Application-Driven Pedagogical Knowledge Optimization of Open-Source LLMs via Reinforcement Learning and Supervised Fine-Tuning

Large language models (LLMs) trained to answer questions are natively poor at teaching. Reinforcement Learning (RL) against a simulated student is a promising approach to improve their pedagogy, but existing RL-trained tutors reward the student's success on the tutored problem with the tutor's words still in context. The reward is then easiest to raise by telling the student the answer, and a tuned penalty is needed to reduce telling. Drawing on learning sciences, we introduce a masked near-transfer post-test: the student is tested on an unseen variant of the tutored problem with the tutor's utterances masked, so the reward can rise only through what the student wrote in its own turns. This discourages cognitive offloading by the student and allows the continuous penalty to be replaced by two binary reward gates (factual correctness of tutor response, no solution handover). A leave-one-out ablation shows that the learning-gain reward on its own does not separate teaching from telling: the gates reduce solution handover while the near-transfer post-test improves out-of-domain transfer. Using these reward designs we develop Eduardo, a multi-turn RL recipe for training LLM tutors, and use it to train 4B, 9B, 14B and 27B models from two distinct LLM architectures. Our post-trained Eduardo-27B model matches Gemini-3.1-Pro on MathTutorBench and Claude Opus 4.8 on TutorMoments at 2.4-6.2x fewer thinking tokens than frontier models, which matters for interactive tutoring. Without being named in the reward, the model more than doubles its use of the push-for-justification teacher move while support fading (e.g., assigning independent work), whose payoff lies beyond a single-problem dialog episode, is trained out. We open-source our training environment, an 8,671-problem near-transfer dataset, and trained models for further development.

Large Language Models (LLMs) show strong potential as educational tutors. Existing approaches typically train them to solve problems and provide correct answers, but this problem-solving-centered paradigm overlooks key requirements of effective tutoring: progressive guidance and the coordination of multiple pedagogical objectives across multi-turn interactions. Developing such tutors remains challenging because student behavior varies substantially with individual knowledge states, pedagogical effectiveness depends on multiple factors beyond final-answer correctness, and coordinating these objectives over tutor-student interactions is inherently difficult. To address these challenges, we propose PEARL, a PEdagogically Aligned Reinforcement Learning framework for training Socratic tutoring agents. First, we introduce a controllable student simulator that disentangles latent cognitive states from response generation, enabling simulation of diverse abilities and misconceptions. Second, we develop a pedagogically aligned reward model that jointly assesses pedagogical quality and objective correctness. Finally, we propose a stable multi-objective reinforcement learning approach that balances competing pedagogical objectives during tutor training. Experiments across multiple benchmarks show that PEARL performs competitively against tutoring-specific open-source systems and leading proprietary LLMs.

Large language models (LLMs) have become increasingly capable problem solvers, but being able to solve a problem is not the same as being able to teach it. Existing approaches to training LLMs as teachers rely on demonstrations, preference data, or predefined pedagogical criteria that specify what good teaching looks like. However, these signals are often not grounded in individual student learning outcomes, where effective teaching strategies can vary substantially across learners. To address this, we introduce Sherpa, a multi-turn reinforcement learning framework that instantiates multiple student archetypes with LLMs conditioned on distinct learning preferences and trains a teacher model to adapt its instruction by directly maximizing their learning outcomes. Teacher LLMs trained with Sherpa improve instructed students' performance across all archetypes by an average of 20.5 percentage points. Under MathTutorBench's evaluation, Sherpa raises the overall pedagogy score from 52.5% to 79.2%, indicating better teaching responses. Our human studies show that the trained teacher is preferred over the base model in 79.6% of pairwise comparisons. Together, Sherpa trains LLM teachers to adapt to diverse simulated students and become better aligned with human teachers, paving the road towards AI tutors teaching real students.