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Implementation of Challenging Tasks in Mathematics Education
Růžičková, Lucie ; Kopáčková, Alena (advisor) ; Harminc, Matúš (referee) ; Tichá, Marie (referee)
Title: Implementation of Challenging Tasks in Mathematics Education Author: PhDr. Lucie Růžičková Department: Department of Mathematics and Mathematics Education Supervisor: RNDr. Alena Kopáčková, Ph.D. ABSTRACT The thesis deals with practical implementation of challenging tasks in mathematics education. The methodology for examining "the fidelity of implementation of mathematical tasks" is being designed to describe whether the task is used according to the original intention of the teacher or according to the intention of its author. This methodology is employed in the analysis of four experiments to examine mathematical tasks and task environments. Then, based on the experience with the analysis, the methodology is adapted to the needs of both the teaching practice and educational research. The main result of the thesis is the creation of the methodology for examining the fidelity of implementation of mathematical tasks which is based on contrasting the descriptions of four general elements of the mathematical task at different phases of its implementation. KEY WORDS: mathematics education, mathematical task, challenging task, implementation of tasks
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Linear Algebra at Business Universities and High Schools
Ulrychová, Eva ; Málek, Josef (advisor) ; Tůma, Jiří (referee) ; Hájková, Vladimíra (referee)
The thesis consists of two equal parts - of a part dealing with didactic aspects of teaching linear algebra, and of an unconventionally approached textbook Fundamentals of Linear Algebra, which is appended as a separate attachment. The didactic part deals with teaching mathematics, especially linear algebra, at the University of Economics in Prague, namely from the historical and methodological point of view. The thesis also includes a detailed evaluation of students' knowledge tests. The conclusions are largely portable to other non- technically oriented universities. The textbook is designed with respect to two levels of difficulty; it is written in the form accessible for students with lighter assumptions for the study of mathematics. The textbook is designed especially for students of universities where mathematics is not the main focus; it may also serve to interested high schools students as an introduction to a more advanced study of linear algebra.
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Web application for teaching of volume and surface area of solilds in secondary schools
Rakušanová, Lucie ; Robová, Jarmila (advisor) ; Surynková, Petra (referee)
This thesis is focused on the volume and surface area of solids, particularly on the volume and surface area of polyhedra, which are part of the high school curriculum of geometry (stereometry). The purpose of website is to provide supporting and comple- mentary material for students as well as for their teachers. The website contains several photographs, illustrations and interactive components that make it easier to understand the topics. Interactive elements include applets created in a dynamic geometry appli- cation called GeoGebra, hyperlinks, and step-by-step exercise solving. Furthermore, the thesis is supplemented by solved problems and a final summary test. 1
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The Factors Influencing the Usage of Modem Technologies in Teaching Mathematics
Havelková, Veronika
The aim of this thesis is to explore the factors influencing the usage of modern technologies in teaching Mathematics. Modern technologies have been gradually earning their place in Czech schooling for a while now, but they are not always used in the way we might expect. To address such a question, upon consulting various literary sources, this thesis presents a model of factors which influence the usage of technologies in teaching Mathematics and aims to answer the following questions. What factors influence the intended usage of technologies in teaching Mathematics? How do these factors influence the intended usage of technologies in teaching Mathematics? What are the differences between the intended usage and the real usage and what factors influence them? How do these factors influence the real usage in teaching Mathematics? The individual factors have been further explored by a multiple-case study of three Czech Mathematics teachers during their teaching and subsequential interviews. It was the form of a multiple-case study which allowed for deeper observation of the mutual relationships between the individual factors in teachers with very different approaches to teaching and modern technologies. The differences between the considered cases then provided an insight into what could help...
