Abstract-algebraic modelling of the pedagogical system in the situation of the interdisciplinary approach

In the article one of the possible variants of modelling on the abstract-algebraic level of an open, nonlinear, complex, unstable pedagogical system is presented. A well-known graphical model of the control system is used as a basic invariant. During the simulation, the role of the subject of management is provided not only for the teacher, but also for students, including student groups. For the transition to the abstract-algebraic level, the method of analogy with theoretical mechanics, where external and internal forces are considered as the causes of motion, is applied. The dynamics of academic achievements of the individual student and academic group is analogous to the movement in mechanics. In particular, the dynamics in the experience of self-government activity, in the experience of interaction with others, in the experience of a certain type of transformation activity are considered. The reflection of this dynamics on the abstract-algebraic level is carried out using the available language of the linguistic level of the description of the control system in cybernetics. In particular, the following formulations are used: 1) feedback principle; 2) the law of requisite variety; 3) principle of emergence; 4) principle of complementarity (according to St. Beer, N. Bohr, W. R. Ashby, M. M. Moiseyev, N. Wiener). These principles characterize the forces that operate in the pedagogical system and determine its dynamics.

A set of variables is proposed for the implementation of the corresponding abstract-algebraic modelling in the pedagogical system, their symbols and formulas reflecting the relationships between them.

The simulation on the abstract algebraic level of the description of the pedagogical system as a control system does not deny the realization of the humanistic approach at other stages of the study of pedagogical systems and the corresponding organization of the educational process in practice, on the other hand, creates the premises for combining the theoretical and empirical results of a particular study, more precise measurement and forecasting.

The procedure for determining the set of relationships and principles of interaction between the system and the environment remains outside of the review in this article and it requires further consideration.