educational software developers

Abstract: Mathematical supervision for language models is typically flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original sources. We introduce TOME-Math (Textbook-Oriented Mathematical Evidence), a large-scale corpus that converts 2,118 textbooks spanning the core areas of university-level mathematics subjects into approximately 380K structured proof-supervision records while preserving chapter order, proposition-proof links, dependency references, and source provenance. Leveraging these structural signals, we explore curriculum learning across multiple mathematical subjects and characterize scaling patterns with supervision volume and source breadth. At full scale, fine-tuning on TOME-Math raises the unweighted mean score across our held-out evaluations and established public benchmarks by 16.7 percentage points over the base model, while exceeding all three public instruction-data baselines evaluated in aggregate. Our findings highlight structured textbooks as both a scalable source of mathematical supervision and an empirical framework for studying the impact of data organization on mathematical reasoning. We will release the corpus to facilitate further research on structured mathematical supervision.

Abstract: Generative AI in education is usually judged by the output of human-AI teams. That focus overlooks a second outcome: what people can still understand, challenge, repair, and adapt when assistance changes or disappears. We call this tension the generative paradox and distinguish four manifestations: performance, assistance, ownership, and capability stock. We propose developmental function allocation, which complements operational function allocation and meaningful human control by treating retained human capability as a design objective alongside current joint performance. The Anti-Prompt paradigm reverses the default interaction order: when immediate generation would preempt a consequential human act, AI should first create the conditions for human construction. We distinguish the validity of a product, responsibility for its construction, and evidence of capability after support changes. Representative Anti-Prompts, a canonical interaction sequence, and stress tests spanning mathematical reasoning, experimental science, software diagnosis, and lesson design make these distinctions concrete. We conclude with falsifiable predictions about retained capability and a system-level hypothesis about the reproduction and distribution of expertise.

Abstract: Generative artificial intelligence (GenAI) is increasingly embedded in university learning, yet effective human-GenAI interaction depends not only on access to these tools but also on students' ability to formulate, evaluate, and refine prompts for academic tasks. This study examined university students' perceived GenAI prompting capability and reported prompting strategies. Questionnaire data from 234 students were analyzed using descriptive statistics, measurement modelling, scenario comparisons, structural associations, and qualitative coding of optional comments. Students reported using GenAI across diverse academic activities and generally expressed confidence in their prompting capabilities, particularly in providing relevant context and refining prompts following initial outputs. However, prompting strategies showed limited sensitivity to task types: specifying output format was more strongly endorsed in a creative workshop preparation scenario than in a research-oriented assignment, whereas other matched strategies showed no adjusted differences. Students also commonly endorsed both concise instructions and providing all relevant information at the outset, suggesting that effective brevity may depend more on selecting and organizing task-relevant information than on prompt length alone. By contrast, fixed prompt templates received lower endorsement than other prompting strategies. In the adopted factor model, perceived cognition showed the clearest unique association with perceived prompting capability, while open-ended responses highlighted prompt-intent alignment as a common challenge.

Abstract: In early mathematics, children learn abstract concepts through concrete representations, such as manipulating objects, drawing, and speaking. Learning with peers can enrich this process by exposing children to diverse strategies and enabling them to exchange ideas through interaction. We realized this potential with virtual peers in Peers4U, a multimodal learning system to enhance children's mathematical conceptual understanding. Virtual peers driven by LLMs are personalized to the learner's cognitive level and assigned multimodal solutions with inspectable processes. During learning, peers engage in mixed-initiative interactions by responding, initiating topics, and advancing discussions along a pedagogical progression. A user study with 22 children and two experts showed our learner-centered topic orchestration significantly outperformed a persona-centered baseline, and children spontaneously authored new artifacts to demonstrate inspired ideas or share their own strategies, producing significantly more solutions when grouped with more Leading Peers. We contribute design insights for multimodal, learner-centered virtual peer systems.

Abstract: Understanding how university students perceive the development of their generative artificial intelligence (GenAI) skills over time can clarify how GenAI use relates to learning and academic outcomes. This study examined perceived skill-development trajectories, changes in learning practices, and associated academic gains using a retrospective questionnaire with 313 analyzed responses and interviews with 18 students across subject areas. Descriptive and comparative analyses and exploratory structural equation modeling (SEM) were integrated with thematic analysis. Perceived developmental trajectories were heterogeneous: 34.2% of students reported rapid early improvement followed by a plateau, 28.4% steady improvement, and 21.1% delayed acceleration. Development was also uneven across skills, with improvement in evaluating GenAI outputs perceived as more challenging; assignments were the most frequently selected driver of skill growth. Interviews further indicated increasingly specific prompting, tailored verification, and selective delegation, although some students reported stable routines, dependence, skipped reasoning, or improvements attributable partly to better GenAI tools. Academic gains were reported more often for assignments than for examinations. The SEM indicated a positive indirect association between perceived skill growth and academic gains through adaptation of assignment processes, whereas academic gains did not clearly differ across developmental trajectory groups after multiplicity correction. The findings suggest that perceived GenAI skill development varies in both trajectory and skill domain and is associated with changes in learning practices and differentiated academic benefits.

Abstract: Advancing physics reasoning in large language models requires scalable training data that connect physical laws, concrete problem scenarios, and verifiable numerical answers. Expert-designed problems offer top-down control over physical laws, conditions, and scenarios, but require costly human effort. LLM-based synthesis from texts scales efficiently, but model-generated answers and assessments leave supervision vulnerable to hallucinations. We introduce TIRE, a framework for Top-Down Formula Instantiation with Reliable Execution that brings knowledge-driven problem construction to large-scale data generation. Top-down instantiation uses reusable physical formulas and their applicability conditions to control the physical relations and numerical configurations of generated problems. Reliable execution establishes reference answers before problem generation, providing a common numerical foundation for problem construction and teacher distillation. Together, these mechanisms combine control over problem content with execution-grounded supervision for both supervised fine-tuning and reinforcement learning. Using TIRE, we construct TIRE-19k, spanning nine subfields of physics. Across 3 backbone LLMs and 4 benchmarks, TIRE-19k outperforms 5 representative datasets with equal amounts of SFT data, exceeding the strongest baseline by 2.86 percentage points on average. Further GRPO raises Qwen3-8B's average accuracy by 1.52 percentage points over its TIRE-19k SFT checkpoint. These results demonstrate the value of generating physics training data from explicit physical knowledge with reliable execution.

Abstract: Reinforcement learning from internal feedback can improve language models without ground-truth answers or external verifiers. However, confidence and correctness can diverge during training, and continued optimization of average self-certainty can increase confidence while degrading reasoning accuracy. We introduce SIF, a reinforcement learning method that combines comparative reward construction with selective policy updates. SIF compares ranked token-level self-certainty profiles across multiple windows and peers, assigning positive rewards only when both levels of voting provide sufficient support. Sample and group level filtering determines which responses contribute to policy optimization. Experiments on three backbones across 12 mathematical and scientific reasoning benchmarks show that SIF's final checkpoints achieve higher average accuracy than the best-validation checkpoints of Intuitor and Vigor, with a gain of 4.71 percentage points over Intuitor on Qwen2.5-Math-1.5B. Further analyses show better retention of accuracy during continued optimization, while test-time training experiments demonstrate sustained improvements with as few as four rollouts per prompt.

