Meng Cao

Spacing and repetition are two fundamental principles of learning, yet under limited instructional time, increasing repetitions necessarily shortens the intervals between encounters. Prior research found that more repetitions with shorter spacing produced better learning than fewer repetitions with longer spacing, but the respective contributions of spacing and repetition remained unclear. The present study sought to disentangle these contributions and replicate prior findings. Data were collected in 2026 from 120 English-speaking U.S. adults. Participants learned Indonesian-English word pairs three or six times under both massed and spaced schedules within a fixed instructional time. Retention was assessed immediately, one day, and three days later, and forgetting curves were used to estimate initial memory strength and forgetting rate. We replicated the advantage of more repetitions with shorter spacing. Spaced practice produced greater initial memory strength and slower forgetting than massed practice, whereas additional repetitions increased initial memory strength only when practice was spaced. These findings suggest that, under time constraints, additional repetitions benefit learning primarily when spaced, indicating that the advantage of repeated practice depends on the accumulation of learning across spaced encounters.

Spaced retrieval enhances retention but is often time-intensive, limiting its practical use in educational settings. When study time is constrained, should learners prioritize fewer, widely spaced repetitions or more repetitions with shorter intervals? We tested spacing, repetition, and boundary-condition accounts by manipulating item difficulty and practice schedules across three experiments (N = 1,944). Participants learned Indonesian vocabulary under four conditions that traded off repetition frequency and spacing interval. Results showed that increasing repetitions with shorter spacing improved immediate performance and delayed retention, particularly for difficult items, whereas easy items reached an asymptote after a moderate number of repetitions. These findings support a boundary-condition account, indicating that the effectiveness of spacing and repetition depends on item difficulty and sufficient successful retrievals. Together, repetition, spacing, and item difficulty jointly regulate retrieval success. The results refine retrieval-based learning theory and offer guidance for efficient study under time constraints.

Practice can improve learning, yet the mechanisms through which learning changes across practice remain unclear. Existing theories propose that learning can arise through repeated exposure, error correction, and successful retrieval, but the relative contributions of these mechanisms are rarely evaluated systematically. In the present work, we use a computational modeling approach to examine how these mechanisms jointly contribute to learning. Across two learning contexts, results showed that the mechanisms supporting learning differed across practices with and without feedback. When feedback was provided, learning was best explained by a combination of exposure and effortful successful retrieval, whereas the contribution of error correction depended on the complexity of the learning materials and the type of feedback provided. When feedback was absent, learning primarily depended on retrieval success, with no additional contribution of retrieval effort. These findings suggest that learning is a context-dependent process in which the contributions of multiple mechanisms vary across task structures and feedback conditions. The present work provides a unified framework for understanding how these mechanisms contribute to learning over time.

The present study examined whether the effectiveness of spaced practice in authentic K–12 classrooms depends on the variability of instructional materials. Data were collected from 52 classrooms, including 1,050 middle and high school students across multiple subjects. Results showed that spaced practice improved long-term retention when practice repeatedly targeted the same item, even when questions varied in format. In contrast, spacing benefits were attenuated when practice involved different items aligned with the same instructional standard. Spaced practice also produced a modest benefit for transfer to novel items regardless of variability. These findings suggest an important boundary condition of spacing effects: the benefits of spacing depend on the extent to which practice opportunities preserve overlap that supports retrieval of prior learning. More broadly, the results refine theoretical accounts of spacing by highlighting potentially distinct mechanisms underlying retention and transfer and provide practical guidance for implementing spaced practice in educational settings.

The ability to generalize and apply knowledge to new situations is the hallmark of effective learning. There are multiple ways to improve learning towards generalization. Retrieval practice and worked examples have both been shown to improve learning, retention, and generalization. The literature on category learning also suggests that exposure to more varied examples, rather than the same example repeatedly, improves generalization. However, while retrieval practice is usually investigated with repeated items, worked examples are usually investigated using varied content. Across two experiments, we investigated how combining content variability with worked examples or retrieval practice promoted generalization when learners received initial instruction before practice (Experiment 1) and when they did not (Experiment 2). We found that when learners received initial instruction, retrieval practice led to better generalization than worked examples, regardless of whether the stimuli were repeated or varied. When initial instruction was not provided, worked examples resulted in better generalization than retrieval practice when items were repeated. However, retrieval practice produced comparable generalization to worked examples when items were varied. These findings suggest that variability supports generalization, particularly when learners must induce underlying rules, and that retrieval practice, traditionally associated with memory retention, can also facilitate inductive learning when applied to varied items. This study emphasizes the importance of adapting learning strategies to align with the instructional context and task demands.

