Noun-MWP: Math Word Problems Meet Noun Answers

Noun-MWP: Math Word Problems Meet Noun Answers Taehun Cha∗, Jaeheun Jung∗and Donghun Lee† Department of Mathematics Korea University {cth127,wodsos,holy}@korea.ac.kr 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 ap- ply the method on Expression-Pointer Trans- former (EPT). Our model, N-EPT, solves Noun- MWPs significantly better than other mod- els, 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. 1 Introduction Question-answering (QA) (Woods, 1968) and QA problems involving mathematics (Bobrow, 1964) are one of the classic NLP problems in com- puter science. Later, mathematics education com- munity investigated a class of problems coined as Math Word Problems (MWPs) (Nesher and Ka- triel, 1977; Caldwell and Goldin, 1979; Ballew and Cunningham, 1982). Research in solving MWPs with computers started from purely rule-based ap- proaches (Hosseini et al., 2014) and statistics-based approaches (Kushman et al., 2014), through hy- brids (Roy and Roth, 2015), and more recently deep-learning-based approaches (Wang et al., 2017, 2018; Li et al., 2019). Proportionally, the number of publicly available dataset for MWPs increased; for example, Alg514 (Kushman et al., 2014), DRAW (Upadhyay and Chang, 2015), MAWPS (Koncel-Kedziorski et al., 2016), Math23K (Wang et al., 2017), AllArith (Roy and Roth, 2017), Dolphin18K (Huang et al., 2016), and ASDiv-A (Miao et al., 2020). 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} Table 1: Highlighted examples comparing MWP, Noun- MWP, and Extractive QA problems. Relevant numbers, nouns, and a novel element in Noun-MWP are marked in red, blue, and green, respectively. problems whose answer is a non-numeric substring of the inputs are frequently seen in real-world math problems in mathematics education. Our Contribution • We bring attention to Noun-MWP, a class of MWPs whose answer is a noun-substring of the input string. • We propose a systematic approach to em- power existing MWP solvers to …

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