Abstract: Chemistry evaluation has moved past multiple-choice probes toward open-ended expert problems, yet the benchmarks that define the current frontier still score answer endpoints alone. Such scoring conflates memorized facts with stepwise derivation, treats visual and textual inputs as interchangeable, and confounds long-horizon planning with stepwise execution. These blind spots prevent any diagnosis of where the reasoning chain breaks in a model. We present ChemArgus, a competition-level chemistry benchmark drawn from chemistry competition material, textbooks, and research papers, whose scoring replaces the answer endpoint with three measurement properties. Fine-grained scoring grades every subquestion point by point with partial credit, so a score lands at the level of the step rather than the outcome. Multimodal capability is priced on every problem containing a real image, paired with a controlled text description, so visual understanding is measured against text on identical tasks. Diagnostic attribution reads paired metrics that share one scoring unit and differ only in context construction, so a gap between two scores isolates a single cause, namely integration, propagation, or local reasoning. GPT-5.6-Sol scores 23.2% on unassisted whole-problem solving against 28.8% and 30.4% under the two sequential metrics, a gap measuring the integration burden. Through rubric partial credit and these cause-isolating score gaps, ChemArgus shows not only whether a model answers chemistry correctly but where its reasoning chain fails, so that every score it reports doubles as a diagnosis, a readout of the chain rather than a verdict, aiming to guide language models step by step on their path toward chemistry expertise, one corrected step at a time, each step priced by the rubric, point by point.

Abstract: Simulated students let researchers test tutoring systems and teaching strategies before real learners are available, but only if the simulation reproduces where a particular learner succeeds and fails. The common approach asks a large language model to role-play a student, but a role does not model what this learner knows or will do next, so the model's own competence fills the gap. Simulated students perform at a level set by the model, differ little from one another, and seldom make the real learners' errors. We model the learner's behavior and recast student simulation as third-person prediction of the learner's next action. HACHIMI-II builds a student model from the learner's history, infers the learner's state for the current item or tutor turn, and compiles it into a behavior harness that constrains the next action. On three item-response datasets, the Wasserstein-1 distance between simulated and real student ability is 2.4--8.4$\times$ smaller than that of the strongest baseline. On two dialogue datasets, HACHIMI-II reproduces real student errors with the same knowledge type, locus, and mechanism 1.8--5.1$\times$ more often than the strongest baseline, and ablations trace the gains mainly to the explicit learner state. Predicting the learner makes capable models usable as simulated students.

Abstract: Existing student models in educational applications largely focus on student responses to questions. However, as tutoring becomes more accessible at large scale, it is important to analyze dialogues between tutors and students, which may reveal fine-grained evidence on student knowledge. In this work, we propose a unified framework that models both student responses to questions and tutor-posed subtasks during dialogues on a shared item response theory (IRT) scale. We first identify mathematical subtasks in tutoring dialogues, rewrite them into self-contained questions, and identify the correctness of student responses to these subtasks. We then develop an IRT framework that estimates question/subtask difficulty from text, tracks students' evolving abilities across question-answering and dialogue interactions, and a novel method to leverages tutor moves between consecutive subtasks to regularize their difficulty values. We evaluate our framework on two real-world math education datasets containing both human- and AI-tutored dialogues. Results show that our framework outperforms strong baselines on both question difficulty prediction and response correctness prediction.

Abstract: Human-AI Interaction is commonly evaluated by what an artificial agent enables during use, yet interaction can also alter the human who acts next. We introduce Residual Human States, a trajectory-based framework for representing the potentially multidimensional human state carried forward after interaction with AI, relative to a relevant alternative trajectory. The framework distinguishes assisted output from human-state transition and derives four empirical propositions: multidimensionality, interaction-policy dependence, horizon dissociation, and temporal persistence. Its central claim is that assisted performance does not by itself determine the human state carried forward. We examine these propositions through four empirical cases with different inferential roles. Published medical-training evidence illustrates how one AI interaction history can be associated with both slightly higher observed accuracy on some later unaided cases and transmission of a systematic decision bias on others. A second diagnostic-learning study shows that later unaided behaviour differs across AI-support policies, while also revealing that aggregate accuracy cannot by itself distinguish improved discrimination from a shifted response criterion. In a classroom experiment, generative-AI tutoring substantially improved assisted practice performance without a corresponding detectable gain on a subsequent unaided exam. A longitudinal reanalysis of personalised AI dialogue further shows that residual contrasts can evolve across post-interaction horizons and that such change may arise from the comparison trajectory as well as from the focal intervention. Evaluating interactive AI systems therefore requires attention not only to contemporaneous performance, but also to which human states alternative interaction trajectories produce, relative to which counterfactuals, and how durably.

Abstract: Generative AI is increasingly studied as a tool for supporting lesson authoring; the creation and adaptation of classroom materials, yet little is known about how it should fit into secondary computing teachers' subject-specific practices. We conducted two complementary qualitative studies with eight secondary computing teachers: focus groups examining existing authoring practices and a think-aloud study using LessonBuilder, a structured AI-supported lesson authoring system, as a research probe. We found that teachers' instructional intentions developed through creating, inspecting, and adapting materials, while teachers selectively delegated tasks to AI and retained responsibility for judging classroom readiness. The think-aloud sessions further showed how examining AI-generated materials prompted teachers to clarify and refine their intentions, making authoring an ongoing negotiation between what teachers intended and what the AI produced. In the context of computing lessons, classroom readiness also involved considering how programming materials and supporting guidance matched students' understanding and intended learning goals. We synthesize these findings into a conceptual model explaining how teachers coordinate instructional intent, AI assistance, and judgments of classroom readiness during lesson authoring. We derive design recommendations for supporting this coordination while preserving teacher control and addressing computing-specific authoring needs.

Abstract: Recent approaches to simulated and synthetic users offer new ways to support design, but raise questions about how computational representations of users should contribute to design practice. We present NeuroDivSim, an interactive tool that explores simulation as an inspectable mechanism for reflecting on cognitive diversity during design and prototyping. Rather than using an LLM to act as a simulated user, NeuroDivSim uses generative AI to construct inspectable task, interface, and environment models from a usage scenario. After human review, these models are combined with explicit cognitive reference configurations and processed through deterministic simulation. This enables designers to hold a modeled usage situation constant while varying cognitive assumptions and tracing their consequences to interaction steps and rule-based design recommendations. We further report an exploratory pilot evaluation (N=10) that provided formative insights into how participants engaged with the workflow and informed subsequent refinements to the presentation of models, simulation results, and recommendations.

Abstract: Automatic Short Answer Scoring (ASAS) is central to NLP for Education. However, openly available benchmarks remain scarce, and existing datasets largely address how well students answer a question directly rather than how well they master underlying concepts (knowledge elements) such as thermal energy or epistemic activities (skills) such as reasoning or claim. To address this gap, we introduce Alice, a large-scale, rubric-based German ASAS dataset that is pedagogically aligned and comprises three subtasks: (i) learning performance (Alice-LP), (ii) knowledge elements (Alice-KE), and (iii) skills (Alice-SK). We further formulate rubric-based ASAS as a rubric-retrieval task and benchmark the dataset with a range of language models, from encoder-only models to lightweight LLMs. We also benchmark the dataset with zero-shot prompting via LLMs and a standard classification baseline. The experiments show that LLMs, in particular, struggle to score knowledge elements and skills in the zero-shot setting. They also indicate that rubric text is often useful, especially for Alice-KE and Alice-SK, while on Alice-LP gains over sample-solution-focused inputs are more modest and vary by model and input format.

