数学教育における文化的価値に関する研究 : 高校数学の基盤をなす代数表現とその文化性

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概要

• 論文の詳細を見る

• 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 education of mathematics of our country. In the process, the following problems have come to the surface. Does the handling of the algebra expression that does the base of high school mathematics really make the best use of cultural value of the algebra expression now? For instance, let's take up the content in the third grade of junior high-school "Square root". When the treated number is limited to the rational number, there is no solution in the second equation x^2 = 2. So, the square root of 2 is thought, it is made to the sign with √<2>, and then it is explained that √<2> is "Number that does the second power and becomes 2". However, the former second equation doesn't request the expression of the solution "√<2>". Doesn't it request the Number that does the second power and becomes 2? Impatience like this making to the sign and formalization makes the essence of the teaching material mistaken. It is necessary to verify the meaning and the significance of the algebra expression that does the base of high school mathematics from the aspect that catches the culture. In this paper, it has approached a part of details how the algebra expression that does the base of high school mathematics was formed, how it developed, and how our country accepted the European calculation when our country took the European mathematics. In the present school mathematics, it is admitted that it are supposed also to speed up making to the sign and formalization that are considered the means too much speeding up the acquisition of "Algebra" and "Analysis". This paper insisted that the following is necessary now. We must catch "Sign algebra" only as no "Means" as "Purpose" again in not losing sight of the essence of the teaching material.

• 全国数学教育学会の論文

著者

• 伊達 文治

  広島県立海田高等学校:広島大学

関連論文

• ユークリッド「原論」第1巻の構造 : 「数学基礎」への教材化を志向して
• A8 数学教育における文化的価値に関する研究 : 数学発達にみる文化性について(A.【教育課程(目標.評価)】,論文発表の部,第III編 第39回数学教育論文発表会発表論文要約)
• J1 数学教育における文化的価値に関する研究 : 明治の算術教育における和算と洋算(J.【数学教育史・数学史の教育活用】,論文発表の部)
• A8 数学教育における文化的価値に関する研究 : 数学発達にみる文化性について(A.【教育課程(目標,評価)】,論文発表の部)
• 4A-2 ユークリッド「原論」第1巻の構造 : 「数学基礎」への教材化を志向して(4数学基礎,高等学校,日本数学教育学会第84回総会 全国算数・数学教育研究(兵庫)大会)
• 数学教育における文化的価値に関する研究 : 高校数学の基盤をなす代数表現とその文化性
• 数学教育における文化的価値に関する研究 : 和算の特質と西洋数学の受容

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