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Methods for overcoming differences in pace of students in mathematics lessons
Plívová, Anežka ; Havlíčková, Radka (advisor) ; Macháčková, Jana (referee)
- 4 - ABSTRACT This diploma thesis is focused on teacher's strategies in mathematics lessons with different work paces of pupils, specifically pupils with above-average pace. The theoretical part of the thesis summarizes and explains the basic concepts related to the identification of smart and gifted pupils. The next part is focused on models of talent, teaching pupils with above- average pace, as well as a transmissive and a constructivist approach to teaching. The used research method was observation and discussion in focus groups. The basis of the practical part of the diploma thesis is a set of collected information and its arrangement into the so- called typology of teacher strategies when working with a pupil who works at an above- average pace in mathematics lessons with the described advantages or risks of individual strategies. The main goal of this diploma thesis was to collect ways in which the teacher copes with the different paces of students in mathematics lessons, mainly focusing on pupils with above-average work rates. Thesis describes benefits as well as risks that could arise in the application of strategies for the described individual methods. KEYWORDS above-average pace, mathematics teaching, gifted pupil, bright pupil, teacher's strategy
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The Factors Influencing the Usage of Modern Technologies in Teaching Mathematics
Havelková, Veronika ; Jančařík, Antonín (advisor) ; Robová, Jarmila (referee) ; Slavíčková, Mária (referee)
The aim of this thesis is to explore the factors influencing the usage of modern technologies in teaching Mathematics. Modern technologies have been gradually earning their place in Czech schooling for a while now, but they are not always used in the way we might expect. To address such a question, upon consulting various literary sources, this thesis presents a model of factors which influence the usage of technologies in teaching Mathematics and aims to answer the following questions. What factors influence the intended usage of technologies in teaching Mathematics? How do these factors influence the intended usage of technologies in teaching Mathematics? What are the differences between the intended usage and the real usage and what factors influence them? How do these factors influence the real usage in teaching Mathematics? The individual factors have been further explored by a multiple-case study of three Czech Mathematics teachers during their teaching and subsequential interviews. It was the form of a multiple-case study which allowed for deeper observation of the mutual relationships between the individual factors in teachers with very different approaches to teaching and modern technologies. The differences between the considered cases then provided an insight into what could help...
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System for Online Teaching of Mathematics
Dohnal, Lukáš ; Bartík, Vladimír (referee) ; Burget, Radek (advisor)
The aim of this bachelor thesis is to design and implement a web application for online teaching of mathematics. The system is primarily intended for students and teachers at secondary schools. The application is implemented in PHP and Javascript languages. The Symfony framework is chosen on the backend and the React framework was used for the frontend implementation.
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Introduction to variables in the teaching of teachers using the method of building schemes in mathematics
Smutná, Anežka ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis deals with an introduction to variables. The aim of the thesis was to compare different approaches to teaching the introduction to variables in teachers who teach a method based on building schemes (known as Hejny method). The theoretical part of the thesis is a search of literature on the topic of introduction to variables and the theoretical background of teaching methods based on building schemes. Further, the thesis analyses textbooks designed for this method with a focus on tasks important for the propaedeutics of the variables. The research itself consisted of interviews with four teachers and observations of the lessons they taught in the 7th and 8th grades of secondary school, the topic of which was an introduction to the "language of letters". In total, there were fifteen lessons taught by these teachers in six classes (2-3 lessons in each class). Data were analyzed by qualitative methods. Although the observed teachers taught using the same method, I identified differences in the approach to the introduction of the variables and in the style of their teaching. There were differences in the organization of the lesson, in the selection of tasks and their style of assignments to pupils, teaching methods and ways in which teachers communicate with pupils. At the moment of entering the...
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Various concepts of teaching of axial symmetry in elementary schools
Bečanová, Veronika ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
The aim of the thesis is to describe and compare two aproaches to the education of axial symmetry in elementary schools. On the basis of the study of specialized literature, the thesis describes different ways of the axial symmetry education and also compares the contributions on the side of pupils as well as the demands on teacher's class preparation. The main goal of the practical part of the thesis was to prepare, realize and evaluate axial symmetry education itself in two classes and to compare it with a different didactic aproach in other two classes of the sixth year. The thesis deals with axial symmerty education containing some of the elements of the constructivist style in classes where pupils have no experience with the method. The teaching itself consisted of the author's own activities and modifications of the worksheets that were subsequently used by pupils, followed by evaluation of their meningfulness. The lessons were evaluated on the basis of audio records, own notices, pupils' solution records and interviews with the assistant of the teacher, the outputs by means of pre- testing and post-testing. The results indicate that the lessons with the elements of constructivist teaching could be more effective for pupils rather than the transmissive teaching. The pupils considered the...
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Didactical situations for teaching mathematics in French
Sovič, Pavel ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
The diploma thesis focuses on learning Maths through French language using the CLIL method at a secondary vocational school. The acronym CLIL (Content and Language Integrated Learning), EMILE (Enseignement de Matières par Intégration d'une Langue Etrangère) or e.g. AICL (Apprentissage Intégré d'un Contenu et d'une Langue) refers to integrated learning of a content-based subject through an additional language. There are always two aims of such tuition. The first aim is the content goal (e.g. to gain particular specialized knowledge or skill in mathematics); the second aim is the language goal (e.g. to learn essential vocabulary and sentence structures in order to lead a discussion concerning the solution of a quadratic equation in the French language). Based on a literary research, analysis of educational CLIL materials, and especially in connection with theoretical grounds of the method (constructivism, problem-solving, critical thinking, active and communicative approach) there was established a study plan focusing on the topic of quadratic equations. The experimental tuition was put into practice with the 1st year students of a secondary school, where the French language is taught as the second foreign language. The main objective, apart from the tuition itself and its analysis, was to assess the...
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