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)

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)

We demonstrate that the key components of cognitive architectures (declarative and procedural memory) and their key capabilities (learning, memory retrieval, probability judgment, and utility estimation) can be implemented as algebraic operations on vectors and tensors in a high‐dimensional space using a distributional semantics model. High‐dimensional vector spaces underlie the success of modern machine learning techniques based on deep learning. However, while neural networks have an impressive ability to process data to find patterns, they do not typically model high‐level cognition, and (...) it is often unclear how they work. Symbolic cognitive architectures can capture the complexities of high‐level cognition and provide human‐readable, explainable models, but scale poorly to naturalistic, non‐symbolic, or big data. Vector‐symbolic architectures, where symbols are represented as vectors, bridge the gap between the two approaches. We posit that cognitive architectures, if implemented in a vector‐space model, represent a useful, explanatory model of the internal representations of otherwise opaque neural architectures. Our proposed model, Holographic Declarative Memory (HDM), is a vector‐space model based on distributional semantics. HDM accounts for primacy and recency effects in free recall, the fan effect in recognition, probability judgments, and human performance on an iterated decision task. HDM provides a flexible, scalable alternative to symbolic cognitive architectures at a level of description that bridges symbolic, quantum, and neural models of cognition. (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)

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)

Given that there is referential uncertainty (noise) when learning words, to what extent can forgetting filter some of that noise out, and be an aid to learning? Using a Cross Situational Learning model we find a U-shaped function of errors indicative of a “Goldilocks” zone of forgetting: an optimum store-loss ratio that is neither too aggressive nor too weak, but just the right amount to produce better learning outcomes. Forgetting acts as a high-pass filter that actively deletes (part of) the (...) referential ambiguity noise, retains intended referents, and effectively amplifies the signal. The model achieves this performance without incorporating any specific cognitive biases of the type proposed in the constraints and principles account, and without any prescribed developmental changes in the underlying learning mechanism. Instead we interpret the model performance as more of a by-product of exposure to input, where the associative strengths in the lexicon grow as a function of linguistic experience in combination with memory limitations. The result adds a mechanistic explanation for the experimental evidence on spaced learning and, more generally, advocates integrating domain-general aspects of cognition, such as memory, into the language acquisition process. (shrink)