Formation of adaptive learning trajectories in computer systems based on Markov representations

<p><strong>Context and relevance.</strong> The development of digital systems provides new opportunities for automating the educational process in secondary schools and higher education institutions. The modern organization of educational activities does not always allow for the precise identification of gaps in knowledge when solving problems based on previously learned didactic materials. This article presents a mechanism for forming an adaptive learning trajectory in computer systems based on Markov representations to solve problems of individualizing the educational process and identifying gaps in previously covered educational materials. <strong>Objective.</strong> Development of a mechanism for forming an adaptive learning trajectory for individualizing the process of mastering mathematical material in computer systems based on Markov representations. <strong>Hypothesis.</strong> An adaptive learning path will allow for the individualization of the learning process and the automated identification of gaps in students' knowledge of previously covered material. <strong>Methods and materials.</strong> The mathematical basis for forming an adaptive learning trajectory is a Markov process with a discrete number of states and continuous time. To create a bank of tasks, errors, and hints, we used mathematics teaching materials from the first to fourth grades of elementary school. <strong>Results.</strong> The study presented a mechanism for forming an adaptive learning trajectory in computer systems based on Markov models, which allows automating the process of identifying gaps in students' knowledge by providing tasks that correspond to the current individual level of preparation of each student. <strong>Conclusions.</strong> The developed mechanism allows teachers to automate the monitoring of student performance, using the system as an assistant to identify gaps in knowledge when solving problems related to previously covered topics.</p>