Abstract: We present TutorLoop, a sensor-in-the-loop system that regulates student learning behaviors by delivering adaptive feedback based on real-time cognitive states. Unlike prior large language model (LLM) tutors that directly depend on scenario-specific content, TutorLoop operates on sensor-derived signals captured via webcams. Moreover, unlike direct cognitive-to-feedback mappings that are short-sighted, the system employs a deep reinforcement learning (DRL) agent to optimize the feedback type across the entire learning process. Finally, another LLM tutor refines feedback into human-like, context-aware messages. We evaluate TutorLoop in a large-scale user study (N=187), where a model trained offline is directly applied to a new learning task without retraining. Results show that TutorLoop provides less frequent yet more effective interventions, improving attention, reducing workload, increasing engagement, and ultimately enhancing learning outcomes. These findings highlight the potential of closed-loop, sensor-driven feedback for scalable human-AI integrated systems to support learning.

Abstract: Autoregressive Large Language Models (LLMs) frequently struggle with deterministic multi-step algorithmic tasks such as multi-digit multiplication and long division. In this paper, we investigate the mechanics of multi-step arithmetic in compact "Tiny" Transformers (~10.6M non-embedding parameters, 49.3M total) trained on synthetic data across four basic operations (+, -, *, /) unrolled as step-by-step scratchpads. First, we establish the necessary training foundations: (1) dataloader sequence padding creates an 83% gradient starvation artifact that collapses accuracy from 40% to 1%, remediated via continuous sequence packing; (2) linguistic pretraining is an essential prerequisite (<= 2.0% without it); and (3) modern architectural primitives (RoPE, RMSNorm, SwiGLU) and Sparse Mixture of Experts (MoE) substantially improve additive reasoning over baseline GPT-2. Second, we demonstrate that algorithmic scratchpad formulation directly dictates success. Introducing a deterministic Digit-by-Digit Long Division scratchpad within a 4-stage Hierarchical Developmental Curriculum dramatically elevates single-digit division from 4.0% to 86.7% accuracy on a 4,000-problem held-out benchmark. In contrast, multi-digit multiplication remained challenging: detailed error analysis revealed that while the model correctly computed single-digit sub-products and place-value zeros, our FOIL scratchpad failed because it forced a simultaneous summation of up to nine multi-digit terms in a single step without pairwise intermediate accumulation. Finally, we identify two key boundaries: performance collapses to 0.00% on unseen 4-digit operands, and unbuffered training induces catastrophic forgetting, collapsing division accuracy from 86.7% down to 0.00%.

Abstract: Large language models (LLMs) have become increasingly capable problem solvers, but being able to solve a problem is not the same as being able to teach it. Existing approaches to training LLMs as teachers rely on demonstrations, preference data, or predefined pedagogical criteria that specify what good teaching looks like. However, these signals are often not grounded in individual student learning outcomes, where effective teaching strategies can vary substantially across learners. To address this, we introduce Sherpa, a multi-turn reinforcement learning framework that instantiates multiple student archetypes with LLMs conditioned on distinct learning preferences and trains a teacher model to adapt its instruction by directly maximizing their learning outcomes. Teacher LLMs trained with Sherpa improve instructed students' performance across all archetypes by an average of 20.5 percentage points. Under MathTutorBench's evaluation, Sherpa raises the overall pedagogy score from 52.5% to 79.2%, indicating better teaching responses. Our human studies show that the trained teacher is preferred over the base model in 79.6% of pairwise comparisons. Together, Sherpa trains LLM teachers to adapt to diverse simulated students and become better aligned with human teachers, paving the road towards AI tutors teaching real students.

Abstract: In K-12 mathematics tutoring, student-tutor dialogue provides rich evidence of learners' problem-solving processes and sources of difficulty. Learning analytics research increasingly relies on large language models (LLMs) to extract such information from dialogue for a variety of downstream tasks, including knowledge tracing, behavioral modeling, and diagnosis of student reasoning errors. However, the validity of these model-generated interpretations remains insufficiently understood. In this exploratory study, we examine the validity of LLM classifications of five student failure modes in mathematics tutoring dialogue using an operational diagnostic codebook: uncertainty, misattribution, operator selection, conceptual gap, and procedural slip. Across models, human-LLM agreement was moderate (kappa = .524-.597), while cross-model agreement was substantially higher (kappa = .755-.781; alpha = .769). These findings show that cross-model agreement can create a misleading appearance of correctness, challenging the assumption that consensus among LLMs constitutes evidence of valid learner interpretation. For learning analytics, the implication is clear: scalable labeling is useful only if the inferred constructs are valid, and model consensus cannot substitute for independent evidence of that validity.

Abstract: The widespread availability of LLMs is challenging written learning activities, as students can increasingly generate responses without necessarily engaging with the learning content. Conversational AI creates an opportunity to redesign these activities as dialogue, while multilingual capabilities may make such dialogue more accessible to students learning through a non-native language. We conducted a field study with 305 native Kannada-speaking undergraduate students at English-medium institutions in Karnataka, India. We compared written response activities with text- and voice-based dialogic activities with AI, each conducted in English-only or bilingual Kannada-English settings. Students who completed dialogic activities spent more time on the activities, contributed more, and reported greater interest and self-efficacy than those completing written responses, although fewer students completed the dialogic activities overall. Knowledge increased across all conditions, with no reliable differences in gains between activity formats or languages. Language shaped participation differently across modalities: bilingual interaction was particularly beneficial in voice dialogue, where it reduced articulation difficulties, increased turns demonstrating understanding, and reduced conversation abandonment. However, students also valued English because of its connection to their academic and professional aspirations. These findings show that designing dialogic learning with AI requires more than choosing between writing and dialogue, voice and text, or English and students' native languages. We highlight opportunities to give learners greater control over modality, information, and pace, and to use native languages as translanguaging support rather than as a replacement for English.

Abstract: Motivated by educational applications, we study the problem of computing all corrections that transform a finite automaton into one recognizing a given regular language L. We show that for deterministic finite automata the set of all corrections can be finitely characterized as a regular tree language. The construction is based on a tree encoding of all deterministic finite automata recognizing L, which is extended to correction trees that make individual corrections and their induced edit-operations explicit. Leveraging the closure properties of regular tree languages, we introduce so-called filters for selecting corrections satisfying didactic constraints, enabling the derivation of individualized feedback from student submissions.

Abstract: Cognitive Diagnostic Models (CDMs) identify which specific skills a student has and has not mastered, the signal a personalized learning path needs and a single aggregate score cannot give. Yet they are rarely deployed. The obstacle is their precondition: the Q-matrix, a mapping from every assessment item to the skills it requires, historically authored by hand. We separate the task into two stages: first construct the curriculum's own knowledge graph, the full space of concepts and skills it contains, independent of any item; then map items against that graph on demand. This paper addresses the first stage only. The item-mapping stage is designed but not implemented here, so the claim that this shifts judgment cost from once per item to once per curriculum is a design rationale rather than a finding. We present Curriculum Brain, a two-repository system pairing a version-controlled knowledge base with an agentic pipeline of eleven single-responsibility agents under a thin deterministic orchestrator. It generates candidate concept-skill mappings from official curriculum documents, checks them against accumulated rules, and compares them with a concept-skill map extracted independently from the textbook, repairing its own failures and escalating to a human only when it cannot resolve a case itself. Across 241 chapter runs (168 distinct chapters), 41.5% produced a Generator output passing both checks without a patch, and 67.6% resolved without escalation. Both are measured against criteria the system itself produced, so both describe internal consistency rather than agreement with an external standard, and both pool two pipeline configurations separated by a single change at run 77; after it the figures are 57.0% and 91.5%. Observed spend was $1.19 per chapter, API spend only, excluding human review. We release both the framework and the resulting curriculum dataset.

