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Cosine and sine theorem at the secondary school
Zenkl, David ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis is concerned with a constructivist approach to the introduction of the cosine and sine theorems at the secondary school. The aim was to develop recommendations for teaching which are based on the idea of motivating teaching cosine and sine theorems. This approach is based on available literature and builds on experience from my own teaching of this topic. By motivating teaching, I mean an approach that is consistent with the principles of constructivism and emphasizes pupils' active learning. Current textbooks for secondary schools were analyzed from a mathematical and didactic point of view. The aim of this analysis is to describe how the topic is elaborated in publications available to teachers, and to get inspiration for my own approach. My own teaching approach was based on the theory of generic models and has been implemented in two classes of the secondary grammar school. Data collected during teaching cosine and sine theorems (video recordings of lessons, field notes from teaching and pupil artifacts) were analyzed in a qualitative way. The thesis describes the teaching in detail, with an emphasis on key phases of the discovery of the two theorems. Pupils' involvement in this process is closely followed. Where teaching did not work as planned, possible reasons are found and...
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Constructivist teaching of percentage in two classes with a different background in teaching mathematics
Pechmanová, Kateřina ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The content of the thesis consists of a description of constructivist teaching of the topic of percentage in the primary school, that is the teaching in which not the teacher, but the pupil is in the center. The principles of constructivist teaching and the learning process in terms of the theory of generic models are described on the basis of literature. In accordance with these principles, a number of textbooks have been analyzed, in which the the topic of percentage is introduced, and experimental teaching based on the above principles has been prepared. Experimental teaching was realized in two classes of the 7th grade with a different experience with the teaching of mathematics in their 6th grade. The main goal of the work was to prepare, implement, describe and evaluate the teaching of percentage based on pupils' activity and their individual discovery. The lessons have been described and evaluated on the basis of audio recordings, notes from the lessons, records of pupilss solutions, interviews, notes and interviews with a teacher assistant, pre-tests and post-tests. The lessons were analyzed mainly in terms of pupils' involvement in teaching, their discoveries and knowledge acquisition, including its anchoring in the knowledge structure. In both classes, part of the pupils managed to find a...
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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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Cosine and sine theorem at the secondary school
Zenkl, David ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis is concerned with a constructivist approach to the introduction of the cosine and sine theorems at the secondary school. The aim was to develop recommendations for teaching which are based on the idea of motivating teaching cosine and sine theorems. This approach is based on available literature and builds on experience from my own teaching of this topic. By motivating teaching, I mean an approach that is consistent with the principles of constructivism and emphasizes pupils' active learning. Current textbooks for secondary schools were analyzed from a mathematical and didactic point of view. The aim of this analysis is to describe how the topic is elaborated in publications available to teachers, and to get inspiration for my own approach. My own teaching approach was based on the theory of generic models and has been implemented in two classes of the secondary grammar school. Data collected during teaching cosine and sine theorems (video recordings of lessons, field notes from teaching and pupil artifacts) were analyzed in a qualitative way. The thesis describes the teaching in detail, with an emphasis on key phases of the discovery of the two theorems. Pupils' involvement in this process is closely followed. Where teaching did not work as planned, possible reasons are found and...
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