図形の動的な見方の構造について : 比喩的認識の視点から  [in Japanese] Revealing the Structures of Geometric Dynamic Views in terms of Figurative Recognitions  [in Japanese]

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Author(s)

Abstract

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。

This study aims at clarifying how students' recognitions of geometric figures in the elementary school can be connected to deductive geometry, and in this paper as a part of the study we will try to reveal the structures of geometric dynamic views that we have already identified in the learning of geometric shapes using the operative sheets and that may be considered to be premises for understanding the logical and relational natures of geometry. We transcribed the aspects of the geometric dynamic views as combinations of simple sentences, characterized each sentence using metaphor, metonymy, or synecdoche, and analyzed them in terms of the compositeness of the figurative recognitions. In our analysis, we found that the dynamic views were consolidated into five views: 1) Producing the different figure based on perceptual analogy, 2) Conceiving the movement of whole figure by the constitutive point, 3) Recognizing the invariants, 4) Reversible views, and 5) Simultaneous identification of invariants and variables. These may suggest the hierarchical nature among the dynamic views when we examine the degrees of compositeness for each dynamic view, which will be investigated in more detail in our future research.

Journal

  • The Bulletin of Japanese Curriculum Research and Development

    The Bulletin of Japanese Curriculum Research and Development 35(2), 53-62, 2012

    Japan Curriculum Research and Development Association

Codes

  • NII Article ID (NAID)
    110009844848
  • NII NACSIS-CAT ID (NCID)
    AN00247430
  • Text Lang
    JPN
  • ISSN
    0288-0334
  • NDL Article ID
    024065245
  • NDL Call No.
    Z7-1475
  • Data Source
    NDL  NII-ELS  J-STAGE 
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