A Model of Teaching Mathematics with the Effect of Developing the Probabilistic Style of Thinking in a Digital Educational Environment: Theoretical Justification and Empirical Verification

The article is focused on the problem of inducing students to develop the non-linear, probabilistic style of thinking in the context of the digitalization of modern education. The purpose of the study is to create effective scientific and methodological tools for organizing the process of teaching mathematics in schools and universities in order to achieve high pedagogical, socially demanded results and, on the basis of these tools, to create an improved didactic model with the effect of developing the probabilistic style of thinking, flexibility, creativity and criticality in students so as to enable them to actively participate in social life. The model of teaching mathematics is constructed in the unity of the target, theoretical and methodological, content, technological, diagnostic and effective components. The structure-forming factor is an information-intensive educational environment for teaching mathematics as a set of digital information and educational content that contributes to the effective development of probabilistic style of thinking. The content component of the model is implemented in the selection and structuring of educational material based on the fractal approach, in the methodological update of a complex of foundation spirals equipped with banks of applied and research tasks, taking into account the depth of the fractal representation of educational elements. To obtain guaranteed learning outcomes while solving technological problems of implementing the model, an adaptive learning system was used as a tool for developing probabilistic style of thinking in students and creating an objective means of management. The results of introducing the model into teaching practice with subsequent statistical verification based on the descriptive statistics methods and Student’s t -test showed positive dynamics for all the structural components of the model with a confidence level of 95%. The prospect of the research is further intellectualization of the technological component of the model based on the hybridization of artificial intelligence methods to ensure the effective development of the probabilistic style of thinking with rapid changes in parameter values according to the set feedbacks.