Using Bayesian learning to classify college algebra students by understanding in real-time

Abstract

The goal of this work is to provide instructors with detailed information about their classes at each assignment during the term. The information is both on an individual level and at the aggregate level. We used the large number of grades, which are available online these days, along with data-mining techniques to build our models. This enabled us to profile each student so that we might individualize our approach. From these profiles, we began to investigate what can be done in order to get students to do better, or at least be less frustrated. Regardless, the interactions with our undergraduates will improve as our knowledge about them increases. We start with a categorization of Studio College Algebra students into groups, or clusters, at some point in time during the semester. In our case, we used the grouping just after the first exam, as described by Dr. Rachel Manspeaker in her PhD. dissertation. From this we built a naive Bayesian model which extends these student clusters from one point in the semester, to a classification at every assignment, attendance score, and exam in the course. A hidden Markov model was then constructed with the transition probabilities being derived from the Bayesian model. With this HMM, we were able to compute the most likely path that students take through the various categories over the semester. We observed that a majority of students settle into a group within the first two weeks of the term.