# Boosting Large Language Models with Socratic Method for Conversational Mathematics Teaching

arXiv: https://arxiv.org/abs/2407.17349 · HTML: https://mlsanity.com/paper/2407.17349/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [BARTScore: Evaluating Generated Text as Text Generation](https://mlsanity.com/paper/2106.11520/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Large Language Models Are State-of-the-Art Evaluators of Translation Quality](https://mlsanity.com/paper/2302.14520/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Why We Need New Evaluation Metrics for NLG](https://mlsanity.com/paper/1707.06875/) (2017)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks](https://mlsanity.com/paper/2305.14201/) (2023)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [The NCTE Transcripts: A Dataset of Elementary Math Classroom Transcripts](https://mlsanity.com/paper/2211.11772/) (2022)
- [The Art of SOCRATIC QUESTIONING: Recursive Thinking with Large Language Models](https://mlsanity.com/paper/2305.14999/) (2023)

## Built on by (most cited first, 16 of 16)

- [One Size doesn't Fit All: A Personalized Conversational Tutoring Agent for Mathematics Instruction](https://mlsanity.com/paper/2502.12633/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Simultaneous Multi-objective Alignment Across Verifiable and Non-verifiable Rewards](https://mlsanity.com/paper/2510.01167/) (2025)
- [Discerning minds or generic tutors? Evaluating instructional guidance capabilities in Socratic LLMs](https://mlsanity.com/paper/2508.06583/) (2025)
- [Simulating Students with Large Language Models: A Review of Architecture, Mechanisms, and Role Modelling in Education with Generative AI](https://mlsanity.com/paper/2511.06078/) (2025)
- [Navigating the Unknown: A Chat-Based Collaborative Interface for Personalized Exploratory Tasks](https://mlsanity.com/paper/2410.24032/) (2024)
- [EduEVAL-DB: A Role-Based Dataset for Pedagogical Risk Evaluation in Educational Explanations](https://mlsanity.com/paper/2602.15531/) (2026)
- [Rewarding How Models Think Pedagogically: Integrating Pedagogical Reasoning and Thinking Rewards for LLMs in Education](https://mlsanity.com/paper/2601.14560/) (2026)
- [AIriskEval-edu: New Dataset for Risk Assessment in AI-mediated K-12 Educational Explanations](https://mlsanity.com/paper/2607.01934/) (2026)
- [Teaching LLMs for Step-Level Automatic Math Correction via Reinforcement Learning](https://mlsanity.com/paper/2503.18432/) (2025)
- [Evolutionary Reinforcement Learning based AI tutor for Socratic Interdisciplinary Instruction](https://mlsanity.com/paper/2512.11930/) (2025)
- [From Solver to Tutor: Evaluating the Pedagogical Intelligence of LLMs with KMP-Bench](https://mlsanity.com/paper/2603.02775/) (2026)
- [BLADE: Better Language Answers through Dialogue and Explanations](https://mlsanity.com/paper/2604.03236/) (2026)
- [Generative Artificial Intelligence for Literature Reviews](https://mlsanity.com/paper/2605.16475/) (2026)
- [DICE: Decoupling Capability from Intervention Necessity in LLM Tutoring](https://mlsanity.com/paper/2610.04825/) (2026)
- [Do LLM Tutors Actually Teach? A Process-Centered Synthesis of the Tutoring Loop](https://mlsanity.com/paper/2610.15692/) (2026)

## Abstract (arXiv)

With the introduction of large language models (LLMs), automatic math reasoning has seen tremendous success. However, current methods primarily focus on providing solutions or using techniques like Chain-of-Thought to enhance problem-solving accuracy. In this paper, we focus on improving the capability of mathematics teaching via a Socratic teaching-based LLM (textttSocraticLLM), which guides learners toward profound thinking with clarity and self-discovery via conversation. We collect and release a high-quality mathematical teaching dataset, named textttSocraticMATH, which provides Socratic-style conversations of problems with extra knowledge. Also, we propose a knowledge-enhanced LLM as a strong baseline to generate reliable responses with review, guidance/heuristic, rectification, and summarization. Experimental results show the great advantages of textttSocraticLLM by comparing it with several strong generative models. The codes and datasets are available on urlhttps://github.com/ECNU-ICALK/SocraticMath.