ON THE CONDITIONAL STABILITY ESTIMATION OF FINITE-DIFFERENCE ANALOGUES OF INTEGRAL GEOMETRY PROBLEM
Keywords:
Arithmetic progression, geometric progression, graph theory, Olympiad problems, scientific search, mathematical induction method, Dirichlet principle, way of thinkingAbstract
Olympiad tasks play a special role in the development of cognitive activity and mathematical abilities of schoolchildren. This article discusses level problems of arithmetic and geometric progressions, complex problems of arithmetic-geometric progression and ways to solve some Olympiad problems.
The study shows the problem of increasing students' abilities to solve Olympiad problems on the topic of progression and the main directions of preparation for the Olympiads. Each topic discussed in detail how to solve several problems using certain methods, including the Dirichlet principle, the invariant method, graph theory, mathematical induction, the method of coordinates, etc.
A pedagogical experiment was conducted, which involved 64 students in the control group, 70 students in the experimental group. As a result of the experiment, based on the methodology of in-depth teaching of schoolchildren to solve problems on the topic of progression, the features of planning work on their implementation, their organization, in-depth training, organization of classes were analyzed, sources of improving the efficiency and quality of work with students were identified. A control work was carried out in order to identify the formation of students' interest in mathematical Olympiad problems.
This work can be useful both for students of schools and gymnasiums who want to prepare for school, city and district Olympiads on their own, and for a math teacher as an additional material.
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