Learning to Automatically Solve Algebra Word Problems

Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, pages 271–281, Baltimore, Maryland, USA, June 23-25 2014. c⃝2014 Association for Computational Linguistics Learning to Automatically Solve Algebra Word Problems Nate Kushman†, Yoav Artzi‡, Luke Zettlemoyer‡, and Regina Barzilay† † Computer Science and Articial Intelligence Laboratory, Massachusetts Institute of Technology {nkushman, regina}@csail.mit.edu ‡ Computer Science & Engineering, University of Washington {yoav, lsz}@cs.washington.edu Abstract We present an approach for automatically learning to solve algebra word problems. Our algorithm reasons across sentence boundaries to construct and solve a sys- tem of linear equations, while simultane- ously recovering an alignment of the vari- ables and numbers in these equations to the problem text. The learning algorithm uses varied supervision, including either full equations or just the final answers. We evaluate performance on a newly gathered corpus of algebra word problems, demon- strating that the system can correctly an- swer almost 70% of the questions in the dataset. This is, to our knowledge, the first learning result for this task. 1 Introduction Algebra word problems concisely describe a world state and pose questions about it. The described state can be modeled with a system of equations whose solution specifies the questions’ answers. For example, Figure 1 shows one such problem. The reader is asked to infer how many children and adults were admitted to an amusement park, based on constraints provided by ticket prices and overall sales. This paper studies the task of learning to automatically solve such problems given only the natural language.1 Solving these problems requires reasoning across sentence boundaries to find a system of equations that concisely models the described se- mantic relationships. For example, in Figure 1, the total ticket revenue computation in the second equation summarizes facts about ticket prices and total sales described in the second, third, and fifth 1The code and data for this work are available at http://groups.csail.mit.edu/rbg/code/ wordprobs/. Word problem An amusement park sells 2 kinds of tickets. Tickets for children cost $1.50. Adult tickets cost $4. On a certain day, 278 people entered the park. On that same day the admission fees collected totaled $792. How many children were admitted on that day? How many adults were admitted? Equations x + y = 278 1.5x + 4y = 792 Solution x = 128 y = 150 Figure 1: An example algebra word problem. Our goal is to map a given problem to a set of equations representing its algebraic meaning, which are then solved to get the problem’s answer. sentences. Furthermore, the first equation models an implicit semantic relationship, namely that the children and adults admitted are non-intersecting subsets of the set of people who entered the park. Our model defines a joint log-linear distribu- tion over full systems of equations and alignments between these equations and the text. The space of possible equations is defined by a set of equa- tion templates, which we induce from the train- ing examples, where each template has a set of slots. Number slots are …

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