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Development of understanding the area of rectangle and triangle
Hájková, Adéla ; Vondrová, Naďa (advisor) ; Zamboj, Michal (referee)
This thesis focuses on developing an understanding of the concept of the area of a rectangle and a triangle in the form of a pedagogical experiment for sixth-grade primary school pupils. Before the experiment, a diagnostic test was conducted to reveal the mechanical knowledge of the students. The tasks in the test were based on the same typology of exercises that can be found in regular student's books and exercise books used for Mathematics teaching and one of the exercises worked with the notion of a square grid. The exercises used within the actual teaching were transformed in order to match the current situation in the classroom. The experiment was subdivided into two parts that followed each other - understanding the notion of a rectangle and understanding the notion of a triangle. The pedagogical experiment was conceived according to the conceptual process of measure in geometry and a hypothetical learning trajectory. The experiment aimed to reeducate the pupils' possible mechanical knowledge, to lead the pupils to a conceptual understanding of the area of rectangles and triangles. At the end of the experiment, a test was again administered to check whether understanding had occurred and whether mechanical knowledge had been removed. The final test shared the same typology of exercises as the...
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Mechanical knowledge in mathematical cognition of an A student
Friesingerová, Tereza ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
Mechanical knowledge is presently considered to be the major problem in di- dactics of mathematics. The aim of this diploma thesis is first, to diagnose possible instances of mechanical knowledge in cognition of an A student, i.e. a student with excellent results in mathematics, and second, to provide a dis- cussion of their probable causes. The thesis consists of two parts. In the first part, i.e. the theoretical one, the concepts which are essential for the empirical part are introduced. The pivotal sections of the theoretical part of this thesis are therefore devoted to the introduction to the theory of generic models and mechanical knowledge. In case of mechanical knowledge, the emphasis is put on a discussion of its possible causes, as well as ways of their diagnostics, reeducation and prevention. The empirical part of the thesis is dedicated to a case study which was conducted. In this study, a number of examples of mechanical knowledge in va- rious branches of mathematics were identified in cognition of a lower-secondary student, based on the analysis of in-depth interviews and teaching materials. It is concluded that the most probable cause of the identified instances of me- chanical knowledge is the transmissive education style, in which the priority is placed on remembering definitions...
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