Abstract: Designing learning interfaces is often an ill-structured problem: effective solutions depend on learning goals, subject matter, learner characteristics, and interaction context that are difficult to generalize. Designers must integrate knowledge from learning sciences, interaction design, and subject domains when translating learning goals into interface decisions. Yet, prior efforts to connect learning theory and design have largely focused on learning activities or specific technologies, leaving interface-level design knowledge fragmented across systems. In this work, we take a bottom-up approach to surface this knowledge from existing educational interfaces. We present LINK (Linking INstructional Knowledge to interfaces), a library of 27 recurring interface patterns, organized under nine higher-level design commitments, which describe broader learning-science-grounded goals for interfaces. As part of developing LINK, we conducted a user study (N=14) with designers to evaluate LINK's generative power. Our findings suggest that LINK helps designers generate interface ideas and articulate theory-grounded rationales for design decisions.

Abstract: Recent benchmarks rely on user simulators to evaluate AI agents in multi-turn interaction. While existing simulation techniques demonstrate surface fidelity to human style and behavior, ecologically valid interactive benchmarking also requires alignment in when and how agents fail across simulated and real user populations. We find that existing simulators lack outcome calibration: agreement with observed success rates and failure patterns when real users interact with the same agent. We introduce Calibrated User Embeddings (CUE), a framework that both encodes observed sessions and samples continuous representations, then decodes them into persona commands to steer LLMs to act as user simulators without training. Through this, we evaluate user-conditioned replay of past sessions and aggregate metric agreement when sampling novel personas for the same tasks. On $τ^2$-Bench, CUEd simulators commit fewer simulator-attributed errors and more faithfully reproduce real-user agent failure modes, aggregate success rates, and outcomes for specific task-user pairs than other persona-based simulation methods. These gains coexist with competitive user fidelity as measured using metrics established in prior work. After being fit to mostly customer support interactions, the same CUEd simulators generalize to document creation, math tutoring, and casual conversation, and remain effective across different simulator LLMs without CUE retraining.

Abstract: This paper describes a mathematics interface intended for both educational applications and exploratory mathematics. Both learners and mathematics practitioners often use pen and paper or a whiteboard to perform equational reasoning, manipulate expressions, or construct proofs. These workflows lead to a variety of problems: transcription errors, tedious writing and notation, and/or unclear standards for proof justification. We extend the Hazel Prover, an equational-reasoning interface in the Hazel live programming environment, to add capabilities for exploratory mathematics, with varying levels of verbosity and automation aimed at both students and expert users. Students require more deliberate practice when learning mathematical concepts and correspondingly more verbose justifications, while experts may benefit from significant mathematical automation. With this in mind, our interface supports multiple levels of mathematical automation and simplification, grounded in a rewrite search architecture. For expert users, motivated by a gap in the accessibility of formal methods, we support proof export to the Rocq theorem prover, extending this rewrite search to proof tactics. This paper closes with several case studies covering elementary- to college-level mathematics.

Abstract: This research full paper examines how undergraduate students use large language models (LLMs) across computer science subfields. As LLMs become increasingly integrated into computing education, understanding how their use varies across technical and pedagogical contexts is essential for designing effective, subfield-aware instruction. This paper presents a cross-subfield analysis of LLM usage among 211 undergraduate students in a problem-solving course intentionally designed to support responsible and effective LLM use through structured instruction and reflection. Using post-assignment reflection data collected across seven instructional modules spanning multiple computer science subfields, we examine prompt counts, LLM role conceptualization, and verification behavior. Results show that LLM adoption varies substantially by assignment, with higher usage in algorithms and web development and lower usage in software engineering. Students predominantly treat LLMs as assistive tools rather than authoritative sources, and verification is common across all subfields, with most students using multiple strategies. Verification behavior also varies by assignment context, with testing more common in structured tasks and web search more common in open-ended tasks. These findings suggest that assignment characteristics play a central role in shaping how students interact with and evaluate LLM outputs, even under a single, consistently applied instructional design. This work contributes empirical evidence on how LLM adoption, role conceptualization, and verification behavior vary across computer science subfields, extending our prior work on structured, reflective LLM instruction to show how its effects differ by task rather than only in aggregate.

Abstract: We present an educator-guided LLM pedagogical agent for scaffolded feedback in conceptual database design. Integrated into an entity--relationship diagram (ERD) editor, the system grounds feedback in the student artifact, assignment requirements, educator-authored rubrics, and instructional resources. Its architecture separates hidden, artifact-grounded diagnosis from the workflow that controls the form and disclosure level of student-facing support. We instantiate the architecture as a four-stage workflow progressing from concept checks and guided application to low-detail feedback and localized clarification. Each feedback request creates a stateful episode linked to versioned ERD states. In a deployment spanning three ERD environments and 383 feedback episodes, 71.1\% of observed target-level changes fully or partially incorporated the hidden diagnostic target, including many after Stages~1--2. Qualitative analysis showed that staged disclosure sometimes withheld inaccurate details, supported selective uptake, or allowed later recovery, though some errors still shaped revisions. Survey responses from a self-selected sample favored delayed disclosure and student agency but noted indirectness and repetition.

Abstract: Large language models are increasingly used as collaborators on deductive-reasoning tasks, but their outputs can hallucinate or pull users away from intended reasoning. Formal proof assistants provide machine-checked verification, but have a steep learning curve and require more granular reasoning than human written proofs. We explore an interface that combines these strengths, allowing users to write and revise free-form natural-language proofs while a verified backend checks their reasoning and returns feedback at the user's granularity. We study this interface in the context of undergraduate mathematics education by developing LeanSide, a formally verified co-reasoning system, which auto-formalizes student reasoning into Lean and informalizes verifier output into understandable feedback. We conducted user studies through classroom deployment and analyzed which system properties helped students make progress and which caused them to get stuck. We use these findings to derive design implications for using a formally verified backend in human-AI co-reasoning systems.

Abstract: Bengali secondary education lacks curriculum-grounded benchmarks for STEM question-solving, and general-purpose language models struggle with the precise terminology, unit conventions, and derivations that physics problems demand. We introduce PhysicsMate, a benchmark of 1834 question-answer pairs built from the National Curriculum and Textbook Board (NCTB) Grade 9-10 physics syllabus and grounded in a multi-relational knowledge graph of 1760 nodes and 2600 edges across ten ontological types. We Low-Rank Adapt at 0.6B, 1.7B, and 4B parameters, with a unified recipe and demonstrate a significant increase in closed-book accuracy in all scales (+5.5, +15.0, and +23.3 percentage points). A node-type analysis shows that the most benefited by adaptation is the structured curricular knowledge, which consists of physical quantities and named laws, while the least benefited is the loosely specified entity-level knowledge. The 4B model has been adapted and quantized to a small offline binary that can be used for local inference in resource constrained environments and offers a viable path to curriculum aligned physics support in environments with limited connectivity and hardware.

Abstract: Mastery-based education increasingly places the reporting of learning progress in students' hands, who record task completion on learning dashboards. The usefulness of such self-reports depends on how closely reported mastery corresponds to demonstrated competence. Most evidence on student self-assessment compares an overall self-rating with an overall examination score and therefore provides limited evidence about which tasks or which students account for the mismatch. This study examines first-year students' self-assessment against viva-demonstrated mastery at the level of individual tasks across a ladder of sixty programming tasks. The study draws on a large first-year programming course taught in 2023, involving 203 students and 12 examiners, in which every reported task was verified through an oral viva. Because a task entered the Viva only after it was reported, the design is one-sided and captures over-estimation but not under-estimation. Of 11,093 reported tasks, 10,885 (98.1%) were demonstrated, indicating a high degree of correspondence between self-report and demonstrated mastery. The remaining 208 overestimations were not evenly distributed. A small number of students accounted for most of the errors, and they occurred mainly on difficult tasks near the end of the task ladder rather than on higher-point tasks. This task-level analysis shows that high overall self-assessment accuracy can coexist with specific areas where reported and demonstrated mastery diverge. It also provides a practical basis for directing additional verification and formative feedback toward students and tasks where such divergence is more likely.

