Mathematical Modeling and Forecasting of Student’s Academic Performance on Massive Online Courses

Mathematical model for calculating the scores' distributions in massive open online courses is proposed. The model is based on the theory of Markov processes. It allows to calculate the probability to find a student in one of the groups according to the results of passing the tests: unsuccessful students, performing satisfactorily and doing well and excellent. It is shown that in the limit of a sufficiently long history of teaching the course on the educational platform, the distribution of scores for the course becomes asymptotically steady. It is shown also that such asymptotically steady distributions, can be calculated on the base of the model proposed, even for the courses without a long history. Such asymptotically steady distributions can be indicators of the quality of control materials and approaches to student scoring. As an example, several courses of Ural Federal University (UrFU), posted on the National Platform of Open Education have been analyzed. The possibility of using the model to predict the results of control tests based on the data on the current progress of students before passing them is shown.