Abstract: Situation model and problem model are two important concepts in arithmetic problem solving and representation. However, researchers have different opinions about their definitions, roles and relationships in the process of problem solving. Therefore, our aim is to talk about their development history, discriminate the concepts, and reveal the controversies and future study direction. On the base of general text comprehension theory(Van Dijk & Kintsch,1983), Kintsch and Greeno（1985）first proposed the construction of problem model in arithmetic problem solving research field. They argued that, problem solvers would construct textbase and problem model, and the latter one was the only high-level representation problem solvers constructed. This made other researchers unsatisfied, and many began to express their own opinions and propose the concept of situation model. Nathan，Kintsch, and Young（1992）argued that, while Kintsch and Greeno（1985）placing too much emphasis on schemata and problem model, situation model was very important for that it could make explicit the implicit conditions in the problem, and could also monitor and even correct the possible mistakes in problem model. Then, Moreau and Coquin-Viennot（2003）studied the nature of representation problem solvers constructed through the information types they chose when doing different tasks, and proved that when solving problems, students would construct different representation according the different task requirements, and meanwhile, the mathematical ability of students had a great impact on the their capability to choose relevant information to construct representation. Not only researchers proved the construction of situation model and problem model , but also someone even proposed that the schemata (and therefore the problem model) was not necessarily, only the situation model was enough to solve the problem. First of all, Thevenot, Devidal, Barrouillet, and Fayol（2007）proposed the situation account for the phenomenon of taking the question ahead of the problem text would improve the performance. They contrasted the predictions of the two different theories——the schemata and the situation model, and then the experiment result confirmed the latter one. Second, Thevenot（2010）tested the situation model construction in the process of problem solving by an unexpected recognition task of the original question sentences. The result showed that people did construct mental model (situation model) while paying much attention to the structure of the question sentences, but not the language expression as the schemata theory supposed. Situation model is the qualitative mental representation of the situation described by the problem, and it is constructed in the working memory for temporary use, and contain information both problem-solving relevant and situation-relevant; and problem model is based on the schema knowledge in the long-term memory, and it represents the mathematical structure of numbers in the problem,containing only the problem-solving-relevant information. There are still some questions to answer: such as the nature of problem model, i.e. it’s proposition or perceptual symbol representation? The relationship of situation model and problem model ,and the influencing factors? Besides, the cognitive neuroscience has provided us powerful tools, such as fMRI and ERP to better and deepen our study on representation of arithmetic problem solving.

Key words: situation model, problem model, schema, representation, arithmetic problem solving

摘要： 情境模型与问题模型是数学问题解决研究中的两个重要概念，前者是对问题所述情境的日常化的定性表征，后者是基于图式知识对问题关键变量的数量关系表征。本文介绍了两种模型的发展历史以及目前存在的争议，并提出了未来研究需要解决的问题。

关键词: 情境模型, 问题模型, 图式, 表征, 数学问题解决