Possibilities of Preparing Pupils for Proof Problems of Synthetic Plane Geometry Solvable by Deductive Methods

Vojtěch Zlámal

doi:10.24297/jam.v20i.9137

Abstract

Proof problems, especially the ones of the synthetic plane geometry solvable by deductive methods, play a significant role in mathematical education and due to their demanding principle also in the above-standard education including mathematical competitions. Therefore, the issue of preparing pupils for solving the proof problems is very important. This study aimed to find out if the contemporary state of the system of pupils’ preparation for synthetic plane geometry proof problems is sufficient enough for the mentioned purpose. From the full set of schools of the Czech Republic, there were 14 schools identified as the successful ones based on the results of the national round of the Mathematical Olympiad. These schools were asked questions about literature used for pupils’ preparation and the publications named in the answers were then deeply inspected. The results showed a narrow range of the literature used by the schools and the didactic-methodical inspection of stated literature detected considerable space for improvements which led the author to the main theme of his dissertation.

Highlights

The area of synthetic plane geometry is included in the curricular documents of the educational system of the Czech Republic1 as an integral part of education, the focus of this article will be the area of above-standard teaching and preparation of secondary school pupils for mathematical competitions
In terms of the type of the school, only grammar schools were present within successful schools, while in the list of all schools, grammar schools represented 96.55% secondary vocational schools 2.59% and primary schools 0.86%
For the publication “School of Young Mathematicians” (1961-1988) and for the commented solutions of individual problems of the Mathematical Olympiad (Mathematical Olympiad, 2020) which are used in the abovehttps://rajpub.com/index.php/jam standard preparation of pupils by the schools, it was not possible, due to their nature, to create similar tables of statistical data

Summary

Introduction

The area of synthetic plane geometry is included in the curricular documents of the educational system of the Czech Republic as an integral part of education, the focus of this article will be the area of above-standard teaching and preparation of secondary school pupils for mathematical competitions. In the field of synthetic plane geometry, secondary school pupils encounter three types of mathematical problems. These are construction, determination and proof problems (Vyšín, 1972). The theme of the research is the role of the proof problems; the text is dealing only with them. It is characteristic of these proof problems that pupils can solve them by computational or deductive methods. It is not possible to say that the problems are always solvable in both ways, so the following text will only deal with the proof problems solvable by deductive methods

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Conclusion