A cognitive semantical study on treatment of mathematical concepts in the school mathematics curriculum

本研究旨在从认知语义学的框架分析学校数学课程中数学概念的处理方式。2000年，对认知科学中的认知语义学理论进行了综述。特别值得关注的是G. Lakoff和R. E. Nunez的研究。2001年，首先对初中数学教师进行了问卷调查研究。在认知语义学框架下对数据进行分析。发现了与Lakoff和Nunez提出的认知模型相似的模型。然而，也发现了反映学生学习状况的模型，显示出数学研究认知模型与教育状况之间的差异。其次，在一所初中的数学教室进行了观察研究。数据由摄像机和MD记录仪记录。分析表明，各种认知模型在课堂上起作用。老师试图采用各种模式来促进学生的理解。学生有时会拘泥于日常生活或以前学习的模式，在学习新概念时遇到困难。2002年，数据分析继续深入。与N. C. Presmeg举行了一次关于认知语义框架使用的会议。心理空间理论与认知语义学密切相关，但在数学教育研究中很少受到重视。它在分析数学问题解决和数学概念方面将是强大的。

This study aimed to analyze the ways mathematical concepts are handled in school mathematics curriculum from the framework of the cognitive semantics. In the year of 2000, an overview of the theories of cognitive semantics in the cognitive sciences was taken. Especially, close attention was paid to studies by G. Lakoff and R. E. Nunez.In the year of 2001, first, a questionnaire study was conducted for junior high school teachers of mathematics. The data was analyzed in the framework of cognitive sematics. Cognitive models similar to those proposed by Lakoff and Nunez were found. Models reflecting the situation of students' learning were also identified, however, showing differences between cognitive models in mathematics research and educational situation.Next, an observation study was conducted at a mathematics classroom of a junior high school. The data were recorded by a video camera and an MD recorder. Analysis showed various cognitive models working during class. The teacher was trying to employ various models to facilitate students' understanding. Students sometimes stuck to models from everyday life or previous learning, and faced difficulties in learning new concepts.In the year of 2002, the data analysis continued further. A meeting with N. C. Presmeg was held about the use of cognitive semantics framework. The mental space theory, which was closely related to the cognitive semantics, but which had been paid little attention in mathematics education research, was found useful. It would be powerful in analyzing mathematical problem solving as well as mathematical concepts.