Intelligent tutoring systems have demonstrated effectiveness in teaching formal propositional logic proofs, but their reliance on template-based explanations limits their ability to provide personalized student feedback. While large language models (LLMs) offer promising capabilities for dynamic feedback generation, they risk producing hallucinations or pedagogically unsound explanations. We evaluated the stepwise accuracy of LLMs in constructing multi-step symbolic logic proofs, comparing six prompting techniques across four state-of-the-art LLMs on 358 propositional logic problems. Results show that DeepSeek-V3 achieved superior performance up to 86.7% accuracy on stepwise proof construction and excelled particularly in simpler rules. We further used the best-performing LLM to generate explanatory hints for 1,050 unique student problem-solving states from a logic ITS and evaluated them on 4 criteria with both an LLM grader and human expert ratings on a 20% sample. Our analysis finds that LLM-generated hints were 75% accurate and rated highly by human evaluators on consistency and clarity, but did not perform as well explaining why the hint was provided or its larger context. Our results demonstrate that LLMs may be used to augment tutoring systems with logic tutoring hints, but require additional modifications to ensure accuracy and pedagogical appropriateness.

Knowledge Components (KCs) are foundational to adaptive learning systems, but their manual identification by domain experts is a significant bottleneck. While Large Language Models (LLMs) offer a promising avenue for automating this process, prior research has been limited to small datasets and has been shown to produce superfluous, redundant KC labels. This study addresses these limitations by first scaling a "simulated textbook" LLM prompting strategy (using GPT-4o-mini) to a larger dataset of 646 multiple-choice questions. We found that this initial automated approach performed significantly worse than an expert-designed KC model (RMSE 0.4285 vs. 0.4206) and generated an excessive number of KCs (569 vs. 101). To address the issue of redundancy, we proposed and evaluated a novel method for merging semantically similar KC labels based on their cosine similarity. This merging strategy significantly improved the model's performance; a model using a cosine similarity threshold of 0.8 achieved the best result, reducing the KC count to 428 and improving the RMSE to 0.4259. This demonstrates that while scaled LLM generation alone is insufficient, combining it with a semantic merging technique offers a viable path toward automating and refining KC identification.

Mastery learning improves learning proficiency and efficiency. However, the overpractice of skills--students spending time on skills they have already mastered--remains a fundamental challenge for tutoring systems. Previous research has reduced overpractice through the development of better problem selection algorithms and the authoring of focused practice tasks. However, few efforts have concentrated on reducing overpractice through step-level adaptivity, which can avoid resource-intensive curriculum redesign. We propose and evaluate Fast-Forwarding as a technique that enhances existing problem selection algorithms. Based on simulation studies informed by learner models and problem-solving pathways derived from real student data, Fast-Forwarding can reduce overpractice by up to one-third, as it does not require students to complete problem-solving steps if all remaining pathways are fully mastered. Fast-Forwarding is a flexible method that enhances any problem selection algorithm, though its effectiveness is highest for algorithms that preferentially select difficult problems. Therefore, our findings suggest that while Fast-Forwarding may improve student practice efficiency, the size of its practical impact may also depend on students' ability to stay motivated and engaged at higher levels of difficulty.

Large language models (LLMs) are increasingly used to generate feedback, yet their impact on learning remains underexplored, especially compared to existing feedback methods. This study investigates how on-demand LLM-generated explanatory feedback influences learning in seven scenario-based tutor training lessons. Analyzing over 2,600 lesson completions from 885 tutor learners, we compare posttest performance among learners across three groups: learners who received feedback generated by gpt-3.5-turbo, those who declined it, and those without access. All groups received non-LLM corrective feedback. To address potential selection bias-where higher-performing learners may be more inclined to use LLM feedback-we applied propensity scoring. Learners with a higher predicted likelihood of engaging with LLM feedback scored significantly higher at posttest than those with lower propensity. After adjusting for this effect, two out of seven lessons showed statistically significant learning benefits from LLM feedback with standardized effect sizes of 0.28 and 0.33. These moderate effects suggest that the effectiveness of LLM feedback depends on the learners' tendency to seek support. Importantly, LLM feedback did not significantly increase completion time, and learners overwhelmingly rated it as helpful. These findings highlight LLM feedback's potential as a low-cost and scalable way to improve learning on open-ended tasks, particularly in existing systems already providing feedback without LLMs. This work contributes open datasets, LLM prompts, and rubrics to support reproducibility.

Human learning relies on specialization--distinct cognitive mechanisms working together to enable rapid learning. In contrast, most modern neural networks rely on a single mechanism: gradient descent over an objective function. This raises the question: might human learners' relatively rapid learning from just tens of examples instead of tens of thousands in data-driven deep learning arise from our ability to use multiple specialized mechanisms of learning in combination? We investigate this question through an ablation analysis of inductive human learning simulations in online tutoring environments. Comparing reinforcement learning to a more data-efficient 3-mechanism symbolic rule induction approach, we find that decomposing learning into multiple distinct mechanisms significantly improves data efficiency, bringing it in line with human learning. Furthermore, we show that this decomposition has a greater impact on efficiency than the distinction between symbolic and subsymbolic learning alone. Efforts to align data-driven machine learning with human learning often overlook the stark difference in learning efficiency. Our findings suggest that integrating multiple specialized learning mechanisms may be key to bridging this gap. A key idea within the learning sciences, popularized by Anderson's ACT -R theory (2013) and expanded upon by others (Koedinger, Corbett, & Perfetti, 2012), is that human performance is enabled by independent knowledge components--individual facts, skills, or principles--that must be understood and retained to exhibit mastery of higher-level capabilities.

