著者

中原 忠男 前田 一誠 山口 武志 岡崎 正和 影山 和也

出版者

環太平洋大学

雑誌

環太平洋大学研究紀要 = Bulletin of International Pacific University (ISSN:1882479X)

巻号頁・発行日

vol.12, pp.237-249, 2018-03-21

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While division is one of the crucial concepts in elementary mathematics, it is hard to understand it. Thus, various research tasks have been tackled so far. We as a research team have investigated the following three tasks: 1) developing the survey which consists of a set of problems that enable to clarify the actual conditions of children’s construction of division concepts comprehensively and systematically, 2) revealing the actual conditions of children’s construction of division concepts based on the survey, and raising the research tasks on the teaching and learning of division, and 3) through examining those research tasks, proposing our alternatives for improving the teaching and learning of division concepts based on multi-world paradigm. In this paper we propose our final research findings by reflecting on our whole studies until now in a comprehensive way according to the following three steps. First, we give a general description of the perspective of multi-world paradigm as our theoretical background. Next, we overview our research results on the above 1) and 2) which have already been published. Finally we examine our alternatives for improving the teaching and learning based on the multi-world paradigm, which will become our final research findings, where we will emphasize the importance of meaningconstruction and tool-construction on division concepts.

著者

山口 武志 影山 和也 中原 忠男 岡崎 正和 前田 一誠

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.23, no.1, pp.1-20, 2017-01-27 (Released:2019-01-17)

参考文献数

20

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It is still very difficult for children to understand the meaning of division although various efforts for the improvement of teaching division have been implemented. Therefore overall researches which both capture difficulties and misconceptions of various kinds of division systematically and propose better way of teaching and learning of it to overcome them are required. From this perspective, as the first step of our research, we developed six sets of test of division, for fifth and sixth graders in the elementary school and first graders in the junior high school, which could reveal difficulties of understanding the meaning of division systematically. In six sets of test, various factors of story problems of division which will be expected to affect the percentage of correct answers, such as effect of the order or value of the dividend and the divisor, effect of figures, number lines, word expressions, key words and so on, were taken into account. It is the main reason for us to develop new tests why most of previous test or studies of division only focused on specific grade or specific kind of division such as division with fractions which children have difficulties. We conducted the longitudinal and cross-sectional survey with six tests for children at both elementary schools and junior high schools located in three prefectures: Okayama, Hiroshima and Kagoshima. This article reported results of children’s performance of solving problems of “partitive division and the extension of its meaning”, and analyzed children’s difficulties and misconceptions of them in terms of various factors of story problems of division.

著者

岡崎 正和 岩崎 秀樹 影山 和也 和田 信哉

出版者

日本教科教育学会

雑誌

日本教科教育学会誌 (ISSN:02880334)

巻号頁・発行日

vol.35, no.2, pp.53-62, 2012

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本研究の一連の目的は,算数から数学への移行という視座から,子どもの図形認識が発展し,証明に繋がる端緒を明らかにすることであり,本稿では図形の論理的・関係的性質の理解の前提になると考えられる図形の動的な見方の構造を明らかにすることを目的とした。その為に,我々がこれまでに同定してきた図形の動的な見方を単純な文の組み合わせとして表し,隠喩,換喩,提喩を用いて特徴付け,それらの複合性について分析した。その結果,動的な見方は次の5つに集約されることが分かった:視覚的類似性に基づく図形の変形,図形全体の動きを点の動きで捉える,不変性を意識化する,可逆的な見方,不変性と変数性の同時的意識化。また,これらを比喩的認識の複合性の視点から分析した結果,図形の動的な見方は階層的に整理され得ることが示唆された。