MATHEMATICAL MODELS OF LEARNING ANALYTICS FOR MASSIVE OPEN ONLINE COURSES

Online education is rapidly developing in Russia and in the world over the last decades. One of the most popular and available online learning technologies is massive open online courses (MOOC), which are successfully used in the university, school, continuing professional education and informal life-long learning. Nowadays the number of MOOC learners in the world is estimated in tens of millions of people. Nevertheless, using MOOC in the educational process has both advantages and disadvantages. The latter include problems connected with individualization of training, assessment of progress and support for students, and assessment of the quality of courses. Analyzing and predicting the success of students is an important task and tool for solving them. The paper is devoted to developing a model of students' progress forecasting, which is based on the information theory and allows one to estimate the probability of students' success in the of the final test when observing the current performance of students. The probabilistic model for group forecasting of the final performance, considered in the paper, allows predicting the distribution of students' final scores and reduce the level of uncertainty in online learning using MOOCs. It can be useful for assessing the quality of the course as a whole and developing measures to improve it. The statistical model for personalized performance prediction allows one to make a forecast of the final progress for each student and can be used to identify negative trends and problems of students in learning, provide them with relevant feedback and necessary support. The application of the models is considered on the example of an engineering online course created by the Ural Federal University