著者

金児 正史 成川 公昭 平野 康之

出版者

鳴門教育大学

雑誌

鳴門教育大学研究紀要 鳴門教育大学 編 (ISSN:18807194)

巻号頁・発行日

vol.30, pp.90-100, 2015

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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.

著者

金児 正史 成川 公昭 宮口 智成 平野 康之 Masafumi KANEKO Kimiaki NARUKAWA Tomoshige MIYAGUCHI Yasuyuki HIRANO

出版者

鳴門教育大学

雑誌

鳴門教育大学研究紀要 = Research bulletin of Naruto University of Education (ISSN:18807194)

巻号頁・発行日

vol.34, pp.97-108, 2019-03-11

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We have taken a class on an isoperimetric problem for lower secondary school students who have high motivation to mathematics. In this paper, we have considered the lesson plan on an isoperimetric problem for the students and decided the goal of this class is to prove the theorem as below. 'A polygon which has the biggest area with same constant perimeter is a regular polygon.' After the class on an isoperimetric problem, we have realized the goal of isoperimetric problem for lower secondary school students will be suitable and have recognized strongly the mathematical experiments will be an important impact for this class.