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Dielectric Relaxation Spectroscopy of Composite Systems
Holcman, Vladimír ; Liedermann, Karel (advisor)
The subject of this doctoral thesis is the study of dielectric properties of a binary composite made up of a polymer matrix and metallic filler. Properties of such composites have been extensively examined in the past and they turned out to depend on temperature, frequency and in particular on filler concentration. The objective of this work was first to experimentally establish and second to describe quantitatively the effect of the size of metallic particles on the properties of the composite concerned, yet at the same filler concentration. This study was carried out on the model system ethylene-vinylacetate copolymer – nickel. The acquisition of experimental results required extensive measurements in a wide frequency and temperature interval, as well as a manufacture and preparation of a large set of samples with different concentrations and Ni filler sizes. Measurements were in part carried out at the Centre for Electronic Correlations and Magnetism, Institute of Experimental Physics V of the University of Augsburg (Germany) and, after the installation of a new cryogenic system, at the Department of Physics at FEEC, BUT Brno. Measurements were performed on a number of meters (Alpha-Analyzer of Novocontrol, HP4284A and HP4285A of Hewlett Packard and E4991A of Agilent) in the frequency range 1 Hz – 1 MHz and in the temperature interval 10 K – 300 K. The nickel concentration in systems studied varied from 0 % to 75 % and nickel particles were of a spherical shape with diameters between 35 and 115 m. The measurement results have shown that in the above frequency and temperature window just a single relaxation and a single conductivity mechanism occur. It was also proved that the frequency dependence of complex permittivity is for different Ni particle sizes at the same concentration different. These results have been quantified and a simple mathematical formula based on the Lichtenecker mixture rule has been proposed for their description. The physical origin of the effect of particle size at the same total nickel concentration is sought in different surface areas of internal interfaces between nickel and polymer in the composite
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Changes in pupils' understanding of models of fractions
Hillebrandová, Eliška ; Janda, David (advisor) ; Kvasz, Ladislav (referee)
Fractions are a dreaded topic not only for students but also for teachers. The reason is that it is a breakthrough subject in primary schools, without which one cannot successfully continue in further studies. Therefore, in the first chapter of this thesis we will focus on understanding fractions through visual models (discrete and continuous - chocolate, circle, line segment, rectangle) that can be commonly found in textbooks aimed at teaching fractions. In the second chapter, using action research tools, we investigated how students' understanding changed over time following the interventions. The research consisted of two pilot tests and three iterations of the test over a two-month period in three seventh grade classes in a Prague elementary school. Specifically, the test focused on part-from- whole and whole-from-part search for the following three models: the discrete ordered model, the fraction-as-part-of-an-area model in a lattice network, and the number axis model. All results were graphically processed using tables, boxplots and we relied on statistical tests. In the third chapter, we summarized these results in detail and also pointed out the shortcomings of the research and how they can be addressed. It showed that there was a positive change in students' understanding of fraction...
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Pupils' solutions of word problems with fractions and percentages
ADAMCOVÁ, Hana
This diploma thesis deals with a topic of mathematics, namely word problems with fractions and percentages. Specifically, this work deals with students' solutions to such word problems. The work acquaints the reader with how selected word problems with fractions and percentages are solved by pupils in the 9th grade of primary schools. It introduces the readers to the various numerical procedures chosen by the students. Some procedures occurred more frequently, others only rarely. Each word problem is supplemented by a graph, which shows the success of students in solving the word problem. The work also includes photographs of students' solutions for the reader's better idea. At the end of the chapter, some word problems are processed using the Concept Cartoons method. The work shows mainly close connections between fractions and percentages. And especially on how primary school students look at the problem from their point of view.
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Worksheets for teaching mathematics at secondary school from selected topics
ONDRÁČKOVÁ, Kamila
The main aim of the thesis is to verify the pupils knowledge in arithmetic on the basis of worksheets at lower-secondary schools and selected grammar schools. The theoretical part of the thesis is focused on the knowledge that each pupil should already know. The practical part contains 4 working sheets intended for pupils of the sixth, seventh, eighth and ninth grades of lower-secondary school and for the pupils of equal corresponding grade of grammar schools. The results with detailed solution of the work sheets is listed in the appendix of the thesis. The practical part includes is the results of the research which show the pupils´ differences of knowledge of the selected schools.
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Inquiry based mathematics education: case of fractions
Podhajská, Kristýna ; Tichá, Marie (advisor) ; Novotná, Jarmila (referee)
The theoretical part deals with approaches to teaching, especially constructivistic, instructivistic and transmissive approach. The goal of this part is to compare the approaches and evaluate them considering the permanency of knowledge and active engagement of students. Simultaneously it aims at evaluating the approaches from the point of their of the mechanical knowledge. The charter dealing with inquiry based mathematics education is focused on teaching related to constructivistic approach. The next chapter describes tool called concept cartoons, which can be used as a mean to research. The theoretical part is focused on the topic of fraction, especially fraction interpretation and models and fraction representation. The second part of the thesis describes a survey realized at basic school. I narrowed the problem to fraction interpretation and representation according to survey of student's work. The next part of research is based on this analysis. Trying to accomplish the aims and find the answers to questions of the survey I chose strategy inspired by action research, because the main goal of the research was to improve and enhance my teaching knowledge and skills. The survey was processed qualitatively. The making of the thesis helped me make it clear, why the topic of fractions is so...
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