Can Vision Language Models Be Adaptive in Mathematics Education? A Learner Model-based Rubric Study

Criterion-level grading connects examination performance to learning outcomes, but manual marking introduces workload and variation between markers. This study evaluates vision-language models (VLMs) for handwritten outcome-based assessment across five dimensions: accuracy, human agreement, repeated-run reliability, error concentration, and explanation quality. Using 1,982 criterion-level records from 485 undergraduate examination answers, we compare 20 configurations spanning Qwen2.5-VL, InternVL3, Pixtral, a Donut baseline, and a cascade ensemble. Evaluation setups include zero-shot prompting, few-shot prompting, partial fine-tuning, and Low-Rank Adaptation (LoRA). Two independent faculty markers regraded all 291 test criteria, providing a human agreement baseline on the same assessment materials. Qwen2.5-VL with LoRA achieved Quadratic Weighted Kappa (QWK) of 0.727 and mean absolute error of 0.435 marks against the examiner, compared with mean human-pair QWK of 0.551. This comparison reflects calibration to the examiner's training marks. LoRA outperformed partial fine-tuning for all three instruction-tuned VLMs, while few-shot prompting reduced QWK in every configuration with valid prompted scores. Aggregate reliability and exact repeatability diverged: intraclass correlations ranged from 0.790 to 0.874, yet 50.2-63.6% of criteria changed marks across five sampled runs. Attention-guided deletion showed no statistically significant advantage over random masking, and four faculty reviewers reached no consensus on explanation usefulness. These findings highlight the need for rubric-specific calibration, repeatable scoring, review of consequential errors, and separate validation of explanations. The released evaluation protocol supports criterion-level assessment research and grading tools with teacher oversight.

Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute.

Vision-Language Models (VLMs) often produce self-reflective statements like "let me check the figure again" during reasoning. Do such statements trigger genuine visual re-examination, or are they merely learned textual patterns? We investigate this via VisualSwap, an image-swap probing framework: after a model reasons over an image, we replace it with a visually similar but semantically different one and test whether the model notices. We introduce VS-Bench, 800 image pairs curated from MathVista, MathVerse, MathVision, and MMMU-Pro. Experiments on Qwen3-VL, Kimi-VL, and ERNIE-VL reveal a striking failure: models overwhelmingly miss the swap, with accuracy dropping by up to 60%. Counterintuitively, thinking models are nearly 3x more vulnerable than their instructed counterparts, and scaling offers no mitigation. Multi-turn user instructions restore visual grounding, but self-generated reflective statements during continuous generation do not. Attention analysis explains why: user instructions substantially elevate attention to visual tokens, whereas self-reflection does not. Current VLMs tend to say rather than actually see when claiming to perform visual re-examination. Our code and dataset are available at the project page: https://visualswap.github.io