科学・技術者の卵を育成する「科学・技術者の発掘・養成講座」の展開 : 数学領域におけるプレマスターコースの学習内容

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  • Deployment of the pre master’s course in a mathematics domain : The contents of the lectures of the pre master’s course in a mathematics domain
  • カガク ・ ギジュツシャ ノ タマゴ オ イクセイ スル 「 カガク ・ ギジュツシャ ノ ハックツ ・ ヨウセイ コウザ 」 ノ テンカイ : スウガク リョウイキ ニ オケル プレマスターコース ノ ガクシュウ ナイヨウ

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The contents of the lectures and the learner’s reaction in the pre master’s course in a mathematical domain are reported here. Two contents in the lectures are designed, the area of a circle and an isoperimetric problem. All learners were middle school students and have got high motivation for mathematics. Although the learners know the formula of the area of a circle well, they have little experiences which make them realize that the formula does really hold. In the first lecture, an argument − to compare the areas of inscribed regular polygons with the one of a unit circle, whose idea comes to the usual measure theory in the future, was explained. Through the process of calculating the areas of various kind of inscribed regular polygons to a unit circle, the learners appreciated that the area of a unit circle is really equal to π and convinced themselves of the fact. In the latter lecture, they have considered an isoperimetric problem and showed that the equilateral triangle has the largest area among the triangles with constant perimeter. Although a few mathematical concepts and treatments have been required to follow the procedure of the arguments, they overcame these difficulties eagerly and recognized two contents of mathematics in the pre master’s course. Through the program in the pre master’s course in a mathematical domain, we noticed that learners with high motivation for mathematics study many advanced contents extensively and extend their interests for themselves only with the help of introducing well−suited orientations and with the proper support to give some necessary concepts.

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