Innovative approach of mathematical modeling of learning processes as an optimal control object

INNOVATIVE APPROACH OF MATHEMATICAL MODELING OF LEARNING PROCESSES AS AN OPTIMAL CONTROL OBJECT


Bobokholova Gulchehra Siroj qizi
Student of Navoi State Pedagogical Institute


Jurakulov Tolib Tokhirovich
Teacher of Navoi State Pedagogical Institute. Research advisor


Annotation: The learning process is perceived in the form of an optimal management object and an innovative approach to the optimal management of the process. The functional structure of the tutorial system "teacher-reader" is given, and on this basis the cyclical structure of calculation experience is created. The results obtained are graphically displayed.
Аннотация: Процесс обучения рассматривается как объект оптимального управления, для управления процесса предлагается последовательность действий инновационного подхода. Дана функциональная структура дидактической системы “Учитель-ученик” и на этой основе создана циклическая структура вычислительного эксперимента. Полученные результаты иллюстрируются в виде графиков.
Keywords: mathematical modeling, optimal control, didactic system, learning process, control object, program control, computational experiment, structure of functioning, functional structure.
Ключевые слова: математическое моделирование, оптимальное управление, дидактическая система, процесс обучения, объект управления, программное управление, вычислительный эксперимент, структура функционирования, функциональная структура.

Introduction
The management problems of didactic systems and the methods of mathematical modeling of learning processes have been studied in numerous works by L.P. Leontyev, O.G. Gokhman, R.V. Mayer, N.F.Talyzin et al. [1-3]. In these works, some aspects of the optimal management of educational processes at the university are considered. In particular, the development of an optimal curriculum, measurement of educational information, communication model of the volume of the stated and learned material, quantization of educational material, the principle of feedback and other statements and solving applied control problems (program and optimal) for studying learning processes begins with the creation of the management structure of the studied processes . The functioning of the created structure of the open control system, as a non-deterministic object, has no regularity of development. At the same time, methods of simulation modeling are applied using the principle of the system approach of control theory [4]. Therefore, the development of mathematical models for solving problems of analysis and synthesis of social objects of management, as a learning process, is highly relevant.


Main part
This article is devoted to theoretical studies with a position of a systematic approach to learning processes with the creation of a structure of a sequence of actions (Fig. 1). The functional structure of the learning process as a didactic system “teacher-student” has been created. The theoretical justification created the structure of functioning and proposed a mathematical model of functioning with the aim of optimal control and analysis of the state of the system as a whole.

Pic.1 Structural subdivision is a novelty in the podcode and didactic