论数学问题解决中情境模型与问题模型的关系

The Situation Model and Problem Model in Arithmetic Problem Solving

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,并提出未来研究需要解决的问题。

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 basis of general text comprehension theory （Van Dijk ＆ Kintsch, 1983）, Kintsch and Greeno （1985）first proposed the construction of problem models 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 left other researchers unsatisfied, and many began to express their own opinions and propose the concept of the situation model. Nathan, Kintsch, and Young （1992） argued that while Kintsch and Greeno（1985） placed too much emphasis on schemata and problem models, the situation model was very important for it could make explicit the implicit conditions in the problem, and could also monitor and even correct possible mistakes in problem models. 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 representations according to different task requirements, and meanwhile, the mathematical ability of students had a great impact on the their capability of choosing relevant information to construct representation. Not only researchers proved the construction of situa- tion models and problem models , but also some even proposed that the schemata （ and therefore the problem model） was not necessary, as the situation model alone 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 models, 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 models （ situation models ） while paying much attention to the structure of question sentences, but not the language expression as the schemata theory supposed. The 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 contains 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, con- taining only the problem-solving-relevant information. There are still some questions to answer： such as the nature of problem models. Is it a proposition or perceptual symbol representation？ How are situation models, problem models, and the influencing factors related？ Besides, the cognitive neuroscience has provided us powerful tools, such as fMRI and ERP to better and deepen our study on the representation of arithmetic problem solving.