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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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Ways for self development of teaching strategy
Pešinová, Karolína ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
Ways for self development of teaching strategy Abstract: The aim of this thesis is to analyse the diagnostic tools designed by M. Hejny and his team. These tools focus on teaching styles in education, observing the personal development of a mathematics intern teacher. The study materials i have obtained during my practice are used to describe and analyse the teacher's educational style, with the use of twenty defining parameters. My thesis is based on Gabriela Hlavata's master thesis, a teacher who describes her own shift from transmissible to constructive teaching in mathematics classes. Hlavata depicts this shift clearly, hence the reason I have decided to describe it with a set of parameters measuring the intern teacher's educational style. The subsequent aim is to trace my own evolution in teaching mathematics. Practice and materials gained in my graduation, together with the twenty educational parameters as outlined in my thesis, will serve to analyse and describe my own educational style. In choosing this topic, I am trying to answer the following question; whether the observation of a teacher's educational style will impact on the delivery and quality of mathematics lessons? Furthermore, is improvement possible, or have I reached the capacity of my own teaching ability? Additionally this thesis...
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Critical places in primary school mathematics taught by Hejný's method
Landíková, Kristýna ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
The thesis on "Critical places at the first stage of primary school in the teaching of mathematics by the Hejný method" focuses on the problematic places of the Hejný method, which make it difficult for teachers and especially their pupils at the first stage of primary schools. In the theoretical part of the thesis, the constructivist and transient educational style teaching of mathematics using the Hejný method are characterized. The critical points in mathematics identified in the project of the Grant Agency of the Czech Republic are also introduced and conceived into a unified structure. The theoretical part also includes an analysis of pupil solutions to mathematical tasks from the 2015 TIMSS international survey. The empirical part deals with the experience and view of primary school teachers in teaching mathematics by the Hejný method. The first research survey finds from future primary school teachers their experience and opinions on this method. The second research survey focuses on the identification of problematic places and roles in the teaching of mathematics by the Hejný method from the point of view of teachers who teach mathematics using the Hejný method at the first stage of primary schools. The questionnaire survey was carried out using the questionnaire method, which identifies...
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Word problems with different results at primary school
Švihnosová, Kristýna ; Havlíčková, Radka (advisor) ; Kvaszová, Milena (referee)
The diploma thesis is focused on the issue of word problems with different results, to which is not given systematic attention in the specialized literature. The focus of the work is to observe how pupils and teachers of elementary school work with a word problem with different results. The theoretical part focuses on the typology of word problems, the phases of their solution and solving strategies. Furthermore, the classification of word problems according to the number of results and the typology of word problems with different results is proposed. A significant part consists of the goals with which this type of task can be assigned in the teaching of mathematics and which change depending on the teacher and his approach to teaching. The work also deals with the basic characteristics of teaching styles. The selected qualitative research using the method of observation and questionnaire allows to describe the work of teachers with a word problem with different results and to identify elements of teaching styles, namely transmissive and constructivist approaches, which are reflected in the actions of teachers. An additional method is the analysis of selected textbooks in terms of the presence of word problems with different results, which reveals whether such tasks occur in textbooks and what...
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Approaches to teaching primary school mathematics
Ždímalová, Eva ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
Approaches to teaching primary school mathematics Abstract: The main goal of this thesis is to clarify the differences between two distinct approaches to teaching mathematics at primary school, the transmissive approach and so called genetic constructivism. The theoretical part of the thesis describes main features of these two approaches to teaching mathematics. The practical part shows approaches of two concrete teachers of the first grade, which are investigated by observation, analysis of videorecordings from mathematics lessons and interviews with the teachers. The videorecordings analysis shows didactic aspects of each teacher's approach to teaching. Dealing with pupil's error has been chosen as leading didactic aspect and is analysed in more detail. Furthermore, the author's development of her own approach to teaching mathematics is analysed. Key words: approach to teaching, method, technique, constructivist approach, transmissive approach, dealing with errors, individualisation, teacher's professional development
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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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Ways for self development of teaching strategy
Pešinová, Karolína ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
Ways for self development of teaching strategy Abstract: The aim of this thesis is to analyse the diagnostic tools designed by M. Hejny and his team. These tools focus on teaching styles in education, observing the personal development of a mathematics intern teacher. The study materials i have obtained during my practice are used to describe and analyse the teacher's educational style, with the use of twenty defining parameters. My thesis is based on Gabriela Hlavata's master thesis, a teacher who describes her own shift from transmissible to constructive teaching in mathematics classes. Hlavata depicts this shift clearly, hence the reason I have decided to describe it with a set of parameters measuring the intern teacher's educational style. The subsequent aim is to trace my own evolution in teaching mathematics. Practice and materials gained in my graduation, together with the twenty educational parameters as outlined in my thesis, will serve to analyse and describe my own educational style. In choosing this topic, I am trying to answer the following question; whether the observation of a teacher's educational style will impact on the delivery and quality of mathematics lessons? Furthermore, is improvement possible, or have I reached the capacity of my own teaching ability? Additionally this thesis...
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Collection of problems in algebra and geometry
SIGMUNDOVÁ, Alexandra
The aim of the bachelor thesis is to create a collection of solved exercises on topic: "Problematic algebraic and goniometric exercises". This collection is designed for pupils from 5th to 9th class of basic school and should help them to develop their logical thinking using tables, graphs or images. The exercises are divided into three chapters, which are alphabetically sorted into sections.
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