A dilemma faced by teachers, and increasingly by designers of educational software, is the trade-off between teaching new material and reviewing what has already been taught. Complicating matters, review is useful only if it is neither too soon nor too late. Moreover, different students need to review at different rates. We present a mathematical model that captures these issues in idealized form. The student’s needs are modeled as constraints on the schedule according to which educational material and review are spaced over time. Our results include algorithms to construct schedules that adhere to various spacing constraints, and bounds on the rate at which new material can be introduced under these schedules.
We hope these results contribute to a theory which will serve as a foundation for intuition for practitioners designing algorithms for educational software, much the way Algorithmic Game Theory does for practitioners working in online ad auctions and similar domains.
Joint work with Jon Kleinberg and Steve Strogatz.