RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning
Yiteng Mao, Kenan Xu, Yijia Lyu, Wenhao Li, Jianlong Chen, Xiangfeng Wang
Why It Matters
What makes this one worth your time
Understanding the evaluation gap is crucial for improving LLMs and ensuring they can accurately assess diverse human reasoning in educational contexts.
RealMath-Eval highlights the limitations of LLMs in evaluating authentic student reasoning.
Summary
The paper introduces RealMath-Eval, a benchmark for evaluating LLMs against real high school math exam responses, revealing a significant evaluation gap between human and synthetic solution assessments.
Key contributions
- Introduction of the RealMath-Eval benchmark with 224 annotated real-world exam responses.
- Empirical evidence demonstrating the evaluation gap between LLMs and expert human grading.
- Analysis of semantic embedding differences between human and synthetic errors.
Notable insights
- The stark difference in evaluation accuracy between human and synthetic solutions suggests that LLMs may not generalize well to real-world reasoning tasks.
- The concept of 'structural collapse' in synthetic errors indicates a fundamental limitation in how LLMs interpret and generate mathematical reasoning.
Possible limitations
- Not stated in the abstract.
Abstract
arXiv:2606.10254v1 Announce Type: new 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.