НАУЧНО-МЕТОДИЧЕСКИЕ ВОПРОСЫ ПОДГОТОВКИ СТУДЕНТОВ К ОЛИМПИАДАМ ПО НАЧЕРТАТЕЛЬНОЙ ГЕОМЕТРИИ

Abstract

Academic Olympics on descriptive geometry are an important form of educational process in conditions when the discipline study’s teaching hours are reduced. The Academic Olympics allow identify talented students and motivate them to find possibilities on solutions for non-standard situations, to promote the formation of such qualities as persistence, endurance, accuracy. The Academic Olympics carrying requires not only organizational measures. Due to a low level of the geometrical knowledge gained at school, students need an additional theoretical training. Without it realizing of young people’s creative potential is impossible. The experience on carrying of the Academic Olympics on descriptive geometry at Bauman Moscow State Technical University and in other higher education institutions of this country allowed develop a technique of students training for such activities. In this paper scientific and methodical questions related to solution for tasks of increased complexity are considered. Simplification of solution algorithm and increase of its visualization can be reached by reduction of metric conditions to affine ones, and them, in turn — to projective ones. The attention in training for the Academic Olympics should be paid to the method of loci. School leavers know only about limited quantity of loci on a plane and have practically no ideas on the elementary loci in space. Therefore studying of loci on a plane and in space is necessary. For the method of loci the essence of simplification, decomposition and increments rules is revealed. If a return problem is solved more simply than a straight one, it is reasonable to use reverse ability method. Often the problem solution becomes simpler when using transformations, in particular, homothety and stretching (compression) transformations. The considered methods are illustrated by specific examples. Assimilation of the methods described in this publication isn't a complete guarantee of students’ success at the Academic Olympics, but, undoubtedly, it will be useful for them as will allow expand knowledge of the subject matter.