Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations

Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 4225–4240 November 7–11, 2021. c⃝2021 Association for Computational Linguistics 4225 Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations Tianqiao Liu, Qiang Fang, Wenbiao Ding, Hang Li, Zhongqin Wu, Zitao Liu∗ TAL Education Group, Beijing, China {liutianqiao,fangqiang,dingwenbiao,lihang4}@tal.com {wuzhongqin,liuzitao}@tal.com Abstract There is an increasing interest in the use of mathematical word problem (MWP) genera- tion in educational assessment. Different from standard natural question generation, MWP generation needs to maintain the underlying mathematical operations between quantities and variables, while at the same time ensuring the relevance between the output and the given topic. To address above problem, we develop an end-to-end neural model to generate diverse MWPs in real-world scenarios from common- sense knowledge graph and equations. The proposed model (1) learns both representations from edge-enhanced Levi graphs of symbolic equations and commonsense knowledge; (2) au- tomatically fuses equation and commonsense knowledge information via a self-planning module when generating the MWPs. Exper- iments on an educational gold-standard set and a large-scale generated MWP set show that our approach is superior on the MWP genera- tion task, and it outperforms the SOTA models in terms of both automatic evaluation metrics, i.e., BLEU-4, ROUGE-L, Self-BLEU, and hu- man evaluation metrics, i.e., equation relevance, topic relevance, and language coherence. To en- courage reproducible results, we make our code and MWP dataset public available at https:// github.com/tal-ai/MaKE_EMNLP2021. 1 Introduction A mathematical word problem (MWP) is a coher- ent narrative that provides clues to the underlying correct mathematical equations and operations be- tween variables and numerical quantities (Cetintas et al., 2010; Moyer et al., 1984). MWPs challenge a student from a wide range of skills such as liter- acy skills for understanding the question, analytical skills for recognizing the problem type and apply- ing arithmetical operators (Rembert et al., 2019; Moon-Rembert and Gilbert, 2019). Table 1 shows ∗ The corresponding author: Zitao Liu one such problem1 where students are asked to infer the counts of chickens and rabbits. Math Word Problem Chickens and rabbits were in the yard. Together they had 27 heads and 86 legs. How many rabbits were in the yard? Equations x+y=27 Solutions x=11 2x+4y=86 y=16 Table 1: An illustrative example of an MWP. In this paper, our objective is to automati- cally generate well-formed MWPs. Such automa- tion will not only reduce the teachers’ burden of manually designing MWPs, but provide students with a sufficiently large number of practice exer- cises, which help students avoid rote memorization (Williams, 2011; Wang and Su, 2016). A large spectrum of models have been developed and successfully applied in a broad area of natu- ral question generation (NQG) (Pan et al., 2019; Li et al., 2018; Liu et al., 2020; Sun et al., 2018; Zhang and Bansal, 2019; Kurdi et al., 2020; Guan et al., 2021a,b) and there has been a recent movement from the NQG community towards automatic gen- eration of MWPs (Koncel-Kedziorski et al., 2016a; Polozov et al., 2015; Zhou and …

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