Frame-Based Calculus of Solving Arithmetic Multi-Step Addition and Subtraction Word Problems

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.