Personalization Through the Application of Inverse Bayes to Student Modeling

Abstract

Personalization, the idea that teaching can be tailored to each students’ needs, has been a goal for the educational enterprise for at least 2,500 years (Regian, Shute, & Shute, 2013, p.2). Recently personalization has picked up speed with the advent of mobile computing, the Internet and increases in computer processing power. These changes have begun to generate more and more information about individual students that could theoretically be used to power personalized education. The following dissertation discusses a novel algorithm for processing this data to generate estimates of individual level attributes, the Inverse Bayes Filter (IBFi). A brief introduction to the use of Bayes Theorem is followed by a theoretical chapter and then two empirical chapters that describe alternately how the model is constructed, and how it performs on real student data. The theoretical chapter presents both the theory behind Inverse Bayes, including subjective probability, and then relates this theory to student performance. The first empirical chapter describes the prediction accuracy of IBFi on two proxies for students’ subjective probability, partial credit and cumulative average. This prediction performance is compared to the prediction accuracy of a modified Bayesian Knowledge Tracing model (KTPC) with IBFi performing reasonably, out-predicting the KTPC model on a per-student basis but not across all predictions. In the second empirical chapter I validate the theory behind the Inverse Bayes Filter through testing whether student certainty (or confidence) improves prediction performance. The inclusion of student certainty is shown to improve the predictive performance of the model relative to models that do not use certainty. This evidence supports the IBFi model and its underlying theory, indicating that students’ judgments about their levels of certainty in their answers contains information that can be successfully identified by the model. A final summary chapter describes the consequences of using this model for education broadly.