学校数学における数体系の研究(I) : 高等学校における複素数の導入について

概要

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The purpose of this paper is to consider the structure of number system in school mathematics and the possibility of constructive teaching, from a viewpoint of instructional contents in mathematics education. In the algebraic structure, the real number field is a extension field of raitional number field, and the complex number field is a extension field of real number field. But, when it thinks about the extension of field, real number field can't be finitely generated from the rational number field, though complex number field can be finitely generated from the real number field. This difference suggests that we must be careful in teaching of number system in school mathematics. Moreover, we must pay attention so that a student can compose mathematical knowledge when it thinks from the actual teaching. I thought about these points, and showed one idea about the teaching of the complex number at the high school. This idea is based on the finitely generation of a field, and it thinks to be effective in the constructive teaching of school mathematics.
全国数学教育学会の論文