Abstract: Generative AI has changed how students produce writing assignments. The final artifact is no longer sufficient to understand the process through which it was produced. We introduce DraftTrace, a writing environment that jointly captures three complementary views of writing: the final product, the writing process and interactions with an integrated AI-assistant. DraftTrace reconstructs how a document develops over time and organizes these signals into submission, longitudinal, and class-level analytics for instructors. We deployed DraftTrace in a graduate NLP course with 81 students and compared their sessions with LLM-generated responses entered by automated tools and with copy-typed responses. While product measures distinguish differences in text formulation, process measures distinguish differences in how text is entered. Considering both views together helps characterize cases such as copy-typing. Interaction traces show that students use the assistant differently across stages of writing: to clarify the question at an early stage and to verify answers at a later stage. A preliminary instructor survey highlights the importance of multi-view writing analytics and their interpretability.

Abstract: Scientific discovery requires not only recovering mathematical laws that describe observable behavior, but also identifying the mechanisms that generate them. Existing benchmarks for symbolic regression and scientific agents primarily evaluate phenomenal-law recovery, leaving mechanism discovery largely untested. We introduce MechBench, a benchmark that explicitly separates these two capabilities. Each task is defined by a mechanistic model, a structured set of scientifically meaningful relations whose joint consequences entail an observable phenomenal law, while agents receive only observational data and scientific context. We evaluate mechanism recovery through mechanism probes, which query internal scientific consequences that cannot be inferred from the phenomenal law alone. To reduce reliance on memorized textbook mechanisms, we construct unfamiliar variants through controlled, scientifically interpretable mutations of canonical mechanisms, and screen for mechanistic indistinguishability to exclude ambiguous instances admitting comparable competing mechanisms. Experiments across representative scientific agents reveal a substantial phenomenal--mechanism recovery gap: for Codex with GPT-5.6-sol, phenomenal-law accuracy reaches 35.00% on the Core-set while mechanism accuracy is only 13.75%, with mechanism recovery failing in 64.29% of cases where the phenomenal law is correctly recovered. The gap widens as mechanisms become increasingly mutated, and even providing the correct phenomenal law leaves mechanism recovery below 50%. These results reveal a substantial generalization gap in mechanistic reasoning and establish mechanism discovery as a distinct challenge beyond recovering observable scientific laws.

Abstract: While recent studies have explored human behavior and preference simulation using large language models (LLMs), it remains unclear how well LLMs can simulate subjective evaluations from real learners in educational settings. We investigate this question using real learner evaluation data on feedback for high-school biology questions at both the group and individual levels. We compare performance with and without learner-specific information, such as personality traits and evaluation examples, across six models. Our results show that LLMs still have a limited ability to simulate learner evaluations. Providing learner profiles and examples improves score calibration and individual-level simulation, but more often fails to improve group-level consistency. These findings highlight the need to investigate which learner information and adaptation strategies are effective for learner preference simulation.

Abstract: Large Language Models (LLM) have become popular tools in education. Therefore, understanding how students interact with LLMs for learning purposes is an important aspect of the responsible design and development of LLM based learning tools. However, existing research has focused on evaluating model performance, specific use cases, and students' attitudes toward LLM in education. There has been limited empirical work exploring students' interaction strategies with LLMs in computing education. This study draws on Self Regulated Learning (SRL) theory and conducts a survey of 225 undergraduate and graduate computing students to investigate how students use LLM tools during learning, the perceived learning impact, and the strategies they rely upon when using these tools. Students used LLMs across nine functional categories, most often to explain concepts, learn new material, find information, debug, and generate ideas. They also adopted some strategies such as supplying detailed context and iterative prompting. The most common difficulties encountered with LLM tools were incorrect information, generic responses, and difficulty trusting the model's reasoning. We synthesized these patterns through an SRL lens and offer a Probe Monitor Shape heuristic to map students' LLM interaction strategies onto the phases of self-regulated learning.

Abstract: Revision traces provide valuable evidence about students' writing processes, but their usefulness for learning analytics depends on how individual revisions are represented. Automated draft-comparison methods often produce granular edit operations that can fragment a single purposeful revision into multiple analytic units. This study evaluates whether LLMs can identify meaningful revision unit boundaries in structured revision operation data and whether they provide value beyond simple non-LLM baselines. Using 113 matched draft--revision pairs from undergraduate writing, expert annotation yielded 4,344 candidate boundaries. We compared zero- and few-shot GPT-5.5 and base Qwen3-32B, parameter-efficient fine-tuning of Qwen3-32B, and majority and proximity-based baselines. Despite receiving revision context and task instructions, no prompted LLM condition outperformed the proximity heuristic (macro-F1 = .825). In contrast, fine-tuned Qwen3-32B using the two context representation achieved the highest macro-F1 (.859), identifying more same-unit relationships while maintaining precision comparable to the heuristic. Deterministic post-processing substantially improved the prompted models but added little benefit to the strongest fine-tuned model. These findings suggest that LLMs can support revision boundary judgment when task-adapted, but general purpose prompting alone may not outperform transparent structural heuristics.

Abstract: Worked examples are a powerful form of instruction, but learners must infer how the demonstrated steps were produced. A naive simulation of this self-explanation process can generate thousands of numerical explanations that reproduce one observed change without capturing its underlying procedure. We propose structure-mapping-guided self-explanation as a computational account of the cognitive biases that reduce search effort and make this inference tractable. The model represents mathematical expressions as typed relational structures and uses structure mapping to identify corresponding source and target regions. For each changed target value, the corresponding source region serves as an anchor: it guides abductive search toward structurally relevant values and operations before broader alternatives, yielding ordered, executable candidate procedures with inspectable source evidence. Across 70 mathematical transformations containing 120 changed numeric components, the model recovered every intended procedure. It returned the intended procedure before any other computation producing the same target value in 104 subproblems (86.7%), compared with a median of 32 (26.7%) across 100 unguided runs that tested candidate calculations in random order. Our proposed model also tested 93.8% fewer combinations of values and operations than unguided search before reaching the intended procedures. These results provide an efficient, interpretable account of how relational structure can guide procedural learning and a testable hypothesis about human self-explanation from worked examples.

Abstract: Large language models (LLMs) are increasingly integrated into educational settings, yet educators lack robust, standards-aligned tools to evaluate their effectiveness in K-12 science contexts. Existing benchmarks predominantly assess general language or advanced scientific reasoning, leaving a critical gap in understanding LLMs' performance on content directly relevant to secondary science curricula. To address this gap, we developed a comprehensive NGSS-aligned benchmark for both middle and high school science using a rigorous synthetic data pipeline, multi-judge validation, and item-level psychometric analysis. Nine open-weight LLMs were systematically evaluated using this benchmark, indicating that several smaller, locally deployable models achieved high accuracy across diverse science domains and question types. Our findings indicate that model size did not consistently predict performance, emphasizing the importance of intentional model selection for educational deployment. We then incorporated a human reviewer into the loop, reviewing the items generated by the LLMs for alignment with NGSS standards. The human review indicated that synthetically generated items were not in perfect alignment with the NGSS standards, indicating the benefits of human-in-the-loop item development, the need to explore the intersection of content and pedagogical knowledge, and the need to extend benchmarks to evaluate LLMs' capacity for interactive, evidence-based feedback in educational scenarios.

