The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Rule-based Methods <s> In this paper, I describe a computer program, WORDPRO, which simulates the psychological processes involved when third-grade children understand and solve simple arithmetic word problems. Both the implementation of the program and its performance on a set of sample problems are presented. WORDPRO is a useful research tool in that it demonstrates the sufficiency of the theory upon which it is based, assists in communicating that theory to other researchers, and provides a sources of empirical predictions for experimental tests of the theory. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Rule-based Methods <s> Understanding of free-format multi-step arithmetic word problems with extraneous information is discussed. A model including a full set of general skills necessary for understanding such problems was developed and computer implemented. The validity of the simulation was confirmed by testing on a variety of word problems with extraneous information. The results of this study show the way for moving from an intuitive understanding of word problems to a conscious and controlled process. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Rule-based Methods <s> This article addresses the problem of understanding mathematics described in natural language. Research in this area dates back to early 1960s. Several systems have so far been proposed to involve machines to solve mathematical problems of various domains like algebra, geometry, physics, mechanics, etc. This correspondence provides a state of the art technical review of these systems and approaches proposed by different research groups. A unified architecture that has been used in most of these approaches is identified and differences among the systems are highlighted. Significant achievements of each method are pointed out. Major strengths and weaknesses of the approaches are also discussed. Finally, present efforts and future trends in this research area are presented. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Rule-based Methods <s> Computer-assisted instruction systems have been broadly applied to help students solving math word problems. However, these systems offer little help to students encountering multi-step arithmetic word problems that do not be stored in the predesigned database. MSWPAS is a computer simulation system of people’s arithmetic multi-step addition and subtraction word problems behavior, which composed of MSWPAS-NP and MSWPAS-CP. In MSMPAS-NP, the natural language of word problems are processed and reflected into frames, and in MSMPAS-CP, calculus is performed based on those frames. This paper focuses on MSMPAS-CP. Psychological theoretical foundation and knowledge representation of MSMPAS-CP are presented at first. A method of frame-based calculus for solving multi-step addition and subtraction word problems is proposed, and then the architecture of system and how it works are discussed. Finally, an experiment is carried out, which shows that the method of frame-based calculus can effectively solve multi-step word problems. <s> BIB004
The early approaches to math word problems are rule-based systems based on hand engineering. Published in 1985, WORD-PRO BIB001 solves one-step arithmetic problems. It predefines four types of schemas, including change-in, change-out, combine and compare. The problem text is transformed into a set of propositions and the answer is derived with simple reasoning based on the propositions. Another system ROBUST, developed by Bakman BIB002 , could understand free-format multi-step arithmetic word problems. It further expands the change schema of WORDPRO BIB001 into six distinct categories. The problem text is split into sentences and each sentence is mapped to a proposition. Yun et al. also proposed to use schema for multi-step math problem solving BIB004 . However, the implementation details are not explicitly revealed in BIB004 . Since these systems have been out of date, we only provide such a brief overview to cover the representative ones. Readers can refer to BIB003 for a comprehensive survey of early rule-driven systems for automatic understanding of natural language math problems.