LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring

• URL: http://arxiv.org/abs/2605.27088v1
• Date: Tue, 26 May 2026 14:35:57 GMT
• Title: LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring
• Abstract summary: We investigate whether training-free prompt optimization-evolving only the system prompt via API calls can serve as a practical alternative.<n>We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites.<n> 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.
• Score: 1.4976621159818981
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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