A Theme-Rewriting Approach for Generating Algebra Word Problems

Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pages 1617–1628, Austin, Texas, November 1-5, 2016. c⃝2016 Association for Computational Linguistics A Theme-Rewriting Approach for Generating Algebra Word Problems Rik Koncel-Kedziorski Ioannis Konstas Luke Zettlemoyer Hannaneh Hajishirzi University of Washington kedzior@uw.edu, {ikonstas, lsz, hannaneh}@cs.washington.edu Abstract Texts present coherent stories that have a par- ticular theme or overall setting, for example science fiction or western. In this paper, we present a text generation method called rewrit- ing that edits existing human-authored narra- tives to change their theme without changing the underlying story. We apply the approach to math word problems, where it might help students stay more engaged by quickly trans- forming all of their homework assignments to the theme of their favorite movie with- out changing the math concepts that are be- ing taught. Our rewriting method uses a two- stage decoding process, which proposes new words from the target theme and scores the re- sulting stories according to a number of fac- tors defining aspects of syntactic, semantic, and thematic coherence. Experiments demon- strate that the final stories typically represent the new theme well while still testing the orig- inal math concepts, outperforming a number of baselines. We also release a new dataset of human-authored rewrites of math word prob- lems in several themes. 1 Introduction Storytelling is the complex activity of expressing a plot, its events and participants in words meaning- ful to an audience. Automatic storytelling systems can be used for customized sport commentaries, en- riching video games with personalized or dynamic plot-lines (Barros and Musse, 2007), or providing customized learning materials which meet each indi- vidual student’s needs and interests (Bartlett, 2004). In this paper, we focus on generating narrative-style Jim walked 0.2 of a mile from school to David’s house and 0.7 of a mile from David’s house to his own house. How many miles did Jim walk in all? Star Wars Uncle Owen walked 0.2 of a mile from hangar to Luke Skywalker’s room and 0.7 of a mile from Luke Sky- walker’s room to his own room. How many miles did Uncle Owen walk in all? Cartoon Finn squished 0.2 of a mile from cupboard to Melissa’s dock and 0.7 of a mile from Melissa’s dock to his own dock. How many miles did Finn squish in all? Western Duane strolled 0.2 of a mile from barn to Madeline’s camp and 0.7 of a mile from Madeline’s camp to his own camp. How many miles did Duane stroll in all? Figure 1: An example story and rewrites in 3 themes. math word problems (Figure 1) and demonstrate that it is possible to design an algorithm that can auto- matically change the overall theme of a text without changing its underlying story, for example to create more engaging homework that is in the theme of a student’s favorite movie. A math word problem is a coherent story that provides the student with good clues to the cor- rect mathematical operations between …

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