Development of geometry teaching materials focused on oscillatory activity in geometrical subsystems

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  • 図形領域における複数の下位体系を行き来する活動に焦点を当てた教材開発
  • ズケイ リョウイキ ニ オケル フクスウ ノ カイ タイケイ オ ユキキ スル カツドウ ニ ショウテン オ アテタ キョウザイ カイハツ

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Four subsystems of geometrical inquiry in school mathematics that assist in the transition from concrete manipulation to abstract manipulation were identified: (1) analysis with intuitive and concrete manipulation; (2) elementary geometrical analysis without numerical and algebraic methods; (3) elementary geometrical analysis using numerical and algebraic methods; and (4) coordinate geometrical analysis. After identifying the educational values to treat oscillatory activity in geometrical subsystems, we developed two teaching materials—“folding a golden rectangle” and “making a square by cutting a rectangle”. The characteristics of two teaching materials is to start from concrete manipulation and then consider the problem using numerical and algebraic methods, and finally consider it with only elementary geometrical properties without numerical and algebraic methods. It will enable students to consider the problem concretely and appreciate both the convenience of consideration within subsystem (3) and the beauty of elementary geometrical structure derived from consideration within subsystem (2).

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