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Problems of solving systems of polynomial equations in mathematics teaching
KÖNIGSMARKOVÁ, Soňa
The aim of this thesis is to map the current state of teaching and student problem solving strategies for polynomial equations. A substantial part of the work is devoted to the use of these systems of equations in solving problems of the loci of a given property at different types of schools. On this basis, where warranted, suggestions are made for enriching teaching in this area with methods reflecting current trends in the use of systems of computer algebra. Considering the above objectives, the author focuses on the current state of teaching systems of polynomial equations in terms of the methods of solution used at primary schools, secondary schools and faculties preparing teachers of mathematics. The author does not neglect the solution of more complex problems, especially problems of the loci of a given property, by future mathematics teachers. The potential of computer algebra systems for improving the current state is also mentioned. The thesis is divided into 9 chapters, with the first four chapters justifying the topicality of the topic. The historical development of the solution of problems on systems of equations and especially the current state of the subject from the point of view of the position of the curriculum and the occurrence of relevant problems in textbooks, entrance and final exams and in the Mathematical Olympiad are presented. Considering the topic of the thesis, examples of solving problems by elementary methods and methods based on the theory of Gröbner bases and the use of computer technology are given. The fifth chapter defines the objectives of the thesis. The next three chapters are devoted to the actual research at secondary and higher education institutions, which deals with the solution of systems of polynomial equations and the solution of problems of loci of a given property in terms of the choice of solution methods and the occurrence of errors in their use.The final chapter summarizes the research results and gives some recommendations for secondary school teaching and for the preparation of future mathematics teachers. Appendices contain an original and research-based draft of teaching material on methods of solving systems of polynomial equations and solving problems on sets of points given characteristics for gifted secondary school students and university teaching students.
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Math textbooks for elementary schools and their readiness for distance learning
BRŮŽKOVÁ, Nikola
The number of changes that accompany the current Czech school system is a response for global social and pandemic changes and it is focused on methods of pupils´ education. New educational trends are linked to a requirement to acquire key competences as a basis for lifelong learning with a change of educational content, which are means of a versatile development of a child´s personality, not just a goal. In this context, we also talk about distance learning regarding the transformation of educational content which is addressed in the thesis. The thesis deals with issues and critical points of distance as well as face-to-face learning of geometry. Interactive materials were created, that could help the students to overcome these critical points. At the end of the thesis, a reflection obtained from teachers and students, who worked with the mentioned materials, is attached.
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Problems of pupils of high school in solving geometric construction exercises
Dyntarová, Miroslava ; Zamboj, Michal (advisor) ; Vondrová, Naďa (referee)
Title: Problems of pupils of high school in solving geometric construction exercises Author: Miroslava Dyntarová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Michal Zamboj, Ph.D., Department of Mathematics and Mathema- tical Education Abstract: The aim of this thesis is to reveal various errors and issues that high school students face in triangle construction problems. The thesis is divided into two parts for clarity. In the theoretical part we deal with construction problems in general and look into their various solution methods and formal procedures recommended by high school textbooks. Next, we focus on sets of points of a given property (that are part of the high school curriculum), give related denitions, basic properties and use cases. For better understanding of the demonstrated problems the thesis is lled with au- xiliary graphs made in the program GeoGebra. In the last chapter of the theoretical part, we introduce various problems that are expected to occur during geometry con- struction problem solving by students themselves. Those were the main focus of the following study. The preparation of the study, its implementation and subsequent ana- lysis of collected data is described in the practical part of the thesis. The study was conducted with 10 students....
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Množiny bodů dané vlastnosti na ZŠ
HARAZIMOVÁ, Tereza
The main aim of this thesis is to create a comprehensive overview of mathematical tasks dealing with a set of points with given properties. The examples are designed and divided into seven subchapters according to their specialization. This paper should be primarily an inspiration for primary school teachers; They find here instructions on how to use computer programmes to make teaching of mathematics more playful and interesting for children.
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