Abstract: AI teaching assistants (AI TAs) backed by large language models (LLMs) and pedagogical guardrails are increasingly being integrated into programming courses, providing students with scalable access to hints, conceptual explanations, and code-level feedback. However, guardrails may also create friction. If students feel that the support provided is overly restrictive or poorly contextualized to their current progress, they may bypass approved tools for general-purpose LLMs. To investigate how AI TA design affects students' learning experiences, we conducted a randomized controlled trial with 132 students in an introductory programming course. Students completed three tasks related to code-writing and debugging and were randomly assigned to one of four AI TAs varied across two dimensions: pedagogical guidance style (Socratic vs. Direct instruction) and context awareness (no context vs. full context of the problem and student solution). We examined students' perceptions, interaction behaviors, and evidence of post-task comprehension. Students rated the Socratic AI TA with full context least favorably, reporting significantly lower perceived support for task completion. Descriptively, this condition also showed the highest observed interaction stress, the highest rate of external LLM use, and the lowest proportion of post-task explanations demonstrating full comprehension, though these differences were not statistically significant. These findings suggest that guardrailed AI TAs are not automatically better for learning. Instead, their effectiveness depends on how pedagogical guidance and contextual awareness are balanced in ways that students experience as useful, supportive, and worth continuing to use.

Abstract: Teachers are increasingly using generative AI to support instruction, yet it remains unclear how pedagogical intentions are translated into chatbot configurations and reflected in chatbot behavior. We studied a teacher-facing chatbot authoring tool in professional development workshops with 27 middle school teachers, analyzing focus-group interviews alongside configuration and interaction logs. Teachers envisioned chatbots as instructional scaffolds that could provide differentiated support, extend access to assistance, and preserve student thinking within teacher-defined boundaries. Configuration analysis showed that Purpose primarily captured instructional goals and content focus, whereas Rules more often specified pedagogical behavior, guardrails, and learner-specific adaptations. Log-based evaluation showed stronger alignment for responsiveness (88.9%) and persona (81.5%) than for rules (70.4%) and purpose (59.3%). These findings show that configurable controls alone do not ensure pedagogical fidelity and highlight the need for authoring tools that help teachers express, test, and refine intended chatbot behavior.

Abstract: Students increasingly turn to AI for help with problem-solving, yet too much AI support can undermine learning itself. To benefit from AI, students need to specify the necessary knowledge and scaffold type in their questions. However, they struggle to formulate such targeted questions because they lack metacognitive skills to recognize and select effective help options. We developed HelpCoach, an add-on for chat interfaces that helps students formulate knowledge- and scaffold-specific questions and receive targeted help during problem solving. HelpCoach continuously assesses students' help-seeking performance and prompts students to improve through an adaptive revision template. Whereas prior work has largely taught help-seeking skills apart from learning tasks, HelpCoach's in situ scaffold enables concrete practice on metacognitive skills and immediate revisions to help-seeking behavior. In a study with 40 college students learning web programming, HelpCoach led to more specific questions during chatbot interactions and greater knowledge retention than pre-task help-seeking training alone.

Abstract: We investigate whether state-of-the-art large language models (LLMs) generate feedback that reflects the pedagogical practices of expert teachers in terms of feedback focus and adaptivity. Previous evaluation efforts have examined feedback characteristics, its impact on learning, and its target, yet the focus of feedback and its adaptivity remains largely overlooked. To bridge this gap, we adopt and refine Narciss's taxonomy into seven feedback focus types to annotate teacher and LLM-generated feedback across three university writing courses. We release FeedType, a benchmark containing annotated teacher and LLM feedback from six LLMs under three prompting strategies. We assess the coverage and distribution of feedback focus types, and examine whether LLMs adapt their feedback across draft stages and student performance levels as an expert instructor does. Our findings show that while most LLMs cover most feedback focus types, they fail to reflect teacher feedback distributions and show varying levels of adaptivity, with none matching the teachers' adaptive behavior. We believe FeedType will support future research on pedagogical alignment in LLM feedback generation.

Abstract: The rapidly advancing capabilities of vision-language models (VLMs) present a systemic challenge to academic integrity. VLMs now allow students to bypass meaningful engagement by capturing and submitting graphical problems as singular images, a practice we define as trivial plagiarism. To provide educators with actionable data on VLM limitations, we investigate the efficacy of heuristic adversarial image transformations designed to degrade model performance while remaining human-interpretable. Through a two-phase evaluation of introductory assessments, we manually assess baseline VLM performance on circuit diagrams, followed by an automated large-scale evaluation of topological structures (logic gates) and coordinate geometry (Karnaugh maps). We find that while highly capable VLMs can exhibit appreciable robustness, all models suffer vulnerability to adversarial perturbations. We conclude that while visual perturbations act as a viable near-term stopgap, long-term assessment security requires educators to reapproach assessment design given continually increasing VLM performance.

Abstract: More privileged information does not always make a better teacher. We study this tension in on-policy self-distillation (OPSD), where a frozen copy of the base model scores the student's own rollouts under privileged context, conventionally a complete reference solution that bundles the final answer with one particular reasoning path. Holding the student view and training fixed within each scale, we compare that default against three abstractions compiled offline, a named strategy, a method-independent framing, and a problem category, and against an answer-only control that keeps the destination but removes the path. In the primary runs on competition mathematics, the best intermediate contexts improve the in-domain peak mean over the full solution by 1.4 points at 4B and 1.6 at 8B, while storing an order of magnitude fewer hint tokens. Comparisons across three seeds also show positive mean gains for the framing and category contexts at both scales. Answer-only conditioning remains competitive in the primary runs, within 0.2 points of the full solution at these scales. The preferred context varies with student scale and task. Initial teacher-student KL does not order downstream performance. What a self-teacher should see is therefore not everything it could, but the level of abstraction its student can still act on.

Abstract: Children increasingly interact with AI chatbots, making trust calibration essential to AI literacy. Prior research has examined children's trust in AI mainly as users evaluating systems built by others, rather than as designers of their own chatbots. We developed a chatbot-building environment with adjustable trust-relevant traits (e.g., confidence, transparency, formality, assertiveness), rules, and persona. We conducted mixed-methods study with 115 learners (ages 8-18) who made 119 chatbots. We examined how children configured their chatbots, reasoned about trustworthiness, and how closely chatbot behavior aligned with their designs. Younger students (age 10-13) set significantly higher confidence than older students (age 14-18), and some deliberately built chatbots that gave wrong answers on purpose, yet still called them trustworthy, arguing that a chatbot does what it was built to do. Younger students equated trust with purpose-fulfillment, while older students linked it to transparent, calibrated design. Students also calibrated academic chatbots to be more transparent and formal than hobby chatbots. We identify seven design dimensions describing what children believe makes a chatbot trustworthy, and discuss implications for AI literacy tools.

Abstract: Generative AI can offer students useful feedback, but its value depends on judging which suggestions are accurate and relevant. Prior research shows that strategic friction during human-AI interactions can promote critical uptake, but how to effectively implement such friction in academic contexts remains unclear. We examine whether requiring students to justify decisions to accept or reject AI suggestions can mitigate uncritical uptake in academic writing. In a randomized experiment embedded in a course activity (N=129), students wrote a data analysis proposal, received mixed-quality AI revision suggestions, and decided whether to accept or reject them. Students required to provide written justifications were 24 percentage points less likely to adopt flawed suggestions (65% vs. 41%), with no reduction in acceptance of sound suggestions (81% vs. 86%). However, thematic analysis revealed superficial engagement in the justification task and gaps in metacognitive monitoring and domain knowledge.