Recent improvements in large language model (LLM) performance on academic benchmarks, such as MATH and GSM8K, have emboldened their use as standalone tutors and as simulations of human learning. However, these new applications require more than evaluations of final solution generation. We introduce TutorGym to evaluate these applications more directly. TutorGym is a standard interface for testing artificial intelligence (AI) agents within existing intelligent tutoring systems (ITS) that have been tested and refined in classroom studies, including Cognitive Tutors (CTAT), Apprentice Tutors, and OATutors. TutorGym is more than a simple problem-solution benchmark, it situates AI agents within the interactive interfaces of existing ITSs. At each step of problem-solving, AI agents are asked what they would do as a tutor or as a learner. As tutors, AI agents are prompted to provide tutoring support -- such as generating examples, hints, and step-level correctness feedback -- which can be evaluated directly against the adaptive step-by-step support provided by existing ITSs. As students, agents directly learn from ITS instruction, and their mistakes and learning trajectories can be compared to student data. TutorGym establishes a common framework for training and evaluating diverse AI agents, including LLMs, computational models of learning, and reinforcement learning agents, within a growing suite of learning environments. Currently, TutorGym includes 223 different tutor domains. In an initial evaluation, we find that current LLMs are poor at tutoring -- none did better than chance at labeling incorrect actions, and next-step actions were correct only ~52-70% of the time -- but they could produce remarkably human-like learning curves when trained as students with in-context learning.

Large Language Models (LLMs) hold promise as dynamic instructional aids. Yet, it remains unclear whether LLMs can replicate the adaptivity of intelligent tutoring systems (ITS)--where student knowledge and pedagogical strategies are explicitly modeled. We propose a prompt variation framework to assess LLM-generated instructional moves' adaptivity and pedagogical soundness across 75 real-world tutoring scenarios from an ITS. We systematically remove key context components (e.g., student errors and knowledge components) from prompts to create variations of each scenario. Three representative LLMs (Llama3-8B, Llama3-70B, and GPT-4o) generate 1,350 instructional moves. We use text embeddings and randomization tests to measure how the omission of each context feature impacts the LLMs' outputs (adaptivity) and a validated tutor-training classifier to evaluate response quality (pedagogical soundness). Surprisingly, even the best-performing model only marginally mimics the adaptivity of ITS. Specifically, Llama3-70B demonstrates statistically significant adaptivity to student errors. Although Llama3-8B's recommendations receive higher pedagogical soundness scores than the other models, it struggles with instruction-following behaviors, including output formatting. By contrast, GPT-4o reliably adheres to instructions but tends to provide overly direct feedback that diverges from effective tutoring, prompting learners with open-ended questions to gauge knowledge. Given these results, we discuss how current LLM-based tutoring is unlikely to produce learning benefits rivaling known-to-be-effective ITS tutoring. Through our open-source benchmarking code, we contribute a reproducible method for evaluating LLMs' instructional adaptivity and fidelity.

Instructional designers face an overwhelming array of design choices, making it challenging to identify the most effective interventions. To address this issue, I propose the concept of a Model Human Learner, a unified computational model of learning that can aid designers in evaluating candidate interventions. This paper presents the first successful demonstration of this concept, showing that a computational model can accurately predict the outcomes of two human A/B experiments -- one testing a problem sequencing intervention and the other testing an item design intervention. It also demonstrates that such a model can generate learning curves without requiring human data and provide theoretical insights into why an instructional intervention is effective. These findings lay the groundwork for future Model Human Learners that integrate cognitive and learning theories to support instructional design across diverse tasks and interventions.

Intelligent tutoring systems (ITSs) are effective in helping students learn; further research could make them even more effective. Particularly desirable is research into how students learn with these systems, how these systems best support student learning, and what learning sciences principles are key in ITSs. CTAT+Tutorshop provides a full stack integrated platform that facilitates a complete research lifecycle with ITSs, which includes using ITS data to discover learner challenges, to identify opportunities for system improvements, and to conduct experimental studies. The platform includes authoring tools to support and accelerate development of ITS, which provide automatic data logging in a format compatible with DataShop, an independent site that supports the analysis of ed tech log data to study student learnings. Among the many technology platforms that exist to support learning sciences research, CTAT+Tutorshop may be the only one that offers researchers the possibility to author elements of ITSs, or whole ITSs, as part of designing studies. This platform has been used to develop and conduct an estimated 147 research studies which have run in a wide variety of laboratory and real-world educational settings, including K-12 and higher education, and have addressed a wide range of research questions. This paper presents five case studies of research conducted on the CTAT+Tutorshop platform, and summarizes what has been accomplished and what is possible for future researchers. We reflect on the distinctive elements of this platform that have made it so effective in facilitating a wide range of ITS research.

The field of Knowledge Tracing is focused on predicting the success rate of a student for a given skill. Modern methods like Deep Knowledge Tracing provide accurate estimates given enough data, but being based on neural networks they struggle to explain how these estimates are formed. More classical methods like Dynamic Bayesian Networks can do this, but they cannot give data on the accuracy of their estimates and often struggle to incorporate new observations in real-time due to their high computational load. This paper presents a novel method, Performance Distribution Tracing (PDT), in which the distribution of the success rate is traced live. It uses a Dynamic Bayesian Network with continuous random variables as nodes. By tracing the success rate distribution, there is always data available on the accuracy of any success rate estimation. In addition, it makes it possible to combine data from similar/related skills to come up with a more informed estimate of success rates. This makes it possible to predict exercise success rates, providing both explainability and an accuracy indication, even when an exercise requires a combination of different skills to solve. And through the use of the beta distribution functions as conjugate priors, all distributions are available in analytical form, allowing efficient online updates upon new observations. Experiments have shown that the resulting estimates generally feel sufficiently accurate to end-users such that they accept recommendations based on them.