PRINCIPLE OF CONTINUITY IN LEARNING MATHEMATICAL ANALYSIS USING SPECIALLY SELECTED PROBLEMS

Abstract

Formulation of the problem. The rational application of the principle of continuity in teaching and a teacher's teaching methodology sufficient for this is one of the conditions for the successful mastering of mathematical disciplines by freshmen. From the point of view of the thesaurus approach to teaching, continuity is an injective correspondence between the student's vocabulary and the educational thesaurus of the discipline. The purpose of this article is to describe the methodology for using the system of tasks within the framework of the thesaurus approach based on the principle of continuity in teaching mathematical analysis at a pedagogical university.

Materials and methods. The research materials are pedagogical and methodological literature, the experiences of foreign and domestic teachers. In the course of the study, the following methods were used: observation and analysis to systematize the accumulated information about the expediency of using the thesaurus approach in ensuring continuity in teaching mathematical analysis, synthesis of the student's vocabulary and the educational thesaurus, modeling the system of tasks to establish an injective mapping between the student's vocabulary and the educational thesaurus, generalizing one's own teaching experience.

Results. Methods and means are identified that ensure continuity in teaching mathematical analysis based on the thesaurus approach. On the example of the topic "Sets of real numbers", systems of specially selected problems are constructed.

Conclusions. In the course of the study, it is shown that the solution by the student of specially selected problems contributes to the student's understanding of the basic concepts of mathematical analysis and the expansion of its lexicon, the development of a professional mathematical thesaurus. The proposed system of tasks does not claim to be complete, it has properties, flexibility, additions, modifications, depending on the educational tasks and a specific academic group. Prospects for further research are seen in the study of the issue of the effective use of the thesaurus approach in the process of teaching mathematical disciplines.