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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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Word problems with a sports themes
ČEJKOVÁ, Šárka
Word problems are parts of everyday life and in teaching maths have an irreplaceable place. The aim of the bachelor's thesis is to create an colection of word problems with a sports themes and approximate the applicability of mathematics curriculum in everyday life. Each exercise will be supllying the sample solution. Colection od word problems will be included into different sports games. In most samples are exercises, which work with programs MS Excel and GeoGeobra.
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The effect of DGE on the attainability of mathematical reasoning for geometry problems among mathematics teacher education students.
BLAŽEK, Jiří
Dynamic Geometry Environment (DGE) programs appeared in the early 1980s, but they did not begin to be used in education until the beginning of the new millennium. Today, they are widely used in teaching of mathematics. DGE class programs allow to mediate the abstract world of Euclidean geometry to students due to their features such as precision of construction, illustrativeness and the possibility to change the construction dynamically. It is generally accepted that appropriate implementation of DGE software in teaching improves its quality. A related question is what is the benefit of this software if a student uses it in the process of finding a solution to a solution to a mathematical problem. This question represents the general research problem of this thesis. The objects of the research were prospective teachers of mathematics at the Faculty of Education. The following findings were found in the research: 1) The software significantly facilitates the discovery of relevant hypotheses, even those for which their relationship to the solution of a problem is not evident from the assignment of the problem. 2) The software significantly helps in the development of logical justification. (Yet, a significant number of students in the research were unable to complete the proof even with the maximum help the software could provide.) 3) Finding relevant hypotheses using the software tools depends in most cases on students' ability to apply formal mathematical knowledge and to think logically. Facts that can be discovered with software tools by chance, without specific student intent, are likely strongly limited. Research has also dealt with the question of why some students are unable to complete a proof even with the help of software. The thesis contains seven chapters and an appendix. In the first three chapters, the research topic of the thesis is generally described. In chapter four, the research questions are formulated. In the following chapter, a model is presented to categorize the actions of the problem solver in the DGE with respect to the goal he/she pursues. Chapter six presents the research methodology, the data obtained and their interpretation. The results are summarized in the final chapter. The appendix contains two challenging geometric problems author has worked on during his studies and in whose solutions the DGE software played a crucial role.
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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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Exercises and problems in linear algebra
ČAPKOVÁ, Klára
The aim of this thesis is to create a collection of solved examples and problems of linear algebra, which could serve as a learning tool for the first-year students of the Faculty of Education of University of South Bohemia in České Budějovice. The most important part of this thesis is the electronic processing of the collection in a program GeoGebra and its visual interpretation of examples and problems by 3D pictures, QR codes and hyperlinks that specify the solutions.
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The use of GeoGebra by solving problems in geometry
BUZEK, Štěpán
This diploma thesis is focused on new funkcionalities of dynamic geometry systems and computer algebra systems. In first part of the diploma thesis I research new functions of dynamic geometry systems. Second part is focused on examples which are possible to solve by usage of said methods. Especially it is focused on automatic discovery of locus. Main focus is on finding of equations of locuses. In last example is compared principle of automatic discovery with automatic proving.
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Why should we like math
BENÍŠKOVÁ, Zuzana
This work deals with math as a subject and its popularity among students. The work includes the results of international surveys in the field of math, creative teaching methods and the design of mathematical games and projects that will make it easier for students to understand and master selected terms. The diploma thesis thus presents math in a playful form and can serve not only students of the second grade of primary schools and lower grammar schools, but also teachers of math.
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Solving stereometric problems in GeoGebra
HORÁČKOVÁ, Lenka
The aim of the bachelor's thesis on the subject of 'Solving stereometric problems in GeoGebra' was to create a collection of own solved examples from stereometry from the curriculum in the range from primary school, through secondary school to university training of mathematics teachers. The GeoGebra program is a support tool for this bachelor's thesis. The work focuses mainly on the curriculum of primary and secondary schools, partly also on the curriculum at universities. The work focuses mainly on square figures in the scope of the curriculum at primary and secondary schools and partly also at universities.
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Interactive textbook of descriptive geometry
Krsová, Michaela ; Dvořák, Petr (advisor) ; Zhouf, Jaroslav (referee)
An aim of this diploma thesis is to create interactive descriptive geometry coursebook. As a basis for coursebook creation was used "Present State of Descriptive Geometry Education on High Schools Survey" which was proceeded via questionnaire. Before the creation of coursebook itself were made analyses of accessible textbooks, geometric softwares in use and possible environments for coursebook content presentation. A result is integrated part of subject matter taught on high schools complemented by solved examples and interactive applets created in software GeoGebra. The coursebook content is presented in a form of HTML sites on a public website http://www.sadsam.cz/dg/ and also as an off- line version on DVD disc enclosed.
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