (referee)
1 Abstract: The aim of this thesis is to create websites focused on teaching linear equations and functions and verify their utility from the perspective of pupils and selected teachers. Websites are one of the form called E-learning. Therefore, the thesis deals not only with websites but also with the e-learning. The work is divided into theoretical and practical part. The theoretical part is mainly based on selected literature search and analysis of textbooks from the point of view of linear equations and functions. The practical part is about creating own website and about qualitative research implemented at the basic schools in Obříství and Neratovice. The research was conducted through questionnaires, which were enriched by interviews with selected pupils and teachers. It was found that pupils and teachers consider these created websites beneficial. The List of the strengths and weaknesses of the websites, as well as the possibilities for its improvement are one part of the thesis results. Keywords: websites, e-learning, linear equations, functions, models of implementation linear equations
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Acceleration of numerical computation of heat conduction in solids in inverse tasks
Ondruch, Tomáš ; Komínek, Jan (referee) ; Pohanka, Michal (advisor)
The master's thesis deals with possible ways of accelerating numerical computations, which are present in problems related to heat conduction in solids. The thesis summarizes basic characteristics of heat transfer phenomena with emphasis on heat conduction. Theoretical principles of control volume method are utilized to convert a direct heat conduction problem into a sparse linear system. Relevant fundamentals from the field of inverse heat conduction problems are presented with reference to intensive computations of direct problems of such kind. Numerical methods which are well-suited to find a solution of direct heat conduction problems are described. Remarks on practical implementation of time-efficient computations are made in relation with a two-dimensional heat conduction model. The results are compared and discussed with respect to obtained computational time for several tested methods.
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Equations at high schools
JANŮ, Denisa
The Bachelor's thesis is focused on the issues of equations, taught on elementary and high schools. Students make numerous errors when solving them, which stem from the wrong ways of solving these equations, but more importantly from assembling them. The first part of the thesis is focused on the types of equations (linear, quadratic, ...) and the ways of solving them. In the second part is the usage of equations when solving given problems. These word problems are solved through the usage of equations and the through the student's judgement, that most schools don't develop. There are exercises at the end of the thesis.
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Didactic approaches to the teaching of some mathematical topics at the primary school in teachers ́ diskurse
Vencovská, Jaroslava ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis was through a new analysis of interviews with teachers of mathematics, to describe didactic practices used by teachers while teaching selected topics (namely, proportions, linear equations, divisibility, percent, symmetry, Pythagorean theorem ) and compare them with the practices reported in textbooks and other literature. First, teaching methods, teaching forms and the mechanism of concept development by M. Hejný are given. Based on the analysis of more than thirty interview, it was found that teachers use the usual didactic practices but also create their own methods and procedures. These methods and techniques are provided for each critical issue separately in the fourth chapter of the thesis. Furthermore, the content analysis of selected textbooks is given for each topic. Identified practices of teachers which they use in their teaching practice, form the result of my work.
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Websites in teaching mathematics focused on linear equations and functions
Kloučková, Jana ; Mošna, František (advisor) ; Vondrová, Naďa (referee)
1 Abstract: The aim of this thesis is to create websites focused on teaching linear equations and functions and verify their utility from the perspective of pupils and selected teachers. Websites are one of the form called E-learning. Therefore, the thesis deals not only with websites but also with the e-learning. The work is divided into theoretical and practical part. The theoretical part is mainly based on selected literature search and analysis of textbooks from the point of view of linear equations and functions. The practical part is about creating own website and about qualitative research implemented at the basic schools in Obříství and Neratovice. The research was conducted through questionnaires, which were enriched by interviews with selected pupils and teachers. It was found that pupils and teachers consider these created websites beneficial. The List of the strengths and weaknesses of the websites, as well as the possibilities for its improvement are one part of the thesis results. Keywords: websites, e-learning, linear equations, functions, models of implementation linear equations
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Critical areas of mathematics at the primary school - analysis of teachers' didactic practices (linear equations)
Nováková, Anežka ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Kritická místa matematiky na základní škole (Analýza didaktických praktik učitelů - lineární rovnice) Critical Areas of Mathematics at the Primary School (Analysis of Teachers' Didactic Practices - Linear Equations) Abstract The goal of the diploma thesis is to describe didactic practices used by primary teachers when teaching linear equations, seen as one of the critical moments of primary school mathematics. First, semantic and structural models of linear equations and ways of teaching linear equations as suggested by selected textbooks for primary schools are described. Next, on the basis of literature review, pupil' problems and types of mistakes they make in this area are given. My research consisted of semistructured interviews with five experienced mathematics teachers and observations of their lessons. The interviews and observations were transcribed and the transcriptions were analysed by techniques of grounded theory. It was found out that the teachers use common didactic practices as well as their own which they develop. The practices, models which the teachers use when teaching linear equations, approaches to introducing equivalent operations, as well as a list of critical places within linear equations are the main results of the work. Keywords: Linear equations, models, pupils' problems,...
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