Probabity distributions of the academic performance of online courses's students as a tool for assesment of the quality of control materials
Digitalization of higher education is accompanied by significant changes in the usual way of University life, such as: an increase in the number of students simultaneously studying one course, a reduction in personal contact between teachers and students during training, an expansion of the set of tools for developing courses, more complex approaches to evaluating courses, etc. These changes require new approaches to organizing the activities of all participants in the educational process - students, teachers, authors of online courses, and administrative staff of the educational institution. The scale of the problem statement requires its decomposition and solution in parts. The paper considers the problem of assessing the control materials for online courses, arising in processes of the digital transformation of education. A model for evaluation of control materials and tests on the base of the probability distributions analysis of students' academic performance, developed using the mathematical apparatus of the theory of Markov processes, is proposed. As indicators for the analysis and assessment of the quality of control materials, the probabilities of transitions between groups with different academic performance and asymptotic stable probability distributions of academic performance were chosen. As an example, these indicators were calculated for four online courses of the Ural Federal University. A comparative analysis and conclusions were made regarding the complexity of the courses materials. The possible application of the proposed indicators by various participants in the educational process is discussed. Considered in the work group indices - the probabilities of transitions between groups of progress and sustainable distribution groups progress characterizing the student body, and control and measuring materials of the online course can be useful for students choosing courses for individual educational trajectories, the authors of courses, making decisions on modifications to course materials, managers of educational programs, selecting courses for their programs.