# MATHWELL: Generating Educational Math Word Problems Using Teacher Annotations

arXiv: https://arxiv.org/abs/2402.15861 · HTML: https://mlsanity.com/paper/2402.15861/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 24 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Human-Instruction-Free LLM Self-Alignment with Limited Samples](https://mlsanity.com/paper/2401.06785/) (2024)
- [Learning by Analogy: Diverse Questions Generation in Math Word Problem](https://mlsanity.com/paper/2306.09064/) (2023)
- [GPT-Fathom: Benchmarking Large Language Models to Decipher the Evolutionary Path towards GPT-4 and Beyond](https://mlsanity.com/paper/2309.16583/) (2023)
- [Step-On-Feet Tuning: Scaling Self-Alignment of LLMs via Bootstrapping](https://mlsanity.com/paper/2402.07610/) (2024)
- [A Theme-Rewriting Approach for Generating Algebra Word Problems](https://mlsanity.com/paper/1610.06210/) (2016)

## Built on by (most cited first, 7 of 7)

- [Opportunities and Challenges of LLMs in Education: An NLP Perspective](https://mlsanity.com/paper/2507.22753/) (2025)
- [From Solver to Tutor: Evaluating the Pedagogical Intelligence of LLMs with KMP-Bench](https://mlsanity.com/paper/2603.02775/) (2026)
- [Towards Generating Controllable and Solvable Geometry Problem by Leveraging Symbolic Deduction Engine](https://mlsanity.com/paper/2506.02565/) (2025)
- [From Answers to Questions: EQGBench for Evaluating LLMs' Educational Question Generation](https://mlsanity.com/paper/2508.10005/) (2025)
- [EDUMATH: Generating Standards-aligned Educational Math Word Problems](https://mlsanity.com/paper/2510.06965/) (2025)
- [A self-evolving multi-role collaborative framework with fine-grained difficulty guidance for innovative mathematical problem generation](https://mlsanity.com/paper/2601.11792/) (2026)
- [A Multi-Agent Approach to Validate and Refine LLM-Generated Personalized Math Problems](https://mlsanity.com/paper/2604.05160/) (2026)

## Abstract (arXiv)

Math word problems are critical K-8 educational tools, but writing them is time consuming and requires extensive expertise. To be educational, problems must be solvable, have accurate answers, and, most importantly, be educationally appropriate. We propose that language models have potential to support K-8 math education by automatically generating word problems. However, evaluating educational appropriateness is hard to quantify. We fill this gap by having teachers evaluate problems generated by LLMs, who find existing models and data often fail to be educationally appropriate. We then explore automatically generating educational word problems, ultimately using our expert annotations to finetune a 70B language model. Our model, MATHWELL, is the first K-8 word problem generator targeted at educational appropriateness. Further expert studies find MATHWELL generates problems far more solvable, accurate, and appropriate than public models. MATHWELL also matches GPT-4's problem quality while attaining more appropriate reading levels for K-8 students and avoiding generating harmful questions.