Large Scale AI Grading of Handwritten Physics Assessments: Score Agreement and Olympiad Team Selection Outcomes

Grading in large undergraduate STEM courses often yields minimal feedback due to heavy instructional workloads. We present a large-scale empirical study of AI grading on real, handwritten single-variable calculus work from UC Irvine. Using OCR-conditioned large language models with structured, rubric-guided prompting, our system produces scores and formative feedback for thousands of free-response quiz submissions from nearly 800 students. In a setting with no single ground-truth label, we evaluate performance against official teaching-assistant grades, student surveys, and independent human review, finding strong alignment with TA scoring and a large majority of AI-generated feedback rated as correct or acceptable across quizzes. Beyond calculus, this setting highlights core challenges in OCR-conditioned mathematical reasoning and partial-credit assessment. We analyze key failure modes, propose practical rubric- and prompt-design principles, and introduce a multi-perspective evaluation protocol for reliable, real-course deployment. Building on the dataset and evaluation framework developed here, we outline a standardized benchmark for AI grading of handwritten mathematics to support reproducible comparison and future research.

As large language models (LLMs) are increasingly considered for automated assessment and feedback, understanding when LLM marking is valid is essential. We evaluate LLM-as-a-judge marking across four settings spanning three assessment formats - structured questions, written essays, and scientific plots - comparing GPT-5.2, Grok 4.1, Claude Opus 4.5, DeepSeek-V3.2, Gemini 3 Pro, and committee aggregations against human markers under blind, solution-provided, false-solution, and anchored conditions. We distinguish absolute accuracy from rank-order agreement, since a marking system can match the distribution of human marks while failing to order responses by quality. Across task types, performance is sharply task-dependent. For blind university exam questions ($n=771$) and secondary and university structured questions ($n=1151$), models show robust rank-order agreement with human markers (Spearman $ρ> 0.6$), with official solutions reducing error and strengthening agreement. False solutions degrade absolute accuracy, showing that models defer to provided references, but leave rank-ordering intact. Essay marking behaves fundamentally differently. Across $n=55$ scripts, each containing five essays ($n=275$ essays total), blind AI marking is harsher and more variable than human marking and adding marking guidance does not improve rank-order agreement. Anchored exemplars shift the AI mean close to the human mean and compress variance below the human standard deviation, but rank-order agreement remains near-zero. For code-based plot elements ($n=1400$), models achieve high rank-order agreement ($ρ> 0.83$) with near-linear calibration. LLM marking validity depended strongly on the assessment task, and this held for every contemporary model tested. The results also show that the reliability of the human benchmark constrains the claims that can be made about AI-human agreement.

Student responses in STEM assessments are often handwritten and combine symbolic expressions, calculations, and diagrams, creating substantial variation in format and interpretation. Despite their importance for evaluating students' reasoning, such responses are time-consuming to score and prone to rater inconsistency, particularly when partial credit is required. Recent advances in large language models (LLMs) have increased attention to AI-assisted scoring, yet evidence remains limited regarding how rubric design and LLM configurations influence reliability across performance levels. This study examined the reliability of AI-assisted scoring of undergraduate physics constructed responses using GPT-4o. Twenty authentic handwritten exam responses were scored across two rounds by four instructors and by the AI model using skill-based rubrics with differing levels of analytic granularity. Prompting format and temperature settings were systematically varied. Overall, human-AI agreement on total scores was comparable to human inter-rater reliability and was highest for high- and low-performing responses, but declined for mid-level responses involving partial or ambiguous reasoning. Criterion-level analyses showed stronger alignment for clearly defined conceptual skills than for extended procedural judgments. A more fine-grained, checklist-based rubric improved consistency relative to holistic scoring. These findings indicate that reliable AI-assisted scoring depends primarily on clear, well-structured rubrics, while prompting format plays a secondary role and temperature has relatively limited impact. More broadly, the study provides transferable design recommendations for implementing reliable LLM-assisted scoring in STEM contexts through skill-based rubrics and controlled LLM settings.