---
title: "MathQA: Towards Interpretable Math Word Problem — Amini 2019"
description: "The authors take the noisy AQuA (over 100K multiple-choice problems at the GRE/GMAT level) and rewrite its usable portion in a formal language of…"
authors: ["Aida Amini", "Saadia Gabriel", "Shanchuan Lin", "Rik Koncel-Kedziorski", "Yejin Choi", "Hannaneh Hajishirzi"]
year: 2019
venue: "Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)"
source: "https://aclanthology.org/N19-1245/"
doi: "10.18653/v1/n19-1245"
arxiv: "1905.13319"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/amini-2019-mathqa-interpretable-math-word-problem/"
---
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# MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms

**Authors:** Aida Amini, [Saadia Gabriel](https://md.research.elamur.ai/free/en/authors/saadia-gabriel/), [Shanchuan Lin](https://md.research.elamur.ai/free/en/authors/shanchuan-lin/), [Rik Koncel-Kedziorski](https://md.research.elamur.ai/free/en/authors/rik-koncel-kedziorski/), [Yejin Choi](https://md.research.elamur.ai/free/en/authors/yejin-choi/), [Hannaneh Hajishirzi](https://md.research.elamur.ai/free/en/authors/hannaneh-hajishirzi/) · **Year:** 2019 · **Venue:** Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/N19-1245/) · [PDF](https://aclanthology.org/N19-1245.pdf) · [DOI 10.18653/v1/n19-1245](https://doi.org/10.18653/v1/n19-1245) · [arXiv 1905.13319](https://arxiv.org/abs/1905.13319) · [OpenAlex](https://openalex.org/W2951939640)

**Citations:** 107 citations (openalex-snapshot · 2026-10-14) · [393](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
The authors take the noisy AQuA (over 100K multiple-choice problems at the GRE/GMAT level) and rewrite its usable portion in a formal language of "operation programs". A program is a chain of steps op(arguments), where an argument can be a number from the problem statement, a category constant (e.g., π), or the result of a previous step (#0, #1…). The language has 58 operations, grouped by domain (geometry, physics, probability, gain-loss, general, other). The annotation was done by crowdworkers on a dynamic platform: choosing an operation, choosing an argument from an allowed list, automatically computing the intermediate value, and checking that the final result is close to the correct answer. The result is MathQA: about 37K problems with programs. The model is Seq2prog (an attention-based LSTM encoder-decoder, OpenNMT), plus a category-aware variant: an n-gram lexicon selects the domain, and the domain hard-switches the decoder parameters. For the subtask tree, the paper is valuable as a ready-made corpus of "operation + references to previous results" steps — essentially a computation DAG that the kernel can execute exactly.

## Key points
- **Features:** text tokens; the output vocabulary is split into operations and arguments; numbers are represented not by their values but by their source (constants, numbers from the problem statement in order of appearance, intermediate results in order of steps); domain category from n-gram frequencies.
- **Architecture:** a two-layer BiRNN/LSTM encoder and an LSTM decoder with attention, d=100, Adam lr 0.001; a categorized decoder LSTM_c; beam 200 (AQuA) and 100 (MathQA); among the executed programs, the closest answer option is chosen.
- **Numbers (Table 3, accuracy):** MathQA — Seq2prog 51.9, Seq2prog+cat 54.2, random choice 20.0; AQuA — the Ling et al. model 36.4, Seq2prog 33.0, Seq2prog+cat 37.9.
- **Dataset:** 37,259 problems, 5.3 operations per problem on average; 80/12/8 split; program validity according to validators 94.64%, expert check of 500 problems — 92% valid.
- **Limitations:** errors — long reasoning chains (45%), operations missing from the language (25%, e.g., factorization), wrong category (12.5%), garbled problem text (17.5%); the categorizer agrees with humans 74.5% of the time.
