A cognitive semantical study on treatment of mathematical concepts in the school mathematics curriculum
Project/Area Number 
12680272

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
教科教育

Research Institution  Yamaguchi University 
Principal Investigator 
SEKIGUCHI Yasuhiro Yamaguchi University, Department of Education, Professor, 教育学部, 教授 (40236089)

Project Period (FY) 
2000 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)

Keywords  cognitive semantics / school mathematics / cognitive model / mathematical concept / curriculum / 一次方程式 / メンタル・スペース 
Research Abstract 
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.

Report
(4 results)
Research Products
(10 results)