Abstract: Educational foundation models must solve problems, understand curriculum structure, diagnose learner difficulties, and provide appropriate instructional support. Existing educational language models often focus on either problem solving or tutoring, with training mixtures organized by source or task rather than capability. We present OmniEdu, an open family of foundation models for K-12 learning and teaching. Its instruction-tuning corpus combines over 100 educational resources and general instruction sources, organized around four capabilities: subject competence, curriculum grounding, diagnostic reasoning, and pedagogical action and scaffolding. Our pipeline integrates deterministic cleaning, semantic auditing and rewriting, task-specific quality scoring, token-budgeted diversity selection, and pedagogical instruction assignment. It yields 69,999 examples and 15.96M supervised response tokens, including 60,951 education-specific examples. We fine-tune 4B, 9B, and 27B models and evaluate curriculum grounding, K-12 problem solving, and pedagogical tutoring, alongside general capability. Education-oriented tuning consistently improves all three educational benchmark groups across model scales. OmniEdu-27B achieves 63.12% EM and 76.69% F1 on K12-Bench, 85.89% on MathFish, 86.95% on EDUMATH, and 78.74% in MathTutorBench's Scaffold setting. It also achieves the highest Teaching average on LongTutor among the evaluated models, at 3.02. These results demonstrate the value of curated, capability-balanced supervision for adapting general language models to educational tasks spanning problem solving, curriculum understanding, and instructional support.

Abstract: Visual representations can help lower-primary learners understand Math Word Problems, but generating classroom-usable visuals remains difficult. Existing symbolic systems are controllable but limited in coverage, while end-to-end text-to-image systems often fail to satisfy exact mathematical constraints. This paper presents a symbolic visual generation framework for lower-primary MWP generation with broader problem coverage and more scalable asset generation. The framework includes an LLM-based routing layer, three worksheet-oriented generation modules, and two fallback mechanisms for open-world SVG asset acquisition. A human evaluation comparing Math2Visual-X with Stable Diffusion XL, Nano Banana, and GPT Image showed that the proposed method achieved the strongest overall performance. The results indicate that the framework offers a scalable and pedagogically grounded approach for automatic MWP visual generation.

Abstract: Effective LLM tutoring depends on correctly identifying the specific error in a student's reasoning before generating feedback. We study this problem in propositional-logic proof tutoring, where student actions can be checked against formal inference rules. We introduce a verifier-grounded architecture that separates diagnosis from language generation. Using 600 balanced student actions, we compare a zero-shot LLM detector, a fine-tuned detector, and a symbolic verifier. Each diagnosis is processed by shared rationale and feedback agents, isolating the effect of the initial diagnosis. The zero-shot detector achieves a macro-F1 of 0.191; fine-tuning raises this to 0.709 but retains systematic errors between structurally related classes. Rationales generally preserve the diagnosis supplied to them, showing that an incorrect diagnosis can be faithfully propagated through the pipeline. Feedback can likewise remain faithful to its rationale, non-revealing, and pedagogically appropriate while addressing the wrong error. Verifier-grounded feedback achieves the highest diagnostic correctness, and expert ratings largely uneven with the automatic feedback evaluations. These findings show that apparent feedback quality can conceal upstream diagnostic errors and that faithfulness must be evaluated separately from correctness. Our code is publicly available

Abstract: Cognitive diagnosis infers students' concept mastery from response logs. However, students' responses are not determined by mastery alone: non-cognitive factors such as emotion, engagement, and fatigue can also affect performance. Affective cognitive diagnosis therefore extends conventional cognitive diagnosis by incorporating affective states. Existing methods often assume that the cognitive diagnosis backbone has already explained ability, item, and concept effects, so the remaining errors can be attributed mainly to affect. We argue that this assumption can be insufficient in real educational data: item calibration bias, systematic concept bias, personalized student-concept deviations, and latent student-item matching can form stable cognitive residuals. Without an explicit modeling pathway, these residuals may leak into affective representations, producing affect contamination. To address this problem, we propose an ability-residual decoupled framework for affective cognitive diagnosis. The model first captures unmodeled cognitive residuals through student, item, concept, student-concept, and low-rank student-item components, and then uses an affective module to modulate guess/slip effects. A Q-matrix-constrained concept residual attention mechanism adaptively aggregates only item-relevant concept residuals. Experiments on ASSIST2017, ASSIST2012, ASSIST2009, and Junyi with six cognitive diagnosis backbones show response-prediction gains across the reported comparisons and generally improved affect alignment when affect labels are available. Ablation studies, leakage probes, principal component analysis visualization, long-tail analysis, and case studies further indicate that ability residuals absorb stable cognitive bias, reduce cognitive contamination in the affective branch, and enhance the robustness and predictive accuracy of cognitive diagnosis models.

Abstract: Generative AI can improve students' programming performance, but successful task completion may not reflect what they retain. We examined performance, retention, cognitive load, and ownership in a controlled between-subjects experiment with 59 undergraduate computer science students, 55 were retained for analysis. Participants completed three introductory C programming tasks with access to ChatGPT-4.5 or conventional web search without generative AI. We measured task performance, self-reported mental effort and difficulty, pupillary responses, heart rate variability, and ownership, and assessed cued recall immediately and 48 hours later. ChatGPT-assisted students achieved higher coding scores (89% vs. 69%) but lower recall scores immediately (41% vs. 53%) and after 48 hours (39% vs. 52%). There was no significant difference in the loss of recall information over 48 hours between the groups. Self-reported mental effort increased less across tasks in the ChatGPT condition (Holm-adjusted p = .047), and students attributed less of the submitted code to themselves (45% vs. 81%). Confirmatory physiological tests did not detect significant differences in trajectories between conditions; substantial data loss limits their interpretation. These findings reveal a gap between assisted task performance and subsequent recall and sense of ownership in this setting. They motivate the need for assessment practices and AI learning tools that require students to explain, retrieve, and contribute to the work they submit as active participants in their education.

Abstract: It is well established that students learn best through active engagement, particularly via interactive experiences tied to real-world concepts. Creating such experiences, however, typically requires labor-intensive design, costly development, and continuous teacher guidance to achieve measurably effective outcomes. Recent advances in generative UI open the door for a future of practice where the creation of tailored interactive experiences is automated. However, off-the-shelf models lack optimization for pedagogical precision and learning principles, often yielding unsatisfactory results for complex pedagogical constructs. To address these limitations, we present learning interactives, a structured framework leveraging the generative UI capabilities of Gemini to construct effective customized interactive simulations. We evaluate our approach through both an initial study with educators as well as a pedagogical rating of a varied set of simulations by expert teachers.

Abstract: Despite the widely recognized potential of AI in education, most prior work has focused on individualized student assistance. In contrast, the majority of educational practice worldwide still takes place in collective classroom settings. To enable researchers to study AI assistance in collective teaching, we introduce Edustories, a dataset of 1,492 teacher-written case studies describing real elementary and high-school classroom situations involving challenging student behavior, pedagogical interventions, and their outcomes. Among many other applications, Edustories enables evaluating LLMs' ability to predict the success of teacher interventions, crucial for providing practicing teachers with useful feedback. Comparing the latest models from four language-model families against expert assessments, we find that current models fall short of human expertise in predicting classroom outcomes; the strongest models reach 58% accuracy compared to 64% of human experts. This gap highlights both the limitations and the emerging potential of AI as assistants for practicing teachers.

