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Teaching Mathematics using the CLIL method
Vrbíková, Helena ; Novotná, Jarmila (advisor) ; Kvasz, Ladislav (referee)
The thesis deals with preparation of teaching materials for teaching mathematics using the CLIL method. The chosen topic is statistics at lower secondary level. The thesis is divided into several chapters, first three chapters are more theoretically oriented and the last four chapters deal with the actual preparation and use of teaching materials for the chosen topic. The theoretical part of this theses introduces the CLIL method and several difficulties when using it, as well as suggestions for overcoming them successfully. Next, reasons for the choice of a particular topic in mathematics are given and the choice of English as the secondary language that is taught is justified. Lastly, teaching targets are set in accordance with the basic principles of this method both in mathematics and English as a second language. The specifics of the topic in question are carefully chosen while observing the current curriculum. The practical part of this theses focuses in detail on piloting the use of typically CLIL activities. The conclusions drawn from this first experiment are then used when preparing the actual materials for teaching statistics. The prepared materials are then presented and annotated with explanations for use by other teachers and results of their use in a classroom during the second...
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The influence of a used unit on the difficulty of a word problem
Blatská, Dagmar ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The difficulty of word problems in mathematics is influenced by a number of parameters, both mathematical and non-mathematical. The influence of the esed unit, as one of the linguistic charakteristice, has already been partially tested within the framework of research GAČR 16-6134S. The subject of this testing were pairs of word problems with the same assigment, wich differed only in the unit esed. In one task, there was a commonly used currency unit, the koruna, in the other task, a fictious currency unit, zed. The conclusion of this research were ambiguous. While some tasks showed statistically significant differences in succes, other did not. The aim of this work was to find out what effect the used unit has on the succes of the solution and on the perception of the difficulty of word problems. The subject of testing was a trio of tasks with the same structure, but with different contexts. These tasks varied in the unit used. In one task there is a common currency unit, the koruna, in the second there are unusual units of currency and volume, the US dollar and barrel, in the third task are unusual units of currency unit, zed. The target group was pupils of the 6th and 8th grade of elementary school. The assumption was that the task with a common unit would be more succesful for the solver and that it...
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Flatland and student's perception of the fourth dimension
Bouchalová, Kateřina ; Zamboj, Michal (advisor) ; Kvasz, Ladislav (referee)
This diploma thesis deals with the connection between mathematics and literature, two disciplines that may seem distant from each other. The aim of this work is to analyze whether selected students are able to improve their perception of the fourth dimension with the help of the analogy introduced in an excerpt from Edwin Abbott Abbott's book called Flatland. This thesis begins by introducing firstly, the history of the fourth dimension and the way it is conceptualized, and secondly, the author and the book Flatland. The theoretical part continues by providing a description of the occurrence of analogy, literature, and the fourth dimension in the Framework Education Programme for Secondary General Education as well as other sources focused on teaching mathematics. Next, the theory of the general models introduced by Hejný is summarized, followed by the van Hiele model of geometric thinking. The theoretical part of the thesis ends with a description of our limitations regarding the representations of the fourth dimension. This first part of the work stands as the basis for the practical part of the thesis that introduces a quantitative case study which was realized in the following way. Two tests were given a week apart to the fifth-year students of a sixth-year grammar school. The aim was to...
