  Students have a limited time to study and are typically ineffective at
allocating study time. Machine-directed study strategies that identify which
items need reinforcement and dictate the spacing of repetition have been shown
to help students optimize mastery (Mozer & Lindsey 2017). The large volume of
research on this matter is typically conducted in constructed experimental
settings with fixed instruction, content, and scheduling; in contrast, we aim
to develop methods that can address any demographic, subject matter, or study
schedule. We show two methods that model item-specific recall probability for
use in a discrepancy-reduction instruction strategy. The first model predicts
item recall probability using a multiple logistic regression (MLR) model based
on previous answer correctness and temporal spacing of study. Prompted by
literature suggesting that forgetting is better modeled by the power law than
an exponential decay (Wickelgren 1974), we compare the MLR approach with a
Recurrent Power Law (RPL) model which adaptively fits a forgetting curve. We
then discuss the performance of these models against study datasets comprised
of millions of answers and show that the RPL approach is more accurate and
flexible than the MLR model. Finally, we give an overview of promising future
approaches to knowledge modeling.
