著者

渡邊 公夫

出版者

法政大学沖縄文化研究所

雑誌

沖縄文化研究 (ISSN:13494015)

巻号頁・発行日

no.46, pp.149-202, 2019-03-31

著者

川内 充延 渡邊 公夫

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.24, no.1, pp.61-69, 2018-03-23 (Released:2019-09-09)

参考文献数

19

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Seven companies publish mathematics textbooks for use in junior high schools in Japan. Introducing square roots in mathematics class, all of them discuss the relationship between the area and the side of a square. For example, there is a description of “If the area of a square is 2cm2, how many centimeters is the length of one side of a square?” Hitotsumatsu (1990) casts doubt upon the description of “The solution of x2 - 2 = 0 is + √2 and - √2 ” (p.7). The aim of this paper is to develop a new approach to introduce square roots in teaching for readiness. That lies hidden in Square Dotty Grid and Isometric Grid. Our idea is based on the figures of “If a segment is multiplied by a and one more time running, then it is multiplied by 2 and 5 on Square Dotty Grid, 3 and 7 on Isometric Grid” We carried out classwork study and realized that the approach will succeed. 67 second-grade students in junior high school made three squares or three rhombuses using a diagonal’ length of a square or a rhombus, and responded to a question in worksheets during class. As a result of the survey, their notes gave us three suggestions. First, there is a possibility that students consider with the ratio in length between each one side of three squares or three rhombuses. Second, these teaching materials provide learning opportunities of inductive, analogical and deductive inference for students. Third, students may notice irrationalness themselves.

著者

池田 敏和 渡邊 公夫

出版者

数学教育学会

雑誌

数学教育学会誌 (ISSN:13497332)

巻号頁・発行日

vol.51, no.1, pp.39-50, 2011-02-28

被引用文献数

1

著者

渡邊 公夫 淡川 直樹 前橋女子高等学校

出版者

公益社団法人日本数学教育学会

雑誌

日本数学教育学会誌. 臨時増刊, 総会特集号

巻号頁・発行日

vol.89, 2007-07-29