# Learning by Analogy: Diverse Questions Generation in Math Word Problem

arXiv: https://arxiv.org/abs/2306.09064 · HTML: https://mlsanity.com/paper/2306.09064/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Exploiting Cloze Questions for Few Shot Text Classification and Natural Language Inference](https://mlsanity.com/paper/2001.07676/) (2020)
- [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)
- [A Survey of Data Augmentation Approaches for NLP](https://mlsanity.com/paper/2105.03075/) (2021)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Leveraging Pre-trained Checkpoints for Sequence Generation Tasks](https://mlsanity.com/paper/1907.12461/) (2019)
- [Adversarial Filters of Dataset Biases](https://mlsanity.com/paper/2002.04108/) (2020)
- [Automatic Generation of Socratic Subquestions for Teaching Math Word Problems](https://mlsanity.com/paper/2211.12835/) (2022)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers](https://mlsanity.com/paper/1808.07290/) (2018)
- [Improving Neural Question Generation using Answer Separation](https://mlsanity.com/paper/1809.02393/) (2018)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [Adversarial Examples for Evaluating Math Word Problem Solvers](https://mlsanity.com/paper/2109.05925/) (2021)
- [Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations](https://mlsanity.com/paper/2010.06196/) (2020)
- [Improving Question Generation With to the Point Context](https://mlsanity.com/paper/1910.06036/) (2019)
- [Reverse Operation based Data Augmentation for Solving Math Word Problems](https://mlsanity.com/paper/2010.01556/) (2020)
- [A Theme-Rewriting Approach for Generating Algebra Word Problems](https://mlsanity.com/paper/1610.06210/) (2016)
- [Practice Makes a Solver Perfect: Data Augmentation for Math Word Problem Solvers](https://mlsanity.com/paper/2205.00177/) (2022)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [Unbiased Math Word Problems Benchmark for Mitigating Solving Bias](https://mlsanity.com/paper/2205.08108/) (2022)
- [Counterfactual Data Augmentation via Perspective Transition for Open-Domain Dialogues](https://mlsanity.com/paper/2210.16838/) (2022)
- [Semantic-based Data Augmentation for Math Word Problems](https://mlsanity.com/paper/2201.02489/) (2022)

## Built on by (most cited first, 18 of 18)

- [Large Language Models for Education: A Survey and Outlook](https://mlsanity.com/paper/2403.18105/) (2024)
- [Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist](https://mlsanity.com/paper/2407.08733/) (2024)
- [MathAttack: Attacking Large Language Models Towards Math Solving Ability](https://mlsanity.com/paper/2309.01686/) (2023)
- [Leveraging LLM-Respondents for Item Evaluation: a Psychometric Analysis](https://mlsanity.com/paper/2407.10899/) (2024)
- [MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions](https://mlsanity.com/paper/2405.19444/) (2024)
- [Bringing Generative AI to Adaptive Learning in Education](https://mlsanity.com/paper/2402.14601/) (2024)
- [TheoremExplainAgent: Towards Video-based Multimodal Explanations for LLM Theorem Understanding](https://mlsanity.com/paper/2502.19400/) (2025)
- [A Symbolic Character-Aware Model for Solving Geometry Problems](https://mlsanity.com/paper/2308.02823/) (2023)
- [MATHWELL: Generating Educational Math Word Problems Using Teacher Annotations](https://mlsanity.com/paper/2402.15861/) (2024)
- [Solving Math Word Problem with Problem Type Classification](https://mlsanity.com/paper/2308.13844/) (2023)
- [An Expression Tree Decoding Strategy for Mathematical Equation Generation](https://mlsanity.com/paper/2310.09619/) (2023)
- [Enhancing Quantitative Reasoning Skills of Large Language Models through Dimension Perception](https://mlsanity.com/paper/2312.17532/) (2023)
- [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)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [A Diversity-Enhanced Knowledge Distillation Model for Practical Math Word Problem Solving](https://mlsanity.com/paper/2501.03670/) (2025)
- [Elementary Math Word Problem Generation using Large Language Models](https://mlsanity.com/paper/2506.05950/) (2025)
- [VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification](https://mlsanity.com/paper/2606.14176/) (2026)

## Abstract (arXiv)

Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP solver to better understand same problems which may typically be formulated in diverse ways. However most existing works exploit the shortcut learning to train MWP solvers simply based on samples with a single question. In lack of diverse questions, these methods merely learn shallow heuristics. In this paper, we make a first attempt to solve MWPs by generating diverse yet consistent questions/equations. Given a typical MWP including the scenario description, question, and equation (i.e., answer), we first generate multiple consistent equations via a group of heuristic rules. We then feed them to a question generator together with the scenario to obtain the corresponding diverse questions, forming a new MWP with a variety of questions and equations. Finally we engage a data filter to remove those unreasonable MWPs, keeping the high-quality augmented ones. To evaluate the ability of learning by analogy for an MWP solver, we generate a new MWP dataset (called DiverseMath23K) with diverse questions by extending the current benchmark Math23K. Extensive experimental results demonstrate that our proposed method can generate high-quality diverse questions with corresponding equations, further leading to performance improvement on Diverse-Math23K. The code and dataset is available at: https://github.com/zhouzihao501/DiverseMWP