The spacing effect is often cast as “don’t cram for an examination.” Cramming can help students remember information on the examination however, cramming also leads to rapid forgetting. Tabibian et al.’s ( 3) claim that the benefit of review increases as memory decays is consonant with the spacing effect ( 17), the behavioral finding that temporally distributed practice leads to more robust and durable learning than massed practice. ( 3) provide a compelling theoretical justification for the use of this heuristic. Predicted recall probability has long been used as a heuristic measure for prioritizing material in flashcard-type schedulers, but Tabibian et al. Their key result is a proof that the optimal reviewing intensity is proportional to the student model’s predicted probability of recall failure.
Formally, the penalty function they optimize is quadratic in both recall failure rate and reviewing intensity. The stochastic optimal control problem is to determine the point-process reviewing intensity, that is, the rate of retrieval practice, to maintain memory without excessive practice. Reviewing times for an item are specified via a temporal point process. They characterize the student’s memory state in terms of stochastic differential equations with jumps: When the student reviews a particular item (e.g., a vocabulary word), the memory strength of the item is bumped up and then decays over time.
( 3) identify a class of student models that admit a formal analysis yet are informed by human memory data. Teacher models also lie along a continuum, from hand-constructed heuristic or expert-based approaches ( 2, 9, 13, 14) to those that provably optimize according to some criterion, such as the student model’s score on a postinstruction quiz ( 4, 15). Somewhere in the middle of this continuum are methods that mine corpora of educational data ( 11) to predict the influence of various teaching actions on the student’s subsequent performance ( 2, 12).
Student models range from those motivated heavily by psychological theory ( 7– 10) to those motivated primarily by mathematical elegance and tractability ( 4– 6). The teacher model specifies a policy-in the control-theoretic sense-for administering instructional actions conditioned on the student model. The student model quantifies an individual’s current knowledge state and how it evolves based on instructional actions and the passage of time. ( 3) is formalized by two models: student and teacher. Like every proposal for AI-based instruction, the approach of Tabibian et al. For example, in a semester-long experiment integrated into a middle-school foreign language course, setting aside roughly 30 min per week for AI-guided personalized review of previously introduced material led to a 16.5% improvement in overall course retention on a cumulative examination administered a month after the end of the semester, relative to a time-matched control condition that reflects current educational practice ( 2). Such microinstruction complements the strengths of human teachers and can yield significant benefits. These are decisions which occur on a granularity that human instructors are typically unable to monitor and individualize, and for which students have poor metacognitive strategies ( 1). The synergy among these fields promises to improve the microorganization of human instruction: picking the next exercise for a student to attempt, choosing what sort of hints and feedback to provide, determining when material should be reviewed, and selecting among teaching activities.