Mihail Podaev

The article analyzes some issues of the integration of mathematics and computer science (programming) within the framework of specialized session limited time. The relevance of the considered problem of mathematics and computer science integration in the context of the Olympiad training of schoolchildren in the context of specialized sessions is justified, first of all, by the fact that the subject content of the two courses under consideration often permeates each other, especially if we mean some overlapping sections – discrete mathematics, combinatorial analysis, algorithms theory, number theory, graph theory. In this connection, the success of mastering any of these subjects often correlates with good academic results in another area. The practice shows that there is often a parallel study of mathematics and computer science, simultaneous participation in Olympiads in both subjects. The traditional training system that has developed in some recognized centers for Olympiad training is not always aimed at a close and thoughtful integration of these subjects. The article proposes a formal generalized model of the competence training system within the educational program “Mathematics. Data Analysis ". The structure of the educational program «Mathematics. Data Analysis» includes three modules: «Olympiad Mathematics. Application", "Workshop on Solving Olympiad Tasks", "Special Courses in Programming and Olympiad Mathematics". The theoretical significance of the article lies in the proposed formal generalized model of the system of competence training within the educational program “Mathematics. Data analysis”, which can also be used in programs of a similar orientation, implementing interdisciplinary communications, primarily in mathematics and computer science, with an emphasis on the application of the acquired competences in the digital economy. The practical significance of the research is the presentation and analysis of the relationship between the subjects of classes and the modules of the program, examples of practical tasks that implement this relationship.

In the context of the post-non-classical general scientific paradigm, the modern world seems to be non-linear, dynamic and unpredictable. A graduate of the school should look for a fulcrum within his/her inner self and to introduce at least some certainty into the global uncertainty of the world. In this regard, a mathematics teacher should develop those skills of a student that make a significant contribution to the formation of conceptual thinking. The analysis made it possible to identify the pattern: the student's ability to produce geometric constructions and proof in a generalized way in a teaching / learning situation has a positive effect on his comprehension of geometric concepts. The process of developing in a student the ability to produce geometric constructions and proof in a generalized way is greatly facilitated by the use of the dynamic system GeoGebra resource, which may be identified with the electronic learning environment (ELE). The purpose of the research is the development of the theoretical foundations for the methodological support of the process of grasping geometric concepts by students of grades 8–9 secondary school in electronic learning environment. A didactic condition for the formation of geometric concepts was a specially organized learning activity with the use of the dynamic GeoGebra system and a special tasks system within the “Constructive Geometry on the Euclidean Plane” circle for 8–9th grade students. The results of statistical data analysis confirmed the hypothesis about the significant impact of the level of mathematical training (significance level 0.003), the level of ELE influence in combination with the tested method (significance level 0.001), duration of training with the use of the tested method (significance level 0.01). Methodological support of the process of grasping geometric concepts by means of the ELE resource has a more intensive positive effect on the dynamics of grasping concepts by schoolchildren than without this support. At the same time, the success of the experiment depends on the duration of training with the use of the tested method.