A review of methods for automatic understanding of natural language mathematical problems

By Anirban Mukherjee, Utpal Garain. 2008

107 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Natural Language Processing

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Citations in the corpus

Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, methodology): “Solving MWP requires logical reasoning over the quantities presented in the context (Mukherjee and Garain, 2008) to compute the numerical answer.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, background): “Among them, math word problems (MWPs) are frequently chosen to study natural language understanding and simulate human problem solving (Bakman, 2007; Mukherjee and Garain, 2008; Liang et al., 2016), because the answer is not a span within the given problem text that can be directly extracted.”
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.”
Learning to Automatically Solve Algebra Word Problems (2014, background): “The dominant existing approach is to hand engineer rule-based systems to solve math problem in specific domains (Mukherjee and Garain, 2008; Lev et al., 2004).”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, background): “Systems not included for evaluation: Although the system of Shi et al. (2015) achieves very high performance on number word problems, we do not include it in our evaluation because it is unknown how to extend it to other problem types.”
Automatically Solving Number Word Problems by Semantic Parsing and Reasoning (2015, background): “Please refer to Mukherjee & Garain (2008) for a review of symbolic approaches before 2008.”
Learn to Solve Algebra Word Problems Using Quadratic Programming (2015, methodology): “The word problem solver is traditionally created by the rule-based approach (Lev et al., 2004; Mukherjee and Garain, 2008; Matsuzaki et al., 2013).”
The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers (2018, background): “Those early efforts for automatic understanding of natural language mathematical problems have been thoroughly reviewed in [9].”
Natural Language Processing for Solving Simple Word Problems (2015, background): “In a review of such knowledge-based systems by (Mukherjee and Garain, 2009), it was remarked that there are no datasets to compare performances.”
Tree-structured Decoding for Solving Math Word Problems (2019, background): “In MWPs, it is very common that the input text contains irrelevant numbers, such as date or descriptive text such as ‘third grade stu-dent’.”
A Tag-Based Statistical English Math Word Problem Solver with Understanding, Reasoning and Explanation (2016, methodology): “Previous MWP solvers either adopt rule-based approaches [Mukherjee and Garain, 2008; Hosseini et al., 2014] or purely statistic-based approaches [Kushman et al., 2014; Roy and Roth, 2015] to identify entities, quantities, operations, and get the answer.”
Learning To Use Formulas To Solve Simple Arithmetic Problems (2016, unknown): “Mukherjee and Garain (2008) survey these works.”
DRAW: A Challenging and Diverse Algebra Word Problem Set (2015, background): “Developing automatic solvers which can solve simple mathematical reasoning problems is a long pursued sub-goal of AI (Newell et al., 1959; Bobrow, 1964; Mukherjee and Garain, 2008).”
A Bottom-Up DAG Structure Extraction Model for Math Word Problems (2021, background): “Please refer to Mukherjee and Garain (2008) and Zhang et al. (2019) for a more comprehensive review.”
Learning Fine-Grained Expressions to Solve Math Word Problems (2017, background): “Please see Mukherjee and Garain (2008) for a summary.”