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Spaced repetition is among the most studied learning strategies in thecognitive science literature. It consists in temporally distributing exposureto an information so as to improve long-term memorization. Providing studentswith an adaptive and personalized distributed practice schedule would benefitmore than just a generic scheduler. However, the applicability of such adaptiveschedulers seems to be limited to pure memorization, e.g. flashcards or foreignlanguage learning. In this article, we first frame the research problem ofoptimizing an adaptive and personalized spaced repetition scheduler whenmemorization concerns the application of underlying multiple skills. To thisend, we choose to rely on a student model for inferring knowledge state andmemory dynamics on any skill or combination of skills. We argue that noknowledge tracing model takes both memory decay and multiple skill tagging intoaccount for predicting student performance. As a consequence, we propose a newstudent learning and forgetting model suited to our research problem: DAS3Hbuilds on the additive factor models and includes a representation of thetemporal distribution of past practice on the skills involved by an item. Inparticular, DAS3H allows the learning and forgetting curves to differ from oneskill to another. Finally, we provide empirical evidence on three real-worldeducational datasets that DAS3H outperforms other state-of-the-art EDM models.These results suggest that incorporating both item-skill relationships andforgetting effect improves over student models that consider one or the other.

DAS3H: Modeling Student Learning and Forgetting for Optimally Scheduling Distributed Practice of Skills