educational software developers

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.