APPLICATION OF GAME THEORY AGAINST NATURE TO CHOOSE A LEARNING STRATEGY

The problem of choosing a teaching strategy depending on a heterogeneous contingent of students is considered. It is assumed that one of the following strategies can be used: passive, active or interactive learning. The listed strategies can be combined for a specific group of students, but they cannot be applied individually to each individual student. It is necessary to choose the optimal strategy for a specific contingent of students in order to achieve the best learning outcomes. The model of the educational process is mathematically formalized in terms of theory of game against nature. Four categories of students are introduced, correlated with different strategies (states) of «nature». Students can be characterized not only by the presence of abilities, but also by the level of motivation, and the probabilistic distribution of students by these characteristics can be known (stochastic uncertainty) or unknown. In the conditions of stochastic uncertainty, the criteria for choosing the optimal strategy can be the criteria of the maximum average gain or the minimum average risk. Decision-making in the absence of information about the probability distribution of strategies of nature can be based on the criteria of Wald, Savage, Hurwitz. The same game matrix was used for the calculations, but with different assumptions about the distribution of students by type and with different decision-making criteria.The described approaches allow us to take the choice of a learning strategy with greater responsibility for its results. Practice shows the positive impact of such an analysis on the effectiveness of training.

teaching methods, games with nature, game matrix, stochastic uncertainty, decisionmaking criteria