学校数学における数体系の研究(III) : 数の体系的理解についての一考察

概要

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The purpose of this research is to define the framework of systematic understanding of numbers, and to investigate systematic understanding of numbers under the framework. I looked back upon old government guidelines for teaching, and defined following framework of the systematic understanding of numbers. 1. Understanding of the structure of a set of numbers ・Understanding about a calculation rule ・Understanding of the operation in a set of numbers ・Understanding of the linear order relation in a set of numbers, and understanding of density of a set of numbers 2. Understanding of a relation between sets of numbers ・Understanding of a inclusion-relation of sets of numbers 1 and 2 are complementary rather than independent. Under this framework, I investigated the degree of achievement of systematic understanding of numbers and obtained the following results. ・The gap on a concept exists between real numbers and complex numbers. ・The image to numbers and the definition of numbers are not in agreement. ・Since expression of numbers and the concept of numbers are not distinguished, understanding is ambiguous. A future subject is to consider systematic instruction of number concepts in school mathematics on the basis of these results of an investigation.
全国数学教育学会の論文
2002-00-00