Abstract:

Today online technologies became an integral part of educational system. That created new challenges and arose new problems that concern all participants of the educational process. One of the challenges is to balance massive implementation of online learning with benefits of traditional education models, creating an individual approach to every student. That requires monitoring the results of current academic activities, reflected in passing the massive open online course (MOOC) milestones. Monitoring allows timely reaction on the emerging negative trends and strengthens position of testing as an important mean for monitoring student knowledge and determines requirements for the tools of such monitoring. In this paper, authors attempt to describe a mathematical model for the academic performance evolution used as a base for scrutinizing various aspects of learning success monitoring and prediction. Such model may be also used to validate internal testing systems of MOOCs. Analysis based on this model provide useful insights for all participants of educational process.

In the paper authors derive equations that allow calculation of probabilities for student falling into academic performance groups (unsuccessful, successful, very successful) both in terms of final test in MOOC, and at any checkpoint. In this case, model parameters are determined either according to data on current performance of the students at milestone preceding the analyzed one or based on student performance in previous instances of a course.

It is demonstrated that probability of transition among the academic performance groups in course of passing a milestone depends upon the number of students in each group before going through a checkpoint. These dependencies were defined for the courses conducted on Edex platform of a Ural Federal University. The obtained results were used to examine temporal evolution of distributions for academic performance.

It is demonstrated that distributions can be rather complex, for example, displaying multimodal behavior for certain combinations of inter-group transition probabilities. Authors demonstrate possibility of dynamic chaos type behavior due to feedback influence of information about learning outcomes on academic activities of the students.

Described algorithms allow assessing information contents and quality for tests in course materials, or the entire course. That allows introducing quality indicator for an online course. Indication describes the level of uncertainty related with students achieving overall MOOC study goals, and the rate this uncertainty decreases while students go through checkpoints. In order to illustrate the proposed approach, authors clustered different UrFU online courses using k-means algorithm based on the said quality parameter, and levels of academic activity in course of studies. Authors also analyzed possible reasons for differences in students’ academic performance distribution for representatives from different clusters.

Authors analyzed potential applicability of the proposed mathematical probabilistic model for predicting both group and individual student progress and demonstrated use of the algorithms within the "Online Tutor" special information service framework developed by the authors and implemented in the Ural Federal University.

Keywords:

Massive open online course, mathematical model for the academic performance temporal evolution, quality indicator for an online course, Online Tutor.