児童・生徒の空間思考の発達に関する研究-調査に基づく発達的指標についての一考察-

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  • ジドウ セイト ノ クウカン シコウ ノ ハッタツ ニ カンスル ケンキュウ チョウサ ニ モトヅク ハッタツテキ シヒョウ ニ ツイテ ノ イチ コウサツ

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本研究は, 小学～高校生を対象にした調査をもとに, 立体・空間に関する課題遂行における生徒の空間思考の諸特性を明確にし, 発達的指標を捉え, 空間思考の育成を視座においた空間図形教育を目的とする。本稿では, 近接領域の問題を中心に, 反応の基本集計, 児童・生徒のかく図・記号表示, インタビュー内容を分析し, 次の発達的指標を抽出した。N. 無反応または意味不明の反応 A. 対象を図の全体的形やみえによって, 視覚的に静止的に捉えて反応する。B.対象を物的に捉え, 手などを使って物理的操作に類似させる。「物理的操作」は空間像の操作の源になる。C. 構成要素で把握される対象の空間像の操作を行う。対象の部分への焦点化, 視点の変更が現れる。D. 対象の構造・空間関係を保つ操作の空間像にもとづく。対象の焦点化, 空間像の次元の変化及び像のきり換え操作を伴う。操作そのものへの焦点化に向かう。E..幾何的変換, 投影, 操作のアルゴリズム化または論理的推論にもとづく。子どものかく多様な図・記号表示は, 指標CとDで主に用いられ, 操作の結果の予想, 操作と結果または対象の構造との関係づけの分析や確認などに用いられる。

The main purpose of this study is to clarify students' developmental milestones of spatial thinking on the basis of surveys for elementary, junior and senior high school pupils. From reference to Piaget, J. about mental images, Якиманская И.С. about spatial thinking, Duval R. about visualization and Gorgorio, G. about the functionality of visual and non-visual strategies, 6 points of view of investigations are set up as follows. 1 Mental images of 3D-geometrical objects. 2The 3 types of mental operations: I. Mental operations which change image's position and/or orientation, as spatial rotation, and so on. II. Mental operations which change image's structure, as projection, cross-section, un-folding, folding back and so on. III. Composition of the types Iand II. 3 Flexibility of mental operations among different (visual, symbolic or verbal) representation forms and among different types of drawings, as sketch, developed drawing, orthogonal views, and so on. 4Drawing 2D-visual representation of 3D-geometrical objects,. 5ldentification of spatial orientation. 6Change of points of view and their integration. In the first survey(1998) 7 spatial tasks and in the second(1999) 7 tasks were conducted. Qualitative data were obtained through clinical interviews and students' drawings. Quantitative data and Qualitative data were analyzed. Students' developmental milestones of spatial thinking can be prescribed as follows. N. No responses or meaningless. A. Perceptual and static interpretation of 2D-visual representation of 3D-geometrical objects. B. Physical manipulation of something like materials using his/her hands. C. Mental operation of image which is composed of components of a 3D-geometrical object. Focusing on only some parts or some component and changing of view-points of the object appear. D. Mental operation of image which maintains spatial structure of 3D-geometrical object. Focus on only some parts or some component and change of view-points of the object and their integration and dimensional change of image:from 3D to 2D and from 2D to 3D, and towards 0D. Mental operation amonge 3D- and 2D-images, and so on. E.. Geometrical transformation, projection, algorithm of mental operation or/and logical argument. Mental operation is done very quickly and adequately. In C and D students analyze using drawings of various visual representation forms, but in E usually not use them.

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