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

学校数学课程中数学概念处理的认知语义研究

• 批准号: 12680272
• 负责人: SEKIGUCHI Yasuhiro
• 金额: $ 1.15万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12680272/
• 关键词: cognitive semantics; school mathematics; cognitive model; mathematical concept; curriculum; 一次方程式; メンタル・スペース

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.

本研究从认知语义学的框架出发，分析了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。在认知语义学的框架下对数据进行分析。发现了与莱科夫和努涅斯提出的认知模型类似的模型。同时也发现了反映学生学习情况的模型，但在数学研究和教育情境中的认知模型有所不同。数据由摄像机和MD记录器记录。分析表明，不同的认知模式在课堂上起作用。老师试图运用各种模式来促进学生的理解。学生有时会停留在日常生活或以前学习的模型上，在学习新概念时会遇到困难。2002年，数据分析继续进行。与N.C.Presmeg就认知语义学框架的使用举行了一次会议。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却很少受到重视，这一理论被认为是有用的。它将在分析数学问题解决和数学概念方面发挥强大的作用。

项目成果

Yasuhiro Sekiguchi: "An analysis of cognitive models in explanation of mathematical concepts: From the data of junior high school teachers"Proceedings of the 34th Presentation of Theses on Mathematical Education. 415-420 (2001)

关口泰弘：《数学概念解释中的认知模型分析：来自初中教师的数据》第34次数学教育论文发表论文集。

Yasuhiro Sekiguchi: "Mathematical proof, argumentation, and classroom communication: From a cultural perspective"Tsukuba Journal of Educational Study in Mathematics. vol.21. 11-20 (2002)

Yasuhiro Sekiguchi：“数学证明、论证和课堂交流：从文化角度”筑波数学教育研究杂志。

関口靖広: "数学的概念の説明において用いられる認知モデルの分析:中学校教師のデータより"日本数学教育学会第34回数学教育論文発表会論文集. 415-420 (2001)

Yasuhiro Sekiguchi：“用于解释数学概念的认知模型的分析：来自初中教师的数据”日本数学教育学会第 34 届数学教育论文发表会记录 415-420 (2001)。

関口 靖広: "A teaching experiment on mathematical proof : Roles of metaphor and externalization"Proceedings of PME 24. 4. 129-136 (2000)

Yasuhiro Sekiguchi：“数学证明的教学实验：隐喻和外化的作用”Proceedings of PME 24. 4. 129-136 (2000)

Yasuhiro Sekiguchi: "A teaching experiment on mathematical proof: Roles of metaphor and externalization"Proceedings of the 24th International Conference for the Psychology of Mathematics Education. vol.4. 129-136 (2000)

Yasuhiro Sekiguchi：“数学证明的教学实验：隐喻和外化的作用”第24届国际数学教育心理学会议论文集。