Extending Adaptive Spacing Heuristics to Multi-Skill Items

Adaptive spacing algorithms are powerful tools for helping learners manage their study time efficiently. By personalizing the temporal distribution of retrieval practice of a given piece of knowledge, they improve learners' long-term memory retention compared to fixed review schedules. However, such algorithms are generally designed for the pure memorization of single items, such as vocabulary words. Yet, the spacing effect has been shown to extend to more complex knowledge, such as the practice of mathematical skills. In this article, we extend three adaptive spacing heuristics from the literature for selecting the best skill to review at any timestamp given a student's past study history. In real-world educational settings, items generally involve multiple skills at the same time. Thus, we also propose a multi-skill version for two of these heuristics: instead of selecting one single skill, they select with a greedy procedure the most promising subset of skills to review. To compare these five heuristics, we develop a synthetic experimental framework that simulates student learning and forgetting trajectories with a student model. We run multiple synthetic experiments on large cohorts of 500 simulated students and publicly release the code for these experiments. Our results highlight the strengths and weaknesses of each heuristic in terms of performance, robustness, and complexity. Finally, we find evidence that selecting the best subset of skills yields better retention compared to selecting the single best skill to review.