Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints

Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 5986–5999 November 7–11, 2021. c⃝2021 Association for Computational Linguistics 5986 Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints Zichao Wang 1 Andrew S. Lan 2 1 Rice University 2 University of Massachusetts Amherst 3 OpenStax {zw16,richb}@rice.edu, andrewlan@cs.umass.edu Richard G. Baraniuk 1,3 Abstract We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical com- putation and a context that specifies the prob- lem scenario. Existing approaches are prone to generating MWPs that are either mathemat- ically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem tem- plate, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that lever- ages i) pre-trained language models and a con- text keyword selection model to improve the language quality of the generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantita- tive and qualitative experiments on three real- world MWP datasets demonstrate the superior performance of our approach compared to var- ious baselines. 1 Introduction Math word problems (MWPs) are an important type of educational resource that help assess and improve students’ proficiency in various mathemat- ical concepts and skills (Walkington, 2013; Ver- schaffel et al., 2020). An MWP usually has a cor- responding underlying math equation that students will need to identify by parsing the problem and then solve the problem using this equation. An MWP is usually also associated with a “context”, i.e., the (often real-world) scenario that the math equation is grounded in, expressed in the question’s text. The equation associated with an MWP is often exact and explicit, while the context of the MWP is more subtle and implicit. It is not immediately clear how the context information can be extracted or represented. Table 1 shows an example of an MWP and its associated equation. Table 1: An examples of MWP and its underlying equa- tion. See Table 2 for more information on the datasets. MWP: Joan found 70 seashells on the beach . She gave Sam some of her seashells . She has 27 seashells . How many seashells did she give to Sam ? Equation: x = (70 - 27) In this work, we study the problem of automat- ically generating MWPs from equations and con- text, which is important for three reasons. First, an automatic MWP generation method can aid in- structors and content designers in authoring MWP questions, accelerating the (often costly and labor- intensive) MWP production process. Second, an automated MWP generation method can generate MWPs tailored to each student’s background and interests, providing students with a personalized learning experience (Walkington, 2013) that often leads to better engagement and improved learning outcomes (Connor-Greene, 2000; Karpicke, 2012; Karpicke and Roediger, 2008; Koedinger et al., 2015; Kovacs, 2016; Rohrer and Pashler, 2010). …

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