Inferring history-dependent memory strength
via collaborative filtering:
Toward the optimization of long-term retention

Robert Lindsey, Jeff Shroyer, and Michael C. Mozer
University of Colorado at Boulder

Effective teaching requires an understanding of a student's dynamic knowledge state. To facilitate automated teaching, our goal is to construct models that infer the strength of specific concepts, skills, or facts. Regardless of the nature of the material, forgetting occurs, and the strength of memory depends on the amount and temporal distribution of past study.  The challenge of inference is that available evidence is quite weak. For example, suppose that a student solved four out of five specific long-division problems correctly on a quiz; how well would you expect the student to do on a particular long-division problem assigned a month later? To overcome the sparsity of observations, we use a collaborative filtering approach that leverages information about a population of students studying a population of items to infer how well a specific student has learned a specific item. We propose a hierarchical Bayesian additive-factor model that considers the temporal distribution of past study. We evaluate the efficacy of this model in predicting student recall using data collected from vocabulary drill software we developed which is being used by 180 students in a Denver-area middle school. We further discuss how we are using predictive models to optimize long-term retention of vocabulary.