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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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Constructivist teaching of the area of a triangle and parallelogram in two classes with a different background in teaching mathematics
Sovič, Pavel ; Vondrová, Naďa (advisor) ; Tůmová, Veronika (referee)
The thesis deals with constructivist approaches to teaching mathematics in lower secondary school, which means that a pupil is the centre of learning process. Based on study of literature, textbook analysis, and, in particular, in accordance with the theory of generic models as a theory describing way to build pupils' knowledge, a teaching experiment was prepared, focusing on the area of triangle and parallelogram. Experimental lessons were realized in two 7 grade classes with different experience with being taught mathematics at the elementary school. One class was taught by a highly instructive series of textbooks, while the second by textbooks which respected the principles of constructivism aimed at pupils and allowed individualization of learning process. The main objective of the thesis is to describe the experimental education in both classes and evaluate it from two perspectives. First of all, qualitatively, by analysing video recordings of lessons, pupils' solutions, notes from lessons, print screens from interactive whiteboard, but also by examining attendance sheets from teachers observing some lessons. In the second case, quantitatively, based on pre- and post- tests. The qualitative analysis is mainly focused on key discoveries and didactical situations in teaching and on an assessment...
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