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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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