- **For the subtask tree:** explicit references to previous steps provide ready-made dependency edges; the vocabulary of 58 operations is a good starting point for a node inventory.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [Mathematics & statistics](https://md.research.elamur.ai/free/en/shelves/mathematics/)

## Cited by

Cited by

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## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{amini2019mathqa,
  title = {{MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms}},
  author = {Amini, Aida and Gabriel, Saadia and Lin, Shanchuan and Koncel-Kedziorski, Rik and Choi, Yejin and Hajishirzi, Hannaneh},
  booktitle = {Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)},
  year = {2019},
  doi = {10.18653/v1/n19-1245},
  eprint = {1905.13319},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.18653/v1/n19-1245}
}
```

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## References

27 references, 2 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. \#\# Conclusion In this work, we introduced a representation language and annotation system for large-scale math word problem-solving datasets that addresses unwanted noise in these datasets and lack of formal operation-based representations. We demonstrated the effectiveness of our representation lan… [find](https://scholar.google.com/scholar?q=%5C%23%5C%23+Conclusion+In+this+work%2C+we+introduced+a+representation+language+and+annotation+system+for+large%2Dscale+math+word+problem%2Dsolving+datasets+that+addresses+unwanted+noise+in+these+datasets+and+lack+)
2. Yefim Bakman. 2007. Robust understanding of word problems with extraneous information. In arXiv preprint math/0701393. [find](https://scholar.google.com/scholar?q=Yefim+Bakman%2E+2007%2E+Robust+understanding+of+word+problems+with+extraneous+information%2E+In+arXiv+preprint+math%2F0701393%2E)
3. Daniel G Bobrow. 1964. Natural language input for a computer problem solving system. [find](https://scholar.google.com/scholar?q=Daniel+G+Bobrow%2E+1964%2E+Natural+language+input+for+a+computer+problem+solving+system%2E)
4. Diane J Briars and Jill H Larkin. 1984. An integrated model of skill in solving elementary word problems. In Cognition and instruction 1(3), pages 245–296. [find](https://scholar.google.com/scholar?q=Diane+J+Briars+and+Jill+H+Larkin%2E+1984%2E+An+integrated+model+of+skill+in+solving+elementary+word+problems%2E+In+Cognition+and+instruction+1%283%29%2C+pages+245%E2%80%93296%2E)
5. Rik Koncel-Kedziorski, Subhro Roy, Aida Amini, Nate Kushman, and Hannaneh Hajishirzi. 2016. Mawps: A math word problem repository. In NAACL. [find](https://scholar.google.com/scholar?q=Rik+Koncel%2DKedziorski%2C+Subhro+Roy%2C+Aida+Amini%2C+Nate+Kushman%2C+and+Hannaneh+Hajishirzi%2E+2016%2E+Mawps%3A+A+math+word+problem+repository%2E+In+NAACL%2E)
6. Eugene Charniak. 1968. Calculus word problems. Ph.D. thesis, Massachusetts Institute of Technology. [find](https://scholar.google.com/scholar?q=Eugene+Charniak%2E+1968%2E+Calculus+word+problems%2E+Ph%2ED%2E+thesis%2C+Massachusetts+Institute+of+Technology%2E)
7. Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay. 2014. Learning to automatically solve algebra word problems. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (ACL). [find](https://scholar.google.com/scholar?q=Nate+Kushman%2C+Yoav+Artzi%2C+Luke+Zettlemoyer%2C+and+Regina+Barzilay%2E+2014%2E+Learning+to+automatically+solve+algebra+word+problems%2E+In+Proceedings+of+the+52nd+Annual+Meeting+of+the+Association+for+Computati)
8. Eugene Charniak. 1969. Computer solution of calculus word problems. In Proceedings of the 1st international joint conference on Artificial intelligence, pages 303–316. Morgan Kaufmann Publishers Inc. [find](https://scholar.google.com/scholar?q=Eugene+Charniak%2E+1969%2E+Computer+solution+of+calculus+word+problems%2E+In+Proceedings+of+the+1st+international+joint+conference+on+Artificial+intelligence%2C+pages+303%E2%80%93316%2E+Morgan+Kaufmann+Publishers+Inc%2E)