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Hejný's method in comparison with the Realistic mathematics education of Hans Freudenthal
Jandová, Sára ; Kvasz, Ladislav (advisor) ; Janda, David (referee)
The aim of the content of the thesis is mainly to find and compare the common principles of Hejny's method of teaching mathematics with Realistic mathematics education, the foundations of which were discussed by Hans Freudenthal in his work. Both approaches to teaching are always briefly described theoretically and then presented by examples from exercisebook, from manuals and from practice. Theese are supplemented by a didactic commentary. In order to write the thesis, materials summarizing individual methods were first studied, and then appropriate teaching topics and links were searched for, on which a mutual comparison was made, and which represent different components of mathematics education (arithmetic, geometry and algebra). In the section of examples, the work is oriented to links derived from the 2nd grade of elementary school. For each teaching topic, the specifics that attribute it to the given teaching styles, their similarities and differences are summarized. The basic similarities and differences regarding the organization of teaching and the textbooks used are summarized. At the end of the thesis, the results and evaluation are briefly mentioned. KEYWORDS Mathematics teaching, Realistic mathematics education, Freudenthal, Hejny's method, Hejny
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Goniometric functions in physical applications
Hanzlík, František ; Kvasz, Ladislav (advisor) ; Mošna, František (referee)
This Bachelor thesis gradually presents the properties of goniometric functions as part of physical phenomena which really exist and which people make use of. The phenomena are introduced in four separate chapters named after the experiments which are their central theme. The first chapter describes the movement of the body along the inclined plane. There is shown how we can use such movement to find separate points which lie on the tangent function. However, since all four basic goniometric functions can be expressed by just one function, for example the cosine function, of which the graph is a sinusoid, all next chapters deal with the sinusoid. For the first time it is plotted in the second chapter where are demonstrated some rules of the movement of the harmonic oscillator over time. In this thesis, important sinusoid transformations are also indicated. There is shown that the graphs of sinus and cosine functions differ only in their displacement. Thereby are those functions interlinked to each other. In the third part, when describing the effects of centrifugal acceleration on bodied located on Earth, some other features of the cosine functions are given, making use of the fact that the size of the centrifugal acceleration depends on the cosine of the angle which indicates the latitude. In that...
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Games - teaching mathematics through the medium of a foreign language
Řehák, Jiří ; Novotná, Jarmila (advisor) ; Kvasz, Ladislav (referee)
This thesis is about a study looking into the viability to use Minecraft as a teaching tool in order to teach basic geometry. Using Minecraft Educational edition and based on principles from Self- Determination theory, two specifically tailored maps were created, one was a review towards area and perimeter, and the other one was directed towards volume, a new concept for them to discover. 15 fifth grade students, 9 boys and 6 girls, participated in this study, they were split between two separate groups that participated in this study. Children were given an assessment test to find out what everyone's level is at. Once completed they received tablets with a custom map and some worksheets to go along with it. Students progressed through the maps at an individual pace, with no time restriction they were free to explore in the direction they wished. When finished the children were tested again for comparison. Results have shown that students have the abilities to intuitively discover how to calculate volume after a quick area and perimeter review. Additionally, very positive responses have been expressed during the entire study with increased attentiveness and complete immersion. Potential uses of such discoveries could help alleviate the current work load that our current school system experiences.
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Symbolic notation in selected 16th century arithmetic books from Czech environment: an example of George Goerl
Fantová, Anna ; Zdichynec, Jan (advisor) ; Kvasz, Ladislav (referee)
A primary objective of this bachelor thesis is to characterize mathematical symbolism (the use of substitute signs of usually fixed meaning for a description of objects and processes) in arithmetic books from the 16th century written in the Czech language with a primary focus on the foundations of arithmetic. Firstly, I categorize the period notation based on its form and purpose by analysing the historical sources. Then, I compare the symbolism described in the individual arithmetic books and connect the discovered differences in time. The analysis focuses on an arithmetic book by George Goerl from approximately the second third of the monitored period. Futhermore, I elaborate on an earlier arithmetic book by Andreas Klatovský and a different one by Benes Optát. In general, I arrange the arithmetic books chronologically. Another aim of this paper is to evaluate the above-mentioned arithmetic books from a formal point of view. Therefore, I touch on the contents of each of them, ordering, and literary and pictorial paratexts. I am also interested in particular exercises and examples as sources of knowledge of the everydayness in the age of the authors. I evaluate the suitability of their way of notation and problem solving in some exercises in comparison with today's approach. Throughout the whole...
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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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