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Understanding of the notion of a coordinate system by secondary school students
Klápa, Petr ; Janda, David (advisor) ; Zamboj, Michal (referee)
The aim of a thesis High school students' understanding of the coordinate system concept is to research the level of student's understanding of the topic by using analysis and a description of student's problems with given topic. A written non-standard test with exercises from non- Cartesian coordinate system is used as a tool to analyse the level of students' understanding. The first part of the thesis describes the historical development of the topic with emphasize on the renaissance era, in which were the basics of the modern concept of coordinate system set. The first part also includes the description of educational requirements from course books, curricular documents and the theory of concept image and concept definition, which focuses on understanding of mathematical terms. Second part of the study concentrates on the experiment with a non-standard test given to students at mathematical lessons at high school. The results are presented and analysed by previously specified phenomena and interpreted in the concept image and concept definition theory. Results of the practical part show a great variety of students' level of understanding the examined concept in theoretical and also in practical level. Results of students with good theoretical knowledge but low success in practical part are...
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Simple categorization of mathematical objects: Examining students' decisions
Janda, David ; Vondrová, Naďa (advisor) ; Simpson, Adrian (referee) ; Klusák, Miroslav (referee)
The aim of the thesis is to describe the decision making process of students in the so-called simple categorization, i.e., decision whether a particular object is or is not an element of a category. This process is examined in the context of categories of mathematical objects. The theoretical part of the thesis presents arguments why the study of simple categorization of mathematical objects is important for mathematics education. These arguments are not only based on the available literature in mathematics education, but also partly draw on historical, mathematical and psychological literature. The practical chapters of the thesis describe the design and piloting of a research tool suitable for this research. The dominant elements of this tool are the measurement of the binary answers (yes / no) of the respondent and of his/her reaction time. This tool is then used in the Main study based on mixed, qualitative-quantitative methodology. It was found that with the help of the proposed tool, while adhering to appropriate methodological rules, it is possible to distinguish different approaches of respondents to categorization. In addition, the basic patterns in the decision-making process of the respondents were described. These are, for instance, differences in the categorization of examples and non-...
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