9. Jianpeng Cheng, Siva Reddy, Vijay Saraswat, and Mirella Lapata. 2017. Learning structured natural language representations for semantic parsing. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 44–55. Association for Computatio… [find](https://scholar.google.com/scholar?q=Jianpeng+Cheng%2C+Siva+Reddy%2C+Vijay+Saraswat%2C+and+Mirella+Lapata%2E+2017%2E+Learning+structured+natural+language+representations+for+semantic+parsing%2E+In+Proceedings+of+the+55th+Annual+Meeting+of+the+Associ)
10. Kyunghyun Cho, Bart van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio. 2014. On the properties of neural machine translation: Encoderdecoder approaches. In Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation, pages 103–111. [find](https://scholar.google.com/scholar?q=Kyunghyun+Cho%2C+Bart+van+Merrie%CC%88nboer%2C+Dzmitry+Bahdanau%2C+and+Yoshua+Bengio%2E+2014%2E+On+the+properties+of+neural+machine+translation%3A+Encoderdecoder+approaches%2E+In+Proceedings+of+SSST%2D8%2C+Eighth+Workshop+o)
11. Denise Dellarosa. 1986. A computer simulation of childrens arithmetic word-problem solving. In Behavior Research Methods, Instruments, Computers 18(2), pages 147–154. [find](https://scholar.google.com/scholar?q=Denise+Dellarosa%2E+1986%2E+A+computer+simulation+of+childrens+arithmetic+word%2Dproblem+solving%2E+In+Behavior+Research+Methods%2C+Instruments%2C+Computers+18%282%29%2C+pages+147%E2%80%93154%2E)
12. Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, and Nate Kushman. 2017. Learning to solve arithmetic word problems with verb categorization. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). [find](https://scholar.google.com/scholar?q=Mohammad+Javad+Hosseini%2C+Hannaneh+Hajishirzi%2C+Oren+Etzioni%2C+and+Nate+Kushman%2E+2017%2E+Learning+to+solve+arithmetic+word+problems+with+verb+categorization%2E+In+Proceedings+of+the+2014+Conference+on+Empiri)
13. Chao-Chun Liang, Yu-Shiang Wong, Yi-Chung Lin, and Keh-Yih Su. 2018. A meaning-based statistical english math word problem solver. In Proceedings of NAACL-HLT 2018. [find](https://scholar.google.com/scholar?q=Chao%2DChun+Liang%2C+Yu%2DShiang+Wong%2C+Yi%2DChung+Lin%2C+and+Keh%2DYih+Su%2E+2018%2E+A+meaning%2Dbased+statistical+english+math+word+problem+solver%2E+In+Proceedings+of+NAACL%2DHLT+2018%2E)
14. Christian Liguda and Thies Pfeiffer. 2012. Modeling math word problems with augmented semantic networks. In International Conference on Application of Natural Language to Information Systems, pages 247–252. Springer. [find](https://scholar.google.com/scholar?q=Christian+Liguda+and+Thies+Pfeiffer%2E+2012%2E+Modeling+math+word+problems+with+augmented+semantic+networks%2E+In+International+Conference+on+Application+of+Natural+Language+to+Information+Systems%2C+pages+24)
15. Wang Ling, Dani Yogatama, Chris Dyer, and Phil Blunsom. 2017. Program induction by rationale generation: Learning to solve and explain algebraic word problems. In Proceedings of ACL. [find](https://scholar.google.com/scholar?q=Wang+Ling%2C+Dani+Yogatama%2C+Chris+Dyer%2C+and+Phil+Blunsom%2E+2017%2E+Program+induction+by+rationale+generation%3A+Learning+to+solve+and+explain+algebraic+word+problems%2E+In+Proceedings+of+ACL%2E)
16. Nicholas Locascio, Karthik Narasimhan, Eduardo DeLeon, Nate Kushman, and Regina Barzilay. 2016. Neural generation of regular expressions from natural language with minimal domain knowledge. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 247–2… [find](https://scholar.google.com/scholar?q=Nicholas+Locascio%2C+Karthik+Narasimhan%2C+Eduardo+DeLeon%2C+Nate+Kushman%2C+and+Regina+Barzilay%2E+2016%2E+Neural+generation+of+regular+expressions+from+natural+language+with+minimal+domain+knowledge%2E+In+Proceed)
17. Subhro Roy and Dan Roth. 2018. Mapping to declarative knowledge for word problem solving. In Proceedings of NAACL-HLT 2018. [find](https://scholar.google.com/scholar?q=Subhro+Roy+and+Dan+Roth%2E+2018%2E+Mapping+to+declarative+knowledge+for+word+problem+solving%2E+In+Proceedings+of+NAACL%2DHLT+2018%2E) [our card](https://md.research.elamur.ai/free/en/papers/roy-2018-mapping-declarative-knowledge-word-problem/)
18. Danqing Huang, Jing Liu, Chin-Yew Lin, and Jian Yin. 2018a. Neural math word problem solver with reinforcement learning. In Proceedings of the 27th International Conference on Computational Linguistics, pages 213–223. [find](https://scholar.google.com/scholar?q=Danqing+Huang%2C+Jing+Liu%2C+Chin%2DYew+Lin%2C+and+Jian+Yin%2E+2018a%2E+Neural+math+word+problem+solver+with+reinforcement+learning%2E+In+Proceedings+of+the+27th+International+Conference+on+Computational+Linguistic)
