Noun- MWP : Math Word Problems Meet Noun Answers (2022)

Abstract: We introduce a new type of problems for math word problem (MWP) solvers, named Noun-MWPs, whose answer is a non-numerical string containing a noun from the problem text. We present a novel method to empower existing MWP solvers to handle Noun-MWPs, and apply the method on Expression-Pointer Transformer (EPT). Our model, N-EPT, solves Noun-MWPs significantly better than other models, and at the same time, solves conventional MWPs as well. Solving Noun-MWPs may lead to bridging MWP solvers and traditional question-answering NLP models.

## introduction question-answering (qa) @xcite ) and qa problems involving mathematics @xcite are one of the classic nlp problems in computer science. later, mathematics education community investigated a class of problems coined as math word problems (mwps) @xcite @xcite . research in solving mwps with computers started from purely rule-based approaches @xcite and statistics-based approaches @xcite , through hybrids @xcite , and more recently deep-learning-based approaches @xcite @xcite . proportionally, the number of publicly available dataset for mwps increased; for example, alg514 @xcite , draw @xcite , mawps @xcite , math23k @xcite , allarith @xcite , dolphin18k @xcite , and asdiv-a @xcite . the mathematical depth of the problems in mwp datasets vary, yet the majority of datasets require only numerical answers. on the other hand, math * equal contribution † corresponding author mwp chloe was organizing her bookcase making sure each of the shelves had exactly 6 books on it. if she had 5 shelves of mystery books and 4 shelves of picture books, how many books did she have in total? → (6 × 5) + (6 × 4) extractive qa in 1517, the seventeen-year-old king sailed to castile. there, his flemish court . . . . in may 1518, charles traveled to barcelona in aragon. where did charles travel to first, castile or barcelona? → arg min{castile : 1517, barcelona : 1518} noun-mwp sihyeon collected 64 stamps, and soma collected 1 fewer stamps than sihyeon. junwoo collected 7 bundles of 10 stamps each. who among the three has collected the fewest stamps? → arg min{sihyeon : 64, soma : 64 -1, junwoo : 7 × 10} ## conclusion we introduce noun-mwp, a class of problems that are frequently used in mathematics education, and yet to be handled by mwp solvers. we present a three-step method, candidate selection, expression assignment, and query interpretation, to empower existing mwp solvers to handle noun-mwp as well as the conventional mwps. as a proofof-concept implementation, we construct n-ept using ept as its baseline mwp solver, and the new noun-mwp dataset consists of 604 questionsexpression-answer pairs to validate the model's performance. by modifying the original ept to handle noun information and additional operations, our n-ept significantly outperforms benchmark models in noun-mwps and retains the capacity of the original mwp solver. noun-mwps may serve as a novel testbed for mwp solvers to gauge their understanding of mathematical logic and natural language.