LLMs can personalize education, although current static-prompt tutoring systems struggle to adapt to diverse academic disciplines. We develop and test a system with subject-aware prompting, based on 14 pedagogical features (e.g., tutor scaffolding, student understanding) extracted from raw transcripts. We first train a prompt routing model in a simulation environment, and then deploy it for online adaptation with actual high-school students. The simulation benchmark shows the router outperforming two static baselines ($0.694$ vs. $0.647$ and $0.64$, $p<0.001$). A/B testing ($N=656$ conversations from 359 students) shows sim-to-real transfer where the model switches from analytical to scaffolding learning strategies. Our adaptive prompt selection mechanism improves instructional efficiency, maintains pedagogical quality and reduces interactions by around 3 turns ($p=0.007$). While a greedy router achieves a comparable exercise conversion rate with the baseline ($19.1\%$ vs. $19.6\%$), a stochastic router that samples strategies leads to a higher conversion rate ($28.1\%$).

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