# DICE: Decoupling Capability from Intervention Necessity in LLM Tutoring

arXiv: https://arxiv.org/abs/2610.04825 · HTML: https://mlsanity.com/paper/2610.04825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 25 of 25)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [Can language models learn from explanations in context?](https://mlsanity.com/paper/2204.02329/) (2022)
- [Evaluating Explainable AI: Which Algorithmic Explanations Help Users Predict Model Behavior?](https://mlsanity.com/paper/2005.01831/) (2020)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [Do Explanations make VQA Models more Predictable to a Human?](https://mlsanity.com/paper/1810.12366/) (2018)
- [Training LLM-based Tutors to Improve Student Learning Outcomes in Dialogues](https://mlsanity.com/paper/2503.06424/) (2025)
- [Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors](https://mlsanity.com/paper/2407.09136/) (2024)
- [Towards the Pedagogical Steering of Large Language Models for Tutoring: A Case Study with Modeling Productive Failure](https://mlsanity.com/paper/2410.03781/) (2024)
- [Training Turn-by-Turn Verifiers for Dialogue Tutoring Agents: The Curious Case of LLMs as Your Coding Tutors](https://mlsanity.com/paper/2502.13311/) (2025)
- [From Problem-Solving to Teaching Problem-Solving: Aligning LLMs with Pedagogy using Reinforcement Learning](https://mlsanity.com/paper/2505.15607/) (2025)
- [Can Language Models Teach Weaker Agents? Teacher Explanations Improve Students via Personalization](https://mlsanity.com/paper/2306.09299/) (2023)
- [Boosting Large Language Models with Socratic Method for Conversational Mathematics Teaching](https://mlsanity.com/paper/2407.17349/) (2024)
- [Instruct, Not Assist: LLM-based Multi-Turn Planning and Hierarchical Questioning for Socratic Code Debugging](https://mlsanity.com/paper/2406.11709/) (2024)
- [Intent Matters: Enhancing AI Tutoring with Fine-Grained Pedagogical Intent Annotation](https://mlsanity.com/paper/2506.07626/) (2025)
- [TPD: Enhancing Student Language Model Reasoning via Principle Discovery and Guidance](https://mlsanity.com/paper/2401.13849/) (2024)
- [INTERACT: Enabling Interactive, Question-Driven Learning in Large Language Models](https://mlsanity.com/paper/2412.11388/) (2024)
- [Beyond Discrete Personas: Personality Modeling Through Journal Intensive Conversations](https://mlsanity.com/paper/2412.11250/) (2024)
- [From Solver to Tutor: Evaluating the Pedagogical Intelligence of LLMs with KMP-Bench](https://mlsanity.com/paper/2603.02775/) (2026)
- [Turning Back Without Forgetting: Selective Backward Refinement for Parameter-Efficient Continual Learning](https://mlsanity.com/paper/2606.01379/) (2026)

## Abstract (arXiv)

Fluent guidance is not the same as useful intervention. LLM tutors are typically trained to generate the next teacher utterance, implicitly assuming that every student turn warrants a response. However, our experiments indicate that this conflates tutoring capability (what to say) with intervention necessity (whether to say it). We introduce DICE, a framework that decouples intervention decisions from response generation by first selecting an explicit pedagogical action. To calibrate this action selection policy, we define Intervention Value (IV), a rollout-grounded counterfactual metric that compares each action against non-intervention. IV shows that many prescribed interventions provide little or no marginal benefit. We further introduce DICE-Bench, a multi-variant math tutoring benchmark with skill-preserving problem variants for session-level evaluation. Using IV-weighted and KL-regularized policy optimization, DICE learns to intervene selectively while preserving tutoring effectiveness. In simulated tutoring sessions, DICE reduces the over-intervention rate to near zero while guiding students to correct solutions in approximately 3-4 fewer turns on average than existing Socratic tutoring baselines.