The ability to generalize and apply knowledge to new situations is the hallmark of effective learning. There are multiple ways to improve learning towards generalization. Retrieval practice and worked examples have both been shown to improve learning, retention, and generalization. The literature on category learning also suggests that exposure to more varied examples, rather than the same example repeatedly, improves generalization. However, while retrieval practice is usually investigated with repeated examples, worked examples learning is usually investigated using varied content. Across two studies, we investigated how combining content variability with worked examples or retrieval practice promotes generalization when students receive initial instruction before practice (Experiment 1) and when they do not (Experiment 2). We found that when learners received initial instruction, retrieval practice led to better generalization compared to worked examples, regardless of whether the stimuli were repeated or varied. When initial instruction was not provided, worked examples resulted in better generalization than retrieval practice when items were repeated. However, retrieval practice produced comparable generalization to worked examples when items were varied. These findings suggest that variability supports generalization, particularly when learners must induce underlying rules, and that retrieval practice, traditionally associated with memory retention, can also facilitate inductive learning when applied to varied examples. This study emphasizes the importance of adapting learning strategies to align with the instructional context and task demands.

Despite strong evidence supporting spaced retrieval practice, few studies have implemented this approach in mathematics education in real classrooms while addressing individual differences in prior knowledge and performance. The current study tested adaptive spaced retrieval practice in Algebra I classrooms using a computerized system powered by the SuperMemo 2 (SM2) algorithm. Students practiced 10 selected learning objectives (LOs), with 6 assigned to the adaptive spaced practice condition and 4 to a no-practice control condition. Results revealed that LOs with lower initial accuracy were practiced more frequently with narrower spacing intervals. In contrast, LOs with higher initial accuracy received fewer practices with wider spacing, leading to significant improvements in accuracy from pretest to posttest. Although no significant differences were observed between the spaced practice and no-practice conditions, the findings highlight the potential of adaptive spaced retrieval systems to address individual learning needs to optimize their effectiveness in mathematics education.

Learning performance data, such as correct or incorrect answers and problem-solving attempts in Intelligent Tutoring Systems (ITSs), facilitate the assessment of knowledge mastery and the delivery of effective instructions. However, these data tend to be highly sparse (80% $\sim$ 90% missing observations) in most real-world applications. This data sparsity presents challenges to using learner models to effectively predict learners' future performance and explore new hypotheses about learning. This article proposes a systematic framework for augmenting learning performance data to address data sparsity. First, learning performance data can be represented as a 3-Dimensional (3D) tensor with dimensions corresponding to learners, questions, and attempts, effectively capturing longitudinal knowledge states during learning. Second, a tensor factorization method is used to impute missing values in sparse tensors of collected learner data, thereby grounding the imputation on knowledge tracing tasks that predict missing performance values based on real observations. Third, data augmentation using Generative Artificial Intelligence (GenAI) models, including Generative Adversarial Network, specifically Vanilla Generative Adversarial Networks (GAN), and Generative Pretrained Transformers (GPT, specifically GPT-4o), generate data tailored to individual clusters of learning performance. We tested this systemic framework on adult literacy datasets from AutoTutor lessons developed for Adult Reading Comprehension (ARC). We found that: (1) tensor factorization outperformed baseline knowledge tracing techniques in tracing and predicting learning performance, demonstrating higher fidelity in data imputation, and 2) the Vanilla GAN-based augmentation demonstrated greater overall stability across varying sample sizes, whereas GPT-4o based augmentation exhibited higher variability, with occasional cases showing closer fidelity to the original data distribution. This framework facilitates the effective augmentation of learning performance data, enabling controlled, cost-effective approach for the evaluation and optimization of ITS instructional designs in both online and offline environments prior to deployment, and supporting advanced educational data mining and learning analytics.

Understanding the challenges faced by second language (L2) learners in lexical tone perception is crucial for effective language acquisition. This study investigates the impact of exaggerated acoustic properties on facilitating Mandarin tone learning for English speakers. Using synthesized tone stimuli, we systematically manipulated pitch contours through three key modifications: expanding the fundamental frequency (F0), increasing F0 (female voice), and extending the overall duration. Our objectives were to assess the influence of F0 expansion, higher F0, longer duration, and varied syllables on Mandarin tone learning and generalization. Participants engaged in a non-adaptive trial-by-trial tone identification task. Mixed-effects logistic regression modeling was used to analyze accuracy across learning phases, acoustic factors, and tones. Findings reveal improvements in accuracy from training to testing and generalization phases, indicating the effectiveness of perceptual training to tone perception for adult English speakers. Tone 1 emerged as the easiest to perceive, while Tone 3 posed the most challenge, consistent with established hierarchies of tonal acquisition difficulty. Analysis of acoustic factors highlighted tone-specific effects. Expanded F0 was beneficial for the identification of Tone 2 and Tone 3 but posed challenges for Tone 1 and Tone 4. Additionally, longer durations also exhibited varied effects across tones, aiding in the identification of Tone 3 and Tone 4 but hindering Tone 1 identification. The higher F0 was advantageous for Tone 2 but disadvantageous for Tone 3. Furthermore, the syllable ma facilitated the identification of Tone 1 and Tone 2 but not for Tone 3 and Tone 4. These findings enhance our understanding of the role of acoustic properties in L2 tone perception and have implications for the design of effective training programs for second language acquisition.