数学教育における文化的価値に関する研究--西洋数学受容による数量概念の変容について Research on cultural value of mathematics education: about the transformation of the concept of quantity by the receipt of European mathematics
This paper is a part of "Research on Cultural Value in Mathematics Education". The author has aimed to clarify the problem that the present school mathematics education has by catching the mathematics development as the organic whole, clarifying the culture seen there, and applying this aspect to historical development of the mathematics education of our country. This paper considered what the concept of quantity on "Decimal" cultivated by Japanese mathematics "Wasan" culture was. And, this paper considered how to have transformed the concept of quantity in Japan by receiving European mathematics based on "Fraction" at how to catch the quantity. The transition of the handling of "Decimal" and "Fraction" in the arithmetic textbooks at the last years of the Tokugawa shogunate and the Meiji era period was examined. First of all, the receipt of "Fraction" of European mathematics in study was examined. The modality of two receipts of "Fraction" of European mathematics was confirmed. One is the receipt of "Fraction" being based on the idea of the fraction caused from the result of the multiplication and division calculation, and with "Concrete number" including "Decimal". Another is the receipt of "Fraction" being based on the idea of the fraction caused by the equal dividing operation, and without putting "Decimal". Next, the modality of the receipt of "Fraction" of European mathematics in educational was examined. When the education of the arithmetic at the Meiji era period was developed, development being based on the receipt that was based on "Decimal" deeply related to Japanese mathematics "Wasan" culture and "Concrete number" did the main current such as becoming the model of the authorized textbook. On the other hand, development based on the receipt being based on the idea of the fraction caused by the equal dividing operation saw faddish. However, it can be thought that it was excluded from the authorized textbook, and removed from the main current of the development of the arithmetic education gradually. As a result, it is possible to conclude it as follows. By receiving European mathematics, the concept of quantity of taking root in Japanese mathematics "Wasan" culture managed by "Concrete number" including "Decimal" was transformed to the concept of quantity of developing in the direction where it comprehends past "Decimal" and "Fraction" connected with algebra, through to place based on the treatment by "Concrete number" including "Decimal", to catch "Fraction" of European mathematics based on the fraction caused by the division operation, and to catch "Algebra fraction" caused as a result of the multiplication and division calculation.
数学教育学研究 17(1), 17-33, 2011