keywords:
curriculum alignment
large language models (llms)
educational nlp
Most existing math benchmarks for LLMs focus on evaluating correct solutions. In educational settings, however, it is equally important to understand whether LLMs grasp the pedagogical intent behind math problems, beyond producing the right solution. Tagging curriculum standards is challenging for the same reason: distinguishing fine-grained standards requires understanding subtle pedagogical distinctions. In this paper, we use the MathFish benchmark, which frames alignment as multi-label prediction over 385 Common Core State Standards, to evaluate a three-stage pipeline inspired by baseline failure modes in retrieval and structural reasoning: curriculum-informed hard negatives (M1), a cross-encoder re-ranker (M2), and a ReAct agent paired with an LLM-as-a-judge critic (M3). We additionally evaluate a training-free alternative (A1) combining hybrid sparse-dense retrieval with curriculum graph reranking. M3 achieves 31.3% exact match, roughly 6.5 times the three-shot GPT-4-Turbo baseline, with the largest gains from deliberative multi-step reasoning. Error analysis shows that even with these improvements, the pipeline struggles with missing predictions, grade-level misalignment, and sibling confusion, reinforcing that precise curriculum alignment is a fundamentally hard problem in educational NLP.
