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We demonstrate an application for learning multiplication problems with an adaptive algorithm that is based on a computational cognitive model of the learner's memory. The application helps learners automatise and memorise multiplications through repeated practice over three levels of difficulty. In a naturalistic setting involving more than 500 primary school students (ages 6-10) who together recorded over 300,000 responses, we observed that performance improved as learners using the application progressed through the levels. A model-based analysis of performance revealed that learners' estimated speed of forgetting decreased from the second to the third level. This is consistent with a shift towards stronger declarative knowledge and/or more efficient computation procedures. The model also identified consistent differences in the difficulty of individual multiplication facts that persisted across levels. This study demonstrates the feasibility of using an adaptive fact learning application to help young learners master multiplication, an essential mathematical skill.

In personalized-schedule learning, previous research has shown the benefit of initial attempted retrieval of study-items on short-term retention and later test performance. As a way of prior-knowledge identification, initial attempted retrieval may help to optimize learning and long-term performance further, through the removal (or ‘drop') of items from the learning set that are answered correctly on the first attempt. This study sought to support this hypothesis through a real-world, within-subjects experiment, comparing vocabulary test performance of Dutch middle school students after the use of a drop- and non-drop adaptive learning algorithm. The results show that short- and long-term item retention was higher for material studied using the drop-algorithm, while dropping items did not lead to worse retention compared to items that were kept upon initial correct responses. This suggests that initially-known items are correctly identified as ‘mastered', and that their removal from the learning material allows students to focus their efforts on unknown items, leading to increased learning gains.

While students typically prefer multiple-choice learning, open-answer questions have frequently been found to be more effective, attributed to their role in promoting recall as opposed to recognition. Here, we examine increasing the effectiveness of multiple-choice testing as a learning tool, by using foils (incorrect answer options) that are similar in meaning and word form to the correct answer. Participants studied French-Dutch vocabulary in three learning conditions: one with unrelated foils, another with open questions, and a third using multiple choice questions with related foils. The related foils were either semantically or orthographically similar to the correct answer. The results showed no significant difference between the open questions and the related foils condition, indicating comparable effectiveness. Replicating earlier studies, the unrelated foils condition yielded significantly poorer learning outcomes. Overall, these results suggest that multiple-choice testing can be a viable alternative to open answer testing when utilizing related foils.

Modern educational technology has the potential to support students to use their study time more effectively. Learning analytics can indicate relevant individual differences between learners, which adaptive learning systems can use to tailor the learning experience to individual learners. For fact learning, cognitive models of human memory are well suited to tracing learners' acquisition and forgetting of knowledge over time. Such models have shown great promise in controlled laboratory studies. To work in realistic educational settings, however, they need to be easy to deploy and their adaptive components should be based on individual differences relevant to the educational context and outcomes. Here, we focus on predicting university students' exam performance using a model-based adaptive fact-learning system. The data presented here indicate that the system provides tangible benefits to students in naturalistic settings. The model's estimate of a learner's rate of forgetting predicts overall grades and performance on individual exam questions. This encouraging case study highlights the value of model-based adaptive fact-learning systems in classrooms.

Digital adaptive fact learning systems tailor learning sessions to the individual learner. Most adaptive learning systems assume that the learner has no prior knowledge of the material and therefore use an initial ‘passive rehearsal’ trial for all facts. Here, we test a system that uses active retrieval trials instead of passive study trials when introducing items. This minimizes time loss associated with studying familiar materials and maximizes potential benefits of attempted retrieval before study. We test the system by having participants learn the association between the outlines and names of countries, a domain in which they are likely to have varying degrees of prior knowledge. We show that using attempted retrieval to identify known items is valuable in real-world applications, where partial knowledge of study materials before the start of a learning session is very common.

Models of memory that rely on a single forgetting curve can struggle to simultaneously capture memory performance over short and long timescales. Typically, model parameters that account well for forgetting over a span of seconds or minutes are too pessimistic when it comes to predicting longer-term retention over days or weeks. Crucially, it is precisely the ability to model memory performance within and between study sessions that is valuable in applied educational settings. Previous attempts to address the underestimation of long-term retention involved scaling down between-session time. Here, we investigate how the optimal scaling factor changes as a function of the interval between study attempts, using a rich naturalistic dataset with intervals ranging from several seconds to multiple weeks. By fitting an ACT-R model, we show that the optimal scaling factor changes with time and interacts with the retrieval threshold. This finding has direct practical and theoretical implications.

Performance on cognitive tasks is typically affected by many factors simultaneously. For example, performance on a retrieval practice task is determined not only by memory encoding and retrieval processes, but also by motor processes, executive functions, affective state, etc. Often, these contributing processes also vary over time. This makes it challenging to attribute performance changes to a single mechanism, especially in real-world settings.Here we analyse performance data from multiple retrieval practice sessions completed by special forces trainees before and after a high-intensity speed march. Learning outcomes improved from session to session, which suggests increased memory function. However, a linear ballistic accumulator fitted to the data showed that changes in non-memory processes—a decrease in non-retrieval time in particular—sufficed to explain the observed improvements.This work demonstrates that even with a simple task, assuming that performance changes are attributable to a single cognitive process can lead to erroneous conclusions.

There is conflicting evidence regarding the effect of acute physical exercise on peoples ability to memorise declarativeinformation. Some studies have found that exercising before learning improves memorisation, while others have foundan adverse effect. We measured memorisation in 70 recruits for the Special Forces unit of the Dutch army during theirfirst week of training. Recruits used a computer-guided learning system to study the names of locations on a map directlybefore and directly after a high-intensity speed march. In the learning session following the speed march, responses werefaster but less accurate than before, particularly at the start of the session. We fitted a computational cognitive model ofhuman memory to the responses made in each learning session to obtain a continuous index of memorisation. This indexshowed a small improvement after the speed march, suggesting that memory representations formed after high-intensityphysical exercise were slightly more stable.