STUDIES ON THINKING PROCESS IN GEOMETRICAL PROBLEM SOLVING: IV

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  • 幾何問題解決における思考過程の研究 (IV)
  • キカ モンダイ カイケツ ニ オケル シコウ カテイ ノ ケンキュウ 4
  • ANALYSIS OF FIGURAL STRUCTURE
  • 図形構造の分析