LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918524707930112 |
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| author | Lee, Unggi Shin, Minchul Jeong, Yeil Lee, Sookbun Moon, Jeongsu Joo, Kyungtae Lee, Eunjoo Kwon, Hoilym |
| author_facet | Lee, Unggi Shin, Minchul Jeong, Yeil Lee, Sookbun Moon, Jeongsu Joo, Kyungtae Lee, Eunjoo Kwon, Hoilym |
| contents | Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring Lee, Unggi Shin, Minchul Jeong, Yeil Lee, Sookbun Moon, Jeongsu Joo, Kyungtae Lee, Eunjoo Kwon, Hoilym Computation and Language Machine Learning Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute. |
| title | LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring |
| topic | Computation and Language Machine Learning |
| url | https://arxiv.org/abs/2605.27088 |