The spacing effect is among the most widely replicated empirical phenomena in the learning sciences, and its relevance to education and training is readily apparent. Yet successful applications of spacing effect research to education and training is rare. Computational modeling can provide the crucial link between a century of accumulated experimental data on the spacing effect and the emerging interest in using that research to enable adaptive instruction. In this paper, we review relevant literature and identify 10 criteria for rigorously (...) evaluating computational models of the spacing effect. Five relate to evaluating the theoretic adequacy of a model, and five relate to evaluating its application potential. We use these criteria to evaluate a novel computational model of the spacing effect called the Predictive Performance Equation. Predictive Performance Equation combines elements of earlier models of learning and memory including the General Performance Equation, Adaptive Control of Thought—Rational, and the New Theory of Disuse, giving rise to a novel computational account of the spacing effect that performs favorably across the complete sets of theoretic and applied criteria. We implemented two other previously published computational models of the spacing effect and compare them to PPE using the theoretic and applied criteria as guides. (shrink)

The fields of machine learning (ML) and cognitive science have developed complementary approaches to computationally modeling human behavior. ML's primary concern is maximizing prediction accuracy; cognitive science's primary concern is explaining the underlying mechanisms. Cross-talk between these disciplines is limited, likely because the tasks and goals usually differ. The domain of e-learning and knowledge acquisition constitutes a fruitful intersection for the two fields’ methodologies to be integrated because accurately tracking learning and forgetting over time and predicting future performance based on (...) learning histories are central to developing effective, personalized learning tools. Here, we show how a state-of-the-art ML model can be enhanced by incorporating insights from a cognitive model of human memory. This was done by exploiting the predictive performance equation's (PPE) narrow but highly specialized domain knowledge with regard to the temporal dynamics of learning and forgetting. Specifically, the PPE was used to engineer timing-related input features for a gradient-boosted decision trees (GBDT) model. The resulting PPE-enhanced GBDT outperformed the default GBDT, especially under conditions in which limited data were available for training. Results suggest that integrating cognitive and ML models could be particularly productive if the available data are too high-dimensional to be explained by a cognitive model but not sufficiently large to effectively train a modern ML algorithm. Here, the cognitive model's insights pertaining to only one aspect of the data were enough to jump-start the ML model's ability to make predictions—a finding that holds promise for future explorations. (shrink)

One of the goals of computerized tutoring systems is to optimize the learning of facts. Over a hundred years of declarative memory research have identified two robust effects that can improve such systems: the spacing and the testing effect. By making optimal use of both and adjusting the system to the individual learner using cognitive models based on declarative memory theories, such systems consistently outperform traditional methods. This adjustment process is driven by a continuously updated estimate of the rate of (...) forgetting for each item and learner on the basis of the learner's accuracy and response time. In this study, we investigated to what extent these estimates of individual rates of forgetting are stable over time and across different materials. We demonstrate that they are stable over time but not across materials. Even though most theories of human declarative memory assume a single underlying rate of forgetting, we show that, in practice, it makes sense to assume different materials are forgotten at different rates. If a computerized, adaptive fact-learning system allowed different rates of forgetting for different materials, it could adapt to individual learners more readily. (shrink)

One of the goals of computerized tutoring systems is to optimize the learning of facts. Over a hundred years of declarative memory research have identified two robust effects that can improve such systems: the spacing and the testing effect. By making optimal use of both and adjusting the system to the individual learner using cognitive models based on declarative memory theories, such systems consistently outperform traditional methods (Van Rijn, Van Maanen, & Van Woudenberg, 2009). This adjustment process is driven by (...) a continuously updated estimate of the rate of forgetting for each item and learner on the basis of the learner's accuracy and response time. In this study, we investigated to what extent these estimates of individual rates of forgetting are stable over time and across different materials. We demonstrate that they are stable over time but not across materials. Even though most theories of human declarative memory assume a single underlying rate of forgetting, we show that, in practice, it makes sense to assume different materials are forgotten at different rates. If a computerized, adaptive fact‐learning system allowed different rates of forgetting for different materials, it could adapt to individual learners more readily. (shrink)

We explore the nature of forgetting in a corpus of 125,000 students learning Spanish using the Rosetta Stone® foreign-language instruction software across 48 lessons. Students are tested on a lesson after its initial study and are then retested after a variable time lag. We observe forgetting consistent with power function decay at a rate that varies across lessons but not across students. We find that lessons which are better learned initially are forgotten more slowly, a correlation which likely reflects a (...) latent cause such as the quality or difficulty of the lesson. We obtain improved predictive accuracy of the forgetting model by augmenting it with features that encode characteristics of a student's initial study of the lesson and the activities the student engaged in between the initial and delayed tests. The augmented model can predict 23.9% of the variance in an individual's score on the delayed test. We analyze which features best explain individual performance. (shrink)

We examined whether variations in contextual diversity, spacing, and retrieval practice influenced how well adults learned new words from reading experience. Eye movements were recorded as adults read novel words embedded in sentences. In the learning phase, unfamiliar words were presented either in the same sentence repeated four times (same context) or in four different sentences (diverse context). Spacing was manipulated by presenting the sentences under distributed or non‐distributed practice. After learning, half of the participants were asked to retrieve the (...) new words, and half had an extra exposure to the new words. Although words experienced in diverse contexts were acquired more slowly during learning, they enjoyed a greater benefit of learning at immediate posttest. Distributed practice also slowed learning, but no benefit was observed at posttest. Although participants who had an extra exposure showed the greatest learning benefit overall, learning also benefited from retrieval opportunity, when words were experienced in diverse contexts. These findings demonstrate that variation in the content and structure of the learning environment impacts on word learning via reading. (shrink)

During each school semester, students face an onslaught of material to be learned. Students work hard to achieve initial mastery of the material, but when they move on, the newly learned facts, concepts, and skills degrade in memory. Although both students and educators appreciate that review can help stabilize learning, time constraints result in a trade-off between acquiring new knowledge and preserving old knowledge. To use time efficiently, when should review take place? Experimental studies have shown benefits to long-term retention (...) with spaced study, but little practical advice is available to students and educators about the optimal spacing of study. The dearth of advice is due to the challenge of conducting experimental studies of learning in educational settings, especially where material is introduced in blocks over the time frame of a semester. In this study, we turn to two established models of memory—ACT-R and MCM—to conduct simulation studies exploring the impact of study schedule on long-term retention. Based on the premise of a fixed time each week to review, converging evidence from the two models suggests that an optimal review schedule obtains significant benefits over haphazard (suboptimal) review schedules. Furthermore, we identify two scheduling heuristics that obtain near optimal review performance: (a) review the material from μ-weeks back, and (b) review material whose predicted memory strength is closest to a particular threshold. The former has implications for classroom instruction and the latter for the design of digital tutors. (shrink)