Learning to Automatically Solve Algebra Word Problems

By Nate Kushman, Luke S. Zettlemoyer, Regina Barzilay, Yoav Artzi. 2014

399 citations recorded by the source corpus.

We present an approach for automatically learning to solve algebra word problems. Our algorithm reasons across sentence boundaries to construct and solve a system of linear equations, while simultaneously recovering an alignment of the variables 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, demonstrating that the system can correctly answer almost 70% of the questions in the dataset. This is, to our knowledge, the first learning result for this task.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Natural Language Processing

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Citations in the corpus

SQuAD: 100,000+ Questions for Machine Comprehension of Text (2016, background): “Algebra word problems require understanding a story well enough to turn it into a system of equations, which can be easily solved to produce the answer (Kushman et al., 2014; Hosseini et al., 2014).”
DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs (2019, background): “also contain similar phenomena to what is in DROP (Koncel-Kedziorski et al., 2015; Kushman et al., 2014; Hosseini et al., 2014; Clark et al., 2016; Ling et al., 2017).”
Training Verifiers to Solve Math Word Problems (2021, background): “Early math word problem datasets (Kushman et al., 2014; Roy and Roth, 2015) are relatively small and are not well suited for testing the limits of modern language models.”
MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers (2021, background): “Over the last few years, there are a growing number of datasets (Kushman et al., 2014; KoncelKedziorski et al., 2016; Upadhyay and Chang, 2017; Huang et al., 2016; Wang et al., 2017; Qin et al., 2020; Miao et al., 2020; Patel et al., 2021) and deep learning-based methods that have been proposed to s”
MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms (2019, background): “, 2016), Alg514 (Kushman et al., 2014), and DRAW-1K (Upadhyay and Chang, 2017).”
Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems (2017, methodology): “Extensive efforts have been made in the domain of math problem solving (Hosseini et al., 2014; Kushman et al., 2014; Roy and Roth, 2015), which aim at obtaining the correct answer to a given math problem.”
MAWPS: A Math Word Problem Repository (2016, methodology): “As no current system can process SimulEq-L , we report the performance of the two most general systems (Koncel-Kedziorski et al., 2015; Kushman et al., 2014) on SingleEq and SimulEq-S under different overlap and grammaticality properties in Table 2.”
Language Understanding for Text-based Games using Deep Reinforcement Learning (2015, methodology): “An alternative approach is to convert text descriptions to pre-speciﬁed representations using annotated training data, commonly used in language grounding tasks (Matuszek et al., 2013; Kushman et al., 2014).”
Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, background): “Kushman et al. (2014) and Roy and Roth (2018) designed templates to ﬁnd the alignments between the declarative language and equations.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, background): “For AI2, IL, KAZB, ALGES, AllArith, DRAW, and MathQA, we follow their own either n-fold cross-validation setting or the train/dev/test splits originally specified in each dataset.”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, background): “…features, such as POS tags, paths in the dependency trees, keywords, etc., to allow the model to focus on the quantities in the problems (Kushman et al., 2014; Hosseini et al., 2014; Roy et al., 2015; Roy and Roth, 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Upadhyay et al.,…”
Solving General Arithmetic Word Problems (2016, methodology): “(Hos-seini et al., 2014) mentions the result of running the system of (Kushman et al., 2014) on AI2 dataset, and we report their result here.”
Parsing Algebraic Word Problems into Equations (2015, methodology): “In addition, ALGES overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.”
Reasoning about Quantities in Natural Language (2015, methodology): “Approaches range from using rule-based methods (Bobrow, 1964; Lev et al., 2004; Mukherjee and Garain, 2008) to recent template matching techniques (Kushman et al., 2014) .”
Learning to Solve Arithmetic Word Problems with Verb Categorization (2014, methodology): “Table 3 shows that A RIS signiﬁcantly outperforms KAZB and the majority baseline.”
Analysing Mathematical Reasoning Abilities of Neural Models (2019, background): “, 2017), or more complex mathematical templates like in (Kushman et al., 2014)), which would undoubtedly perform competitively on the tasks we present in this paper, we will limit ourselves to general sequence-processing architectures which are used in other non-mathematical tasks to present the mos”
Deep Neural Solver for Math Word Problems (2017, methodology): “The most frequently used Alg514 (Kushman et al., 2014) dataset contains only 514 linear algebra problems with 28 equation templates.”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, methodology): “For example, the Alg514 dataset used in Kushman et al. (2014) and Zhou et al. (2015) only contains 514 problems of 28 types.”
Combining Retrieval, Statistics, and Inference to Answer Elementary Science Questions (2016, background): “A few systems have attempted standardized tests, e.g., in geometry (Seo et al. 2014) and mathematics (Hosseini et al. 2014; Kushman et al. 2014), and work well due to their limited domains and stylized wording of questions.”