UDC 519.76
doi: 10.26102/2310-6018/2019.24.1.006

A.V. Ganicheva, A.V. Ganichev

The relevance of this work is caused by importance of account in educational process of personal qualities of trainees. Importance of the solution of this problem is defined by the fact that competence-based approach assumes formation of future workers capable independently to work in various situations, to have an impact on others. When training in non-uniform educational collectives (groups) it is possible to allocate subgroups of pupils by different criteria: to abilities, progress, discipline, etc. Subgroups of trainees have an impact at each other. Force of this influence depends on the number of subgroups, of coefficients of influence and time of impact. As a result of mutual influence, it is possible of the trainee to move from one group to another. The article uses the method of mathematical modeling to analyze and account for the dynamic interaction of pupils in the team. The model is based on the system of differential equations of J. Forrester. The analytical solution of a system for a standard case in educational process – existence of three types of subgroups of trainees is received. A numerical example is given to illustrate the results. Results of its decision are presented graphically. Important special cases of the General system of differential equations (setting of relations between the coefficients of influence) are considered. The developed mathematical model will improve the quality of the educational process.

Keywords: : group of trainees, model, coefficients of influence, system of differential equations, solution.

Full text: