Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification

Authors

DOI:

https://doi.org/10.18201/ijisae.2022.271

Keywords:

Solving Arithmetic Word Problems, Information Extraction, Word Problem Classification

Abstract

In the modern era, Intelligent Tutoring Systems (ITS), Computer Based Trainings (CBT) etc. are gaining popularity rapidly in the educational sectors as well as professional sectors and an automatic math word problem solver is one of the crucial sub-fields of ITS. Solving mathematical word problems automatically is a challenging research problem in Artificial Intelligence (AI), Natural Language Processing (NLP) and Machine Learning (ML), since understanding and extracting relevant information from an unstructured text require lots of reasoning abilities. Till date, much research has been carried out in this domain, focusing on solving each type of mathematical word problem, which include solving like arithmetic word problems, algebraic word problems, geometric word problems, trigonometric word problems etc. In this work, we present an approach to solve arithmetic word problems automatically. However, it is limited to solve only single operation and single equation word problems. We used a rule-based approach in classifying word problems. We propose various rules to establish the relationships and dependencies among various key-entities to broadly classify the word problems into four categories (Change, Combine, Compare and Division-Multiplication) and their sub-categories to identify the desired operation among+, -, *, and /. Irrelevant information is also filtered out from input problem texts, based on hand-crafted rules to extract relevant quantities. Later, an equation is formed with the relevant quantities and predicted operation to generate the final answer. The work proposed here, performs well as compared to most of the similar systems reported on the standard SingleOp dataset achieving an accuracy of 93.02%.

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References

L. Verschaffel, B. Greer, and E. De Corte. Making sense of word problems. Leiden, Netherlands: Lisse Swets and Zeitlinger, 2000, doi:10.1023/A:1004190927303.

S. Roy and D. Roth. Solving general arithmetic word problems. in Proc. 2015 Conf. Empirical Methods Natural Language Processing (EMNLP), Lisbon, Portugal, Sep. 17–21, 2015, pp. 1743-1752, doi:10.18653/v1/D15-1202.

M. J. Nathan. Knowledge and situational feedback in a learning environment for algebra story problem solving. Interactive Learn. Environ. vol. 5, no. 1, pp. 135–159, 1998, doi:10.1080/1049482980050110.

D. Arnau, M. Arevalillo-Herr´aez, L. Puig, and J. A. Gonz´alez-Calero. Fundamentals design and the operation of an intelligent tutoring system for the learning of the arithmetical and algebraic way of solving word problems. Comput. & Educ. vol. 63, pp. 119–130, Apr. 2013, doi:10.1016/j.compedu.2012.11.020

D. Arnau, M. Arevalillo-Herr´aez, and J. A. Gonz´alez-Calero. Emulating human supervision in an intelligent tutoring system for arithmetical problem solving. IEEE Trans. Learn. Technol. vol. 7, no. 2, pp. 155–164, Apr./Jun. 2014, doi: 10.1109/TLT.2014.2307306.

C. R. Beal. Animalwatch: An intelligent tutoring system for algebra readiness. in Int. Handbook Metacognition Learn. Technologies. Springer, Mar. 2013, pp. 337–348, doi:10.1007/978-1-4419-5546-3 22.

M. S. Riley, J. G. Greeno, and J. I. Heller. Development of children’s problem-solving ability in arithmetic. Univ. of Pittsburgh, Pittsburgh, PA, USA, Tech. Rep. LRDC-1984/37, 1984. [Online]. Available:https://files.eric.ed.gov/fulltext/ED252410.pdf

C. R. Fletcher. Understanding and solving arithmetic word problems: A computer simulation. Behav. Res. Methods, Instrum., & Comput. vol. 17, no. 5, pp. 565–571, Sep. 1985, doi:10.3758/BF03207654.

A. Mitra and C. Baral. Learning to use formulas to solve simple arithmetic problems. in Proc. 54th Annu. Meeting Association Computational Linguistics (ACL), Berlin, Germany, Aug. 7–12, 2016, pp. 2144–2153, doi: 10.18653/v1/P16-1202.

S. Mandal and S. K. Naskar. Classifying and Solving Arithmetic Math Word Problems—An Intelligent Math Solver. in IEEE Transactions on Learning Technologies. vol. 14, no. 1, pp. 28-41, Feb. 2021, doi: 10.1109/TLT.2021.3057805.

T. P. Carpenter, J. Hiebert, and J. M. Moser. Problem structure and first-grade children’s initial solution processes for simple addition and subtraction problems. J. Res. Math. Educ., pp. 27–39, Jan. 1981, doi:10.5951/jresematheduc.24.5.0428.

P. Nesher, J. G. Greeno, and M. S. Riley. The development of semantic categories for addition and subtraction. Educational Stud. Math. vol. 13, no. 4, pp. 373–394, Nov. 1982, doi:10.1007/BF00366618.

G. Vergnaud. A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. Addition subtraction: A Cogn. perspective, pp. 39–59, 1982, doi: 10.4324/ 9781003046585-4.

T. P. Carpenter, E. Ansell, M. L. Franke, E. Fennema, and L. Weisbeck. Models of problem solving: A study of kindergarten children’s problem-solving processes. J. Res. Math. Educ., pp. 428–441, Nov. 1993, doi:10.5951/jresematheduc.24.5.0428.

N. Kushman, L. Zettlemoyer, R. Barzilay, and Y. Artzi. Learning to automatically solve algebra word problems. in Proc. 52nd Annu. Meeting Association Computational Linguistics (ACL), Baltimore, MD, USA, Jun. 22–27, 2014, pp. 271–281, doi: 10.3115/v1/P14-1026.

R. Koncel-Kedziorski, H. Hajishirzi.+ 90A. Sabharwal, O. Etzioni, and S. D. Ang. Parsing algebraic word problems into equations. Trans. 01Assoc. Comput. Linguistics. vol. 3, pp. 585–597, Dec. 2015, doi: 10.1162/tacl_a_00160.

D.G. Bobrow. Natural language input for a computer problem solving system. 1964.

E. Charniak. Computer Solution of Calculus Word Problem. 1968.

Y. Bakman. Robust understanding of word problems with extraneous information. vol. arXiv preprint math/0701393, 2007.

C. Liguda and T. Peffier. Modeling Math Word Problems with Augmented Semantic Networks. in In: Bouma G., Ittoo A., Métais E., Wortmann H. (eds) Natural Language Processing and Information Systems. NLDB 2012. vol. vol 7337, Springer, Berlin, Heidelberg., 2012, pp. 247-252, Lecture Notes in Computer Science.

M.J. Hosseini, H. Hajishirzi, O. Etzioni, and N. Kushman. Learning to solve arithmetic word problems with verb categorization. in In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing, EMNLP 2014., Doha, Qatar, A meeting of SIGDAT, a Special Interest Group of the ACL., October 25-29,2014, pp. 523-533. [Online]. http://aclweb.org/anthology/D/D14/D14-1058.pdf

S. Shi, Y. Wang, C. Lin, X. Liu, and Y. Rui. Automatically solving number word problems by semantic parsing and reasoning. in In: Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, EMNLP 2015, Lisbon, Portugal, September 17-21, 2015, pp. 1132-1142. [Online]. http://aclweb.org/anthology/D/D15/D15-1135.pdf

S. Roy and D. Roth. Illinois math solver: Math reasoning on the web. in In: Proceedings of the Demonstrations Session, NAACL HLT 2016, The 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies., San Diego California, USA., June 12-17, 2016, pp. 52–56. [Online]. http://aclweb.org/anthology/N/N16/N16-3011.pdf

S. Roy and D. Roth. Unit dependency graph and its application to arithmetic word problem solving. in In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence., San Francisco, California, USA., February 4-9, 2017, pp. 3082–3088. [Online]. http://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14764

S. Roy, T. Vieira, and D. Roth. Reasoning about quantities in natural language. vol. TACL 3, pp. 1–13, 2015. [Online]. https://tacl2013.cs.columbia.edu/ojs/index.php/tacl/article/view/452

S. Roy and D. Roth. Mapping to Declarative Knowledge for Word Problem Solving. Transactions of the Association for Computational Linguistics. vol. Volume 6, pp. 159-172, 2018.

L. Zhou, S. Dai, and L. Chen. Learn to solve algebra word problems using quadratic programming. in In: Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, EMNLP 2015, Lisbon, Portugal, September 17-21, 2015, pp. 817-822.

S. Upadhyay and M. Chang. Annotating derivations: A new evaluation strategy and dataset for algebra word problems. 2016. [Online]. http://arxiv.org/abs/1609.07197

D. Huang, S. Shi, C. Lin, J. Yin, and W. Ma. 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 2016. vol. Volume 1: Long Papers (2016), August 2016. [Online]. http://aclweb.org/anthology/P/P16/P16-1084.pdf

Y. Wang, X. Liu, and S. Shi. Deep Neural Solver for Math Word Problems. pp. 845–854, January 2017. [Online]. https://www.aclweb.org/anthology/D17-1088.pdf

M.S., et al. Riley. Development of children’s problem-solving ability in arithmetic. 1984.

D.J. Briars and J.H Larkin. An integrated model of skill in solving elementary word problems. vol. Cognition and instruction 1(3), pp. 245-296, 1984.

D. Dellarosa. A computer simulation of childrens arithmetic word-problem solving. Behavior Reaearch Methods. vol. Instruments, & Computers 18(2), pp. 147-154, 1986.

DadsWorksheets.com, Available at: https://www.dadsworksheets.com/worksheets/word-problems.html, accessed June 2021.

C. Liang, S. Tsai, T. Chang, Y. Lin, and K. Su. A meaning-based English math word problem solver with understanding, reasoning and explanation. in Proc. 26th Int. Conf. Computational Linguistics (COLING), Osaka, Japan, Dec. 11–16, 2016, pp. 151–155.

Allen Institute for AI, Available at: http://allenai.org/data.html, accessed June 2021.

S. Mandal and S. K. Naskar. Solving Arithmetic Mathematical Word Problems: A Review and Recent Advancements. ICITAM 2017: 95-114

S. Mandal and S. K. Naskar. Solving Arithmetic Word Problems by Object Oriented Modeling and Query-Based Information Processing. Int. J. Artif. Intell. Tools 28(4): 1940002:1-1940002:23 (2019)

S. Mandal, A. A. Sekh and S. K. Naskar. Solving arithmetic word problems: A deep learning based approach. J. Intell. Fuzzy Syst. 39(2): 2521-2531 (2020)

NeuralCoref 4.0: Coreference Resolution in spaCy with Neural Networks, Available at: https://github.com/huggingface/neuralcoref, accessed June 2021.

DependencyParser, Available at: https://spacy.io/api/dependencyparser, accessed June 2021.6

Linguistic Features, Available at: https://spacy.io/usage/linguistic-features, accessed June 2021.

Rule-based_Math_Word_Problem_Solver, Available at: https://github.com/Swagata-Acharya/Rule-based_Math_Word_Problem_Solver.git, accessed August 2021.

System overview of rule-based math word problem solver

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Published

30.03.2022

How to Cite

Mandal, S., Acharya, S., & Basak, R. (2022). Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification. International Journal of Intelligent Systems and Applications in Engineering, 10(1), 87–97. https://doi.org/10.18201/ijisae.2022.271

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Research Article