Modelling Learners in Adaptive Educational Systems: A Multivariate Glicko-based Approach

The Elo rating system has been recognised as an effective method for modelling students and items within adaptive educational systems. A common characteristic across Elo-based learner models is that they are not sensitive to the lag time between two consecutive interactions of a student within the system. Implicitly, this characteristic assumes that students do not learn or forget between two consecutive interactions. However, this assumption seems insufficient in the context of adaptive learning systems where students could have improved their mastery through practising outside of the system or that their mastery may be declined due to forgetting. In this paper, we extend the existing works on the use of rating systems for modelling learners in adaptive educational systems by proposing a new learner model called MV-Glicko that builds on the Glicko rating system. MV-Glicko is sensitive to the lag time between two consecutive interactions of a student within the system and models it as a parameter that captures the confidence of the system in the current inferred rating. We apply MV-Glicko on three public data sets and three data sets obtained from an adaptive learning system and provide evidence that MV-Glicko outperforms other conventional models in estimating students' knowledge mastery.