生徒が生み出す数学 : 民族数学および文化と数学の視点から
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概要
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概要 : この論攷は，ニ部で構成され，その第一部を第一筆者が，第二部を第二筆者がそれぞれ担当する。第一部では，森川が過去において行った提案と対比しながら，D'AmbrosioやP.Gerdesらが提唱する民族数学の特徴を明らかにする。例えば，彼らは，図形や数に関わる話題をその教育素材として取り上げても，物理分野や量を主体にした算術分野の話題を取り上げていないことを述べる。第二部では，山形県内に現存する算額の問題を原問題に，生徒がその発展問題作りに取り組んだ実践の概要と生徒の作った問題のいくつかを紹介する。 こうした民族文化の伝統を生かした生徒主体の問題作りに関わる展開も「民族数学」の提案には見ることができない。 Summary : In the first part, we point out some characteristics things in the ethnomathematic; 1) We can see often the geometrical things in the papers written representational persons to the branch. It would mean that they analyzed the memorial things or heritages being seen in present times from mathematical points. And then, we know that many persons tried to present the themes as mathematics education by analyzing many traditional geometrical constructions from previous days whether they had the recognitions to the ethnomathematics or not. We had the papers to analyze the skills to construct the traditional Japanese constructions as mathematics in junior high school students, also without a recognition to the ethnomathematics. 2) We have not an experience to see the papers to analyze the phenomena often met in the each area; To analyze the phenomena, we need the some methods such as measuring the many quantities, drawing the graphs to them or finding the formulas. To measure the many quantities, we must prepare the tools. Although almost of the modern tools to measure the many quantities were invented in the Europe, phenomena are occurred in each district. So, we think that guessing the many things from mathematical viewing points basing on data in those days are excellent themes in the ethnomathematics. But we can not see the papers written from this point as ethnomathematics unfortunately. We proposed two new themes in mathematics education to the Japanese students as ethnomathematics or the mathematical culture; 1) Japanese received strong influences from the Chinese cultures since ancient periods. For example, we can point out the sources of several mathematical words used in present Japan from the ancient Chinese arithmetic books. So, we treat the arithmetic or astronomy found in ancient China as the themes to the mathematics. In this paper, we proposed new several equations related to the calender basing on some facts found in an ancient astronomy in China. 2) In Japan, at the Edo period many peoples enjoyed the mathematics. Some persons dedicated the own works to the shrines as the ”SANGAKU” - written several mathematical problems with answers on the board -. Many problems of them are requiring the areas or drawing to special figures. And then, many of them belong to the finite mathematics. So, some of them could solve by the mathematics learnt in secondary school. Then, we can treat them as the themes in secondary schools. In later part of this paper, we introduced the outline of the instruction challenging to make new original mathematical problem including the remaking or to modifying an original ”Sangaku” problem. In last part, we introduced as photo 12 problems represented as ”Sangaku” by students.
- 山形大学の論文
- 2001-02-15