Abstract: Cognitive offloading to AI can reduce opportunities to practice skills, creating risks of deskilling. However, it remains unclear how to prevent deskilling without restricting access to AI. Here, we design two interventions to reduce offloading decisions: (1) metacognitive feedback that makes the implications of offloading for users explicit, and (2) an effort-based reward that incentivizes less extensive LLM assistance. We test both in a preregistered online experiment ($N = 704$) with a 2$\times$2 design and a no-AI control. The task was to practice fraction arithmetic with an LLM-based assistant that provided solutions only on explicit request, followed by an unaided test. Metacognitive feedback reduced answer offloading (OR $= 0.47$) and improved test performance (OR $= 1.51$). We found no evidence that the reward affected either outcome. Our results identify metacognitive feedback as a promising design choice to reduce cognitive offloading.

Abstract: In practice-based design courses such as knit yarn design, students must turn visual ideas into feasible material outcomes. This is difficult because creative decisions are tied to yarn properties, stitch structures, machine operation, and limited opportunities for physical sampling. This study presents an integrated pedagogical framework that combines flipped learning, exemplar-based reference, GenAI-assisted visual prototyping, and studio feedback in an undergraduate knit yarn design course. The framework was implemented through a cross-device platform with pre-class micro-videos, formative checks, a curated gallery, and a GenAI-supported ideation module. An exploratory course-based evaluation compared a historical control cohort (N = 12) and an intervention cohort (N = 16), supplemented by questionnaire responses and brief interviews. The findings are interpreted as context-specific indicators rather than confirmatory causal evidence. Exploratory comparisons showed higher scores in creativity thinking, design skills, problem solving, and total course score in the intervention cohort. Student and instructor responses suggested that flipped learning supported studio readiness, while GenAI mainly supported early-stage visual exploration rather than precise technical guidance. Overall, the study offers a practice-based instructional framework for integrating flipped preparation, GenAI-assisted visual prototyping, and studio feedback in design education.

Abstract: Modelling with mathematical formalisms like logical formulas, mathematical equations, or regular expressions is an important yet challenging task for students of computer science and other STEM disciplines. Identifying common mistakes occurring in this context is an important step towards helping struggling students by providing targeted high-quality feedback, e.g. in interactive learning systems. We present a tool-supported workflow that allows to (1) identify candidates for common mistakes that explain many student mistakes in large educational data sets, (2) cluster candidates according to similarities, and (3) visualize resulting clusters for instructors and CS education researchers. The visualization is designed to help researchers to identify common modelling mistakes. The candidates for common mistakes are represented by bug fixing transformations that translate incorrect formalizations into correct formalizations; they are generated by an LLM and validated algorithmically. We show that this approach works well by reproducing common mistakes in propositional logic modelling that were identified by hand in the literature; showing that, unlike other algorithmic approaches, the LLM-based approach is suitable for very large sets of data; and applying it to multiple other formalisms to showcase it generalizes beyond propositional logic.

Abstract: K-12 students increasingly form relationships with AI companions. Schools face growing expectations to teach AI literacy, yet existing frameworks treat AI as a tool rather than a relationship, and little is known about how teachers understand and act on students' relational use of AI. We conducted scenario-based interviews with 33 US K-12 teachers. Teachers welcomed academic companions but worried that intimate companions remove the developmental friction through which students learn to sustain human relationships. Teachers drew the boundaries of their jurisdiction by setting and observable wellbeing: within it they taught, talked, and watched; beyond it they positioned themselves as the adults best placed to notice and connect students with support. They envisioned AI companion literacy as shared work across the jurisdictions of counselors, parents, platforms, and policymakers, spiraling across grade levels. We introduce AI companion literacy as an extension of AI literacy and discuss implications for K-12 AI education.

Abstract: Handwritten mathematical expression recognition (HMER) is conventionally scored by exact-match rates and string-similarity metrics that are blind to where an error occurs: two predictions with identical token-error counts receive identical scores whether they misplace a subscript or swap the operands of a fraction. Render-based character detection matching (CDM) aligns glyphs robustly but remains position-blind---on controlled fraction-operand swaps it scores 0.8595 where position-aware scoring yields 0.6253. Tree-edit metrics exhibit a complementary blind spot: rewrites outside the parser's normalization coverage are penalized as structural errors (0.8552 where render-based metrics score 1.0). We propose PA-CDM, a position-aware metric that couples character detection matching with position-forest encoding and divergence-level weighting; StructPerturb v2.0, a frozen benchmark of 1,340 controlled perturbation pairs across 15 type--intensity cells; and a cross-metric consistency protocol combining a sensitivity matrix, a human study, and LLM-judge calibration. In a six-annotator study, PA-CDM attains the highest correlation with human judgments among seven automatic metrics (Spearman rho=0.9535, n=990). A frontier LLM judge correlates slightly higher (rho=0.9613) but is costly, nondeterministic, and API-dependent; PA-CDM approaches it at zero marginal cost with deterministic, diagnosable behavior.

Abstract: We study how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, we train two specialist checkpoints using supervised fine-tuning and reinforcement learning, and evaluate checkpoint choice, verification, and refinement. Based on these findings, we present an open-model test-time-compute pipeline. The system operates entirely in natural language, with no formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints - the general-availability model and two post-trained specialists - power an iterative search that generates, verifies, and refines candidate proofs; a separate high-compute stage then selects each final submission. The system scored 30 out of 42 points at IMO 2026, reaching the gold-medal threshold. We release the two post-trained checkpoints as well as the training data, the training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems.

Abstract: Plane geometry remains a significant challenge in AI, requiring the integration of visual perception and mathematical reasoning. While Large Multimodal Models (LMMs) naturally handle visuo-linguistic inputs, they are often computationally intensive and opaque. We demonstrate that a pure Large Language Model (LLM), when equipped with specialized modules, can rival state-of-the-art LMMs on complex geometry problems. Our framework integrates a Geometric Vision Parser, which translates diagrams into symbolic form, with a Symbolic Solver that performs formal deductions, thereby mitigating hallucinations and promoting interpretable reasoning. To enable rigorous evaluation, we curate a benchmark of challenging problems from the 2025 Chinese Zhongkao examinations, ensuring data novelty and testing deeper deductive skills. Experiments demonstrate that our approach achieves performance comparable to Gemini 2.5 Pro while delivering clearer, human-like solutions.

Abstract: Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback-Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

Abstract: Learning direct current circuit concepts requires learners to connect invisible physical quantities, such as current, voltage, resistance, and power, with observable outcomes such as bulb brightness. Conventional textbook materials and general-purpose circuit simulators provide opportunities for problem solving and exploration but offer limited support for explaining why circuit behavior changes or diagnosing the reasoning behind incorrect answers. We present CircuTutor, a circuit-state-driven intelligent tutoring system that transforms static textbook circuit problems into an interactive tutoring workflow. CircuTutor first uses multimodal problem parsing to extract the textbook question, circuit topology, component parameters, switch states, and answer options, which are converted into a structured task and validated through circuit simulation. Learners can then interactively explore the circuit (by changing parameters) and submit an answer while a SPICE-compatible solver computes physically consistent circuit states. After the learner submits an answer, CircuTutor presents a before-and-after circuit state animation corresponding to the selected operation, organizes the simulated state changes into a causal reasoning chain that explains the underlying circuit behavior, maps answer discrepancies to likely misconceptions, and generates adaptive follow-up exercises targeted at the diagnosed misconception. Our experimental results demonstrate that CircuTutor effectively improves conceptual learning and the overall learning experience. The proposed framework demonstrates how simulated circuit states can be transformed into intelligent and interactive tutoring for circuit education, with the potential to generalize to other STEM domains.