Keyword: «pedagogical cybernetics»

One of the didactics development directions is associated with the improvement of the mathematical theory of training (MTT), which makes it possible to explain the basic regularities of didactic systems functioning using the analysis of their mathematical models. An actual problem of MTT is the mathematical solution of the optimization task of training, which consists in determining the conditions of the educational process organization, when its effectiveness is the highest. The result of optimization depends on the learner's assimilation coefficient, classes duration, distribution of learning material elements (LME) according to their complexity and importance. The aim of the work is to build the computer model of the didactic system and to find optimal study duration of LMEs which have various complexity and importance in conditions of the fixed classes duration. The methods of mathematical and computer modeling of the learning process are used, as well as the method of stochastic optimization with a return. It presumes creation of the computer program which makes a step in random direction in the multidimensional environment of optimized values and simulates the study of the given set of issues (LMEs) for new study durations. If the test results at the end of training are not better than at the previous step, then the computer returns to the previous state and repeats everything again. If the test results are higher, then the changes of the optimized values are accepted, and the next step is made from the new state. Gradually, the program approaches the optimal values of the study durations for LMEs. The main results of the work include: 1) the computer program which makes it possible to calculate the optimum values of study durations at different distributions of LMEs on the complexity categories; 2) the graphs of the optimal durations for studying LMEs, the student’s knowledge levels of specific LMEs and the total knowledge levels of different importance LMEs depending on their complexity. The theoretical significance of the article is due to the fact that it sets and solves the problem of optimizing the study durations of specific issues (LMEs) that are different in complexity and importance; this problem is a particular optimization task of the mathematical theory of training.