19. Shyam Upadhyay and Ming-Wei Chang. 2017. Annotating derivations: A new evaluation strategy and dataset for algebra word problems. In Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics. [find](https://scholar.google.com/scholar?q=Shyam+Upadhyay+and+Ming%2DWei+Chang%2E+2017%2E+Annotating+derivations%3A+A+new+evaluation+strategy+and+dataset+for+algebra+word+problems%2E+In+Proceedings+of+the+15th+Conference+of+the+European+Chapter+of+the+A)
20. Danqing Huang, Shuming Shi, Chin-Yew Lin, Jian Yin, and Wei-Ying Ma. 2016. How well do computers solve math word problems? large-scale dataset construction and evaluation. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (ACL). [find](https://scholar.google.com/scholar?q=Danqing+Huang%2C+Shuming+Shi%2C+Chin%2DYew+Lin%2C+Jian+Yin%2C+and+Wei%2DYing+Ma%2E+2016%2E+How+well+do+computers+solve+math+word+problems%3F+large%2Dscale+dataset+construction+and+evaluation%2E+In+Proceedings+of+the+54th+A)
21. Yan Wang, Xiaojiang Liu, and Shuming Shi. 2017. Deep neural solver for math word problems. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing (EMNLP). [find](https://scholar.google.com/scholar?q=Yan+Wang%2C+Xiaojiang+Liu%2C+and+Shuming+Shi%2E+2017%2E+Deep+neural+solver+for+math+word+problems%2E+In+Proceedings+of+the+2017+Conference+on+Empirical+Methods+in+Natural+Language+Processing+%28EMNLP%29%2E)
22. Danqing Huang, Jin-Ge Yao, Chin-Yew Lin, Qingyu Zhou, and Jian Yin. 2018b. Using intermediate representations to solve math word problems. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics. [find](https://scholar.google.com/scholar?q=Danqing+Huang%2C+Jin%2DGe+Yao%2C+Chin%2DYew+Lin%2C+Qingyu+Zhou%2C+and+Jian+Yin%2E+2018b%2E+Using+intermediate+representations+to+solve+math+word+problems%2E+In+Proceedings+of+the+56th+Annual+Meeting+of+the+Association+)
23. Diederik P. Kingma and Jimmy Ba. 2015. Adam: A method for stochastic optimization. In the 3rd International Conference for Learning Representations (ICLR). [find](https://scholar.google.com/scholar?q=Diederik+P%2E+Kingma+and+Jimmy+Ba%2E+2015%2E+Adam%3A+A+method+for+stochastic+optimization%2E+In+the+3rd+International+Conference+for+Learning+Representations+%28ICLR%29%2E)
24. G. Klein, Y. Kim, Y. Deng, J. Senellart, and A. M. Rush. Opennmt: Open-source toolkit for neural machine translation. ArXiv e-prints. [find](https://scholar.google.com/scholar?q=G%2E+Klein%2C+Y%2E+Kim%2C+Y%2E+Deng%2C+J%2E+Senellart%2C+and+A%2E+M%2E+Rush%2E+Opennmt%3A+Open%2Dsource+toolkit+for+neural+machine+translation%2E+ArXiv+e%2Dprints%2E) [our card](https://md.research.elamur.ai/free/en/papers/klein-2017-opennmt-open-source-toolkit-neural/)
25. John M. Zelle and Raymond J. Mooney. 1996. Learning to parse database queries using inductive logic programming. In AAAI/IAAI, pages 1050–1055. AAAI Press/MIT Press. [find](https://scholar.google.com/scholar?q=John+M%2E+Zelle+and+Raymond+J%2E+Mooney%2E+1996%2E+Learning+to+parse+database+queries+using+inductive+logic+programming%2E+In+AAAI%2FIAAI%2C+pages+1050%E2%80%931055%2E+AAAI+Press%2FMIT+Press%2E)
26. Luke Zettlemoyer and Michael Collins. 2005. Learning to map sentences to logical form: Structured classification with probabilistic categorial grammars. In UAI 05, Proceedings of the 21st Conference in Uncertainty in Artificial Intelligence, pages 658–666. [find](https://scholar.google.com/scholar?q=Luke+Zettlemoyer+and+Michael+Collins%2E+2005%2E+Learning+to+map+sentences+to+logical+form%3A+Structured+classification+with+probabilistic+categorial+grammars%2E+In+UAI+05%2C+Proceedings+of+the+21st+Conference+i)
27. Luke Zettlemoyer and Michael Collins. 2007. Online learning of relaxed ccg grammars for parsing to logical form. In Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLPCoNLL), pages 678–687. Association for Co… [find](https://scholar.google.com/scholar?q=Luke+Zettlemoyer+and+Michael+Collins%2E+2007%2E+Online+learning+of+relaxed+ccg+grammars+for+parsing+to+logical+form%2E+In+Proceedings+of+the+2007+Joint+Conference+on+Empirical+Methods+in+Natural+Language+Pr)