Towards Pedagogically Aligned LLM Tutors for Math Mistake Remediation

2026-06-19

AI Summary

This work addresses the tendency of large language models to directly provide answers in mathematical tutoring, which contravenes the principles of guided instruction. To mitigate this, the authors propose a two-stage alignment framework grounded in pedagogical theory: first, foundational capabilities are instilled via supervised fine-tuning; second, direct preference optimization (DPO) is applied using a hybrid dataset of real and synthetically generated preferences. The synthetic data are constructed according to key instructional dimensions, including scaffolding and factual accuracy. Experimental results demonstrate that the proposed approach significantly enhances the model’s ability to guide students through error correction in mathematics, outperforming baseline methods in both factual correctness and instructional quality. Human evaluations further show performance on par with state-of-the-art closed-source systems, while maintaining high transparency and reproducibility.

Abstract

Large language models have strong potential for use in intelligent tutoring systems, but they often fail to follow effective pedagogical strategies, such as guiding students without revealing final answers. We study the application of a two-stage alignment pipeline for math mistake remediation, combining supervised fine-tuning on tutoring dialogs with Direct Preference Optimization on synthetic preference pairs. We construct a dataset that integrates existing tutoring corpora with synthetic data generated along pedagogical dimensions, such as scaffolding and factuality, and study different input configurations that incorporate solution correctness and gold answers. Experiments show that this approach improves both factual accuracy and pedagogical quality over base models and existing tutoring models. Human evaluation further indicates that our best model is competitive with a strong proprietary baseline, while providing additional benefits in terms of openness, transparency, and reproducibility. Our results highlight the effectiveness of preference-based pedagogical alignment, while also revealing challenges in reliably evaluating tutoring quality.

Problem

• intelligent tutoring systems
• pedagogical alignment
• math mistake remediation
• large language models
• scaffolding

Innovation

• pedagogical alignment
• math mistake remediation
• direct preference optimization
• scaffolding
• synthetic tutoring data