arXiv:2606.10254v1 Announce Type: cross 
Abstract: While Large Language Models (LLMs) have achieved near-perfect performance in \emph{solving} high-school mathematics, their ability to \emph{evaluate} the diverse reasoning processes of real human students remains under-examined. To bridge this gap, we introduce \textbf{RealMath-Eval}, a rigorously annotated benchmark of 224 real-world exam responses from high schools. Our initial evaluation reveals that even state-of-the-art LLM judges struggle significantly on this task, exhibiting a high Mean Squared Error ($\sim$2.96) against expert human grading. To probe a plausible explanation, we contrast this performance with a control setting where the same judges evaluate synthetic LLM-generated solutions. We identify a stark ``Evaluation Gap'': judges are considerably more accurate and consistent on synthetic text (MSE $\sim$1.17) but struggle to generalize to authentic student reasoning. Through semantic embedding analysis, we find that synthetic errors suffer from a ``structural collapse'' into predictable, low-dimensional linear subspaces, whereas human errors form a more diverse error space. Furthermore, generative probability probes suggest that human reasoning involves significantly higher information-theoretic surprisal, indicating that student reasoning transitions are more out-of-distribution for current models. Finally, we find that surface-level style transfer fails to close this gap. Our findings suggest that current LLM evaluation pipelines relying heavily on synthetic data may not adequately capture the diversity of authentic student mathematical reasoning.

يقدم RealMath-Eval لمحة عن التحديات التي تواجه نماذج اللغة الكبيرة (LLMs) في تقييم التفكير البشري الحقيقي في الرياضيات الثانوية، مما يكشف عن فجوة تقييم كبيرة مقارنةً بتقييم الخبراء البشريين.

La introducción de RealMath-Eval destaca los desafíos que enfrentan los modelos de lenguaje de última generación (LLMs) para evaluar el razonamiento humano real en matemáticas de secundaria, revelando una brecha de evaluación significativa en comparación con la calificación de expertos humanos.

L'introduction de RealMath-Eval met en lumière les défis auxquels sont confrontés les modèles de langage de pointe (LLMs) pour évaluer le raisonnement humain réel en mathématiques au lycée, révélant un écart d'évaluation significatif par rapport à la notation humaine experte.

The introduction of RealMath-Eval highlights the challenges faced by state-of-the-art Large Language Models (LLMs) in evaluating real human reasoning in high school mathematics, revealing a significant evaluation gap compared to expert human grading.