Enhancing human learning via spaced repetition optimization

Abstract

Spaced repetition is a technique for efficient memorization which uses repeated review of content following a schedule determined by a spaced repetition algorithm to improve long-term retention. However, current spaced repetition algorithms are simple rule-based heuristics with a few hard-coded parameters. Here, we introduce a flexible representation of spaced repetition using the framework of marked temporal point processes and then address the design of spaced repetition algorithms with provable guarantees as an optimal control problem for stochastic differential equations with jumps. For two well-known human memory models, we show that, if the learner aims to maximize recall probability of the content to be learned subject to a cost on the reviewing frequency, the optimal reviewing schedule is given by the recall probability itself. As a result, we can then develop a simple, scalable online spaced repetition algorithm, MEMORIZE, to determine the optimal reviewing times. We perform a large-scale natural experiment using data from Duolingo, a popular language-learning online platform, and show that learners who follow a reviewing schedule determined by our algorithm memorize more effectively than learners who follow alternative schedules determined by several heuristics.

The advantage of distributed practice in a blended learning setting

“…It is also one of the most researched learner behaviors that has been replicated in experimental settings (Cepeda et al 2006 ; Janiszewski et al 2003 ) and applied settings (Cepeda et al 2008 ; Kornell et al 2010 ) alike. Current empirical evidence comes from learning analytics and data mining approaches, which highlight the importance of self-regulated learning (Tabibian et al 2019 ; Viberg et al 2020 ). Profiles of learners who study more regularly by following the sequential structure of a course, have been shown to gain a deeper understanding of the course materials (Maldonado-Mahauad et al 2018 ).…”

Self-regulated spacing in a massive open online course is related to better learning

“…How do people choose to incorporate spacing in their own study practices, how do these choices vary across individuals, and how are these choices related to learning outcomes? We know that spacing has benefits for long-term memory and memory maintenance from large scale studies of language learning 23 , but we do not know how these benefits scale up to more naturalistic settings. For example, we do not currently understand if and to what extent spaced study improves learning of complex materials where overlap from one event to another might be only partial or not perceptually salient.…”

Optimizing practice scheduling requires quantitative tracking of individual item performance

“…We also highlighted the possibility of an optimal amount of difficulty to maximize learning, based on arguments by Hebb 43 , Bjork 41 , and Pavlik and Anderson 18 . Tracking probability of retrieval (our operationalization of difficulty) throughout learning was also shown to be achievable, both with our methods and given the existence of several accurate models of memory 38,40,44,45 . The following simulations combine these ideas by evaluating how scheduling according to a model and difficulty thresholds compared to conventional practices schedules and heuristics.…”