# World Models for Math Story Problems

arXiv: https://arxiv.org/abs/2306.04347 · HTML: https://mlsanity.com/paper/2306.04347/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 66 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [A Call for Clarity in Reporting BLEU Scores](https://mlsanity.com/paper/1804.08771/) (2018)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Constituency Parsing with a Self-Attentive Encoder](https://mlsanity.com/paper/1805.01052/) (2018)
- [Constrained Language Models Yield Few-Shot Semantic Parsers](https://mlsanity.com/paper/2104.08768/) (2021)
- [Language Models of Code are Few-Shot Commonsense Learners](https://mlsanity.com/paper/2210.07128/) (2022)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [Multilingual Constituency Parsing with Self-Attention and Pre-Training](https://mlsanity.com/paper/1812.11760/) (2018)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)
- [Compositional Semantic Parsing with Large Language Models](https://mlsanity.com/paper/2209.15003/) (2022)
- [A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models](https://mlsanity.com/paper/2210.12023/) (2022)
- [AMR Parsing as Sequence-to-Graph Transduction](https://mlsanity.com/paper/1905.08704/) (2019)
- [Improving Compositional Generalization with Latent Structure and Data Augmentation](https://mlsanity.com/paper/2112.07610/) (2021)
- [Automatic Generation of Socratic Subquestions for Teaching Math Word Problems](https://mlsanity.com/paper/2211.12835/) (2022)
- [Mapping to Declarative Knowledge for Word Problem Solving](https://mlsanity.com/paper/1712.09391/) (2017)

## Built on by (most cited first, 11 of 11)

- [Cooperate or Collapse: Emergence of Sustainable Cooperation in a Society of LLM Agents](https://mlsanity.com/paper/2404.16698/) (2024)
- [Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?](https://mlsanity.com/paper/2401.18070/) (2024)
- [MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs](https://mlsanity.com/paper/2410.13502/) (2024)
- [Multilingual Performance Biases of Large Language Models in Education](https://mlsanity.com/paper/2504.17720/) (2025)
- [Multi-Agent LLM Actor-Critic Framework for Social Robot Navigation](https://mlsanity.com/paper/2503.09758/) (2025)
- [Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models](https://mlsanity.com/paper/2506.03735/) (2025)
- [Are Language Models Efficient Reasoners? A Perspective from Logic Programming](https://mlsanity.com/paper/2510.25626/) (2025)
- [Enhancing Scientific Visual Question Answering via Vision-Caption aware Supervised Fine-Tuning](https://mlsanity.com/paper/2509.16628/) (2025)
- [Multi-tool Integration Application for Math Reasoning Using Large Language Model](https://mlsanity.com/paper/2408.12148/) (2024)
- [Logic-Guided Socially-aware Robot Navigation World Model](https://mlsanity.com/paper/2510.23509/) (2025)
- [Beyond Pattern Recognition: Probing Mental Representations of LMs](https://mlsanity.com/paper/2502.16717/) (2025)

## Abstract (arXiv)

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.