Insights into Learning Competence Through Probabilistic Graphical Models

One-digit multiplication problems is one of the major fields in learning mathematics at the level of primary school that has been studied over and over. However, the majority of related work is focusing on descriptive statistics on data from multiple surveys. The goal of our research is to gain insights into multiplication misconceptions by applying machine learning techniques. To reach this goal, we trained a probabilistic graphical model of the students’ misconceptions from data of an application for learning multiplication. The use of this model facilitates the exploration of insights into human learning competence and the personalization of tutoring according to individual learner’s knowledge states. The detection of all relevant causal factors of the erroneous students answers as well as their corresponding relative weight is a valuable insight for teachers. Furthermore, the similarity between different multiplication problems - according to the students behavior - is quantified and used for their grouping into clusters. Overall, the proposed model facilitates real-time learning insights that lead to more informed decisions.