# Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints

arXiv: https://arxiv.org/abs/2109.04546 · HTML: https://mlsanity.com/paper/2109.04546/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 73 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Microsoft COCO Captions: Data Collection and Evaluation Server](https://mlsanity.com/paper/1504.00325/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [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)
- [Toward Controlled Generation of Text](https://mlsanity.com/paper/1703.00955/) (2017)
- [Style Transfer from Non-Parallel Text by Cross-Alignment](https://mlsanity.com/paper/1705.09655/) (2017)
- [Tree-to-tree Neural Networks for Program Translation](https://mlsanity.com/paper/1802.03691/) (2018)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Exploring Controllable Text Generation Techniques](https://mlsanity.com/paper/2005.01822/) (2020)
- [Disentangling Factors of Variation with Cycle-Consistent Variational Auto-Encoders](https://mlsanity.com/paper/1804.10469/) (2018)
- [Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems](https://mlsanity.com/paper/1811.00720/) (2018)
- [GANS for Sequences of Discrete Elements with the Gumbel-softmax Distribution](https://mlsanity.com/paper/1611.04051/) (2016)
- [Topic-Guided Variational Autoencoders for Text Generation](https://mlsanity.com/paper/1903.07137/) (2019)
- [Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems](https://mlsanity.com/paper/2010.06823/) (2020)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Semi-Supervised QA with Generative Domain-Adaptive Nets](https://mlsanity.com/paper/1702.02206/) (2017)
- [Adversarial Text Generation via Feature-Mover's Distance](https://mlsanity.com/paper/1809.06297/) (2018)
- [Improving GAN Training with Probability Ratio Clipping and Sample Reweighting](https://mlsanity.com/paper/2006.06900/) (2020)
- [Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations](https://mlsanity.com/paper/2010.06196/) (2020)
- [A Joint Model for Question Answering and Question Generation](https://mlsanity.com/paper/1706.01450/) (2017)
- [Text2Math: End-to-end Parsing Text into Math Expressions](https://mlsanity.com/paper/1910.06571/) (2019)
- [Select and Attend: Towards Controllable Content Selection in Text Generation](https://mlsanity.com/paper/1909.04453/) (2019)

## Built on by (most cited first, 27 of 27)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Adaptive and Personalized Exercise Generation for Online Language Learning](https://mlsanity.com/paper/2306.02457/) (2023)
- [Learning by Analogy: Diverse Questions Generation in Math Word Problem](https://mlsanity.com/paper/2306.09064/) (2023)
- [Improving Socratic Question Generation using Data Augmentation and Preference Optimization](https://mlsanity.com/paper/2403.00199/) (2024)
- [Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models](https://mlsanity.com/paper/2404.02124/) (2024)
- [Tree-Based Representation and Generation of Natural and Mathematical Language](https://mlsanity.com/paper/2302.07974/) (2023)
- [Improving Reading Comprehension Question Generation with Data Augmentation and Overgenerate-and-rank](https://mlsanity.com/paper/2306.08847/) (2023)
- [cPAPERS: A Dataset of Situated and Multimodal Interactive Conversations in Scientific Papers](https://mlsanity.com/paper/2406.08398/) (2024)
- [ChatGPT as a Math Questioner? Evaluating ChatGPT on Generating Pre-university Math Questions](https://mlsanity.com/paper/2312.01661/) (2023)
- [MATHWELL: Generating Educational Math Word Problems Using Teacher Annotations](https://mlsanity.com/paper/2402.15861/) (2024)
- [Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?](https://mlsanity.com/paper/2407.05134/) (2024)
- [MultiQG-TI: Towards Question Generation from Multi-modal Sources](https://mlsanity.com/paper/2307.04643/) (2023)
- [Diversifying Question Generation over Knowledge Base via External Natural Questions](https://mlsanity.com/paper/2309.14362/) (2023)
- [SGSH: Stimulate Large Language Models with Skeleton Heuristics for Knowledge Base Question Generation](https://mlsanity.com/paper/2404.01923/) (2024)
- [Proactive and Reactive Engagement of Artificial Intelligence Methods for Education: A Review](https://mlsanity.com/paper/2301.10231/) (2023)
- [Multi-Agent Collaborative Framework For Math Problem Generation](https://mlsanity.com/paper/2511.03958/) (2025)
- [Synthetic Context Generation for Question Generation](https://mlsanity.com/paper/2406.13188/) (2024)
- [From Objectives to Questions: A Planning-based Framework for Educational Mathematical Question Generation](https://mlsanity.com/paper/2506.00963/) (2025)
- [Enhancing Diversity of LLM-Generated Educational Tasks](https://mlsanity.com/paper/2512.23601/) (2025)
- [DISK: Domain-constrained Instance Sketch for Math Word Problem Generation](https://mlsanity.com/paper/2204.04686/) (2022)
- [Towards Generating Controllable and Solvable Geometry Problem by Leveraging Symbolic Deduction Engine](https://mlsanity.com/paper/2506.02565/) (2025)
- [EDUMATH: Generating Standards-aligned Educational Math Word Problems](https://mlsanity.com/paper/2510.06965/) (2025)
- [Elementary Math Word Problem Generation using Large Language Models](https://mlsanity.com/paper/2506.05950/) (2025)
- [Computational Blueprints: Generating Isomorphic Mathematics Problems with Large Language Models](https://mlsanity.com/paper/2511.07932/) (2025)
- [EduAgentQG: Multi-Agent Personalized Mathematics Question Generation with Explicit Diversity and Objective-Aware Evaluation](https://mlsanity.com/paper/2511.11635/) (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)
- [Agentic Retrieval and Reinforcement Learned Equation Chains: A Controlled Generation Framework for Complex and Novel Physics Word Problems](https://mlsanity.com/paper/2606.15591/) (2026)

## Abstract (arXiv)

We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical computation and a context that specifies the problem scenario. Existing approaches are prone to generating MWPs that are either mathematically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem template, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that leverages i) pre-trained language models and a context keyword selection model to improve the language quality of the generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantitative and qualitative experiments on three real-world MWP datasets demonstrate the superior performance of our approach compared to various baselines.