An empirical mathematical model for studying the psychological stability of students in the context of distance education

The article is devoted to the current problem of the psychology of education, which is due to the contradiction between the inevitable process of the spread of distance technologies in educational practice and the lack of substantiated research. Particular attention is paid to mathematical modeling in the study of multidimensional psychological phenomena. The specifics of the development and application in the organization of research of the psychological stability of students in the changing conditions of education of an empirical mathematical model (EMM), which consists of an a priori (conceptual) model and a posteriori (procedure for applying multidimensional methods). The main stages of the development of the a priori model and the methodological foundations of the phenomenon of "psychological stability" are revealed. This phenomenon is considered through the category of the attitude of young people to life situations (including the changing conditions of education — ILE) from the point of view of cognitive ("Subjective image of a life situation and oneself in it"), emotional-evaluative (assessment of emotional (not) well-being of both individual and personal stability and social stability, value-semantic orientations) and behavioral components (strategies of behavior in ILE. influencing the attitudes of students towards the changing conditions of education, the emerging value orientations of young people and strategies of behavior. a posterior empirical mathematical model. The procedures and results of comparison of three spatio-temporal slices are disclosed: mathematical and statistical verification of the psychometric reliability of the presented scales (internal consistency of indicators for each scale based on the alpha-Cronbach criterion, analysis of the internal structure of the scale and levels of generalization using factor analysis (FA); study of effects influence on generalized factors (ANOVA with repeated measurements); comparative analysis (U-Mann–Whitney test) to identify recurring structural components of psychological stability and its dynamics in new conditions; cluster analysis (CA) to build a typology of students with different levels and characteristics of psychological sustainability model. The role of the empirical mathematical model in confirming the leading components of psychological stability, their influence on value orientations and strategies of behavior in the changing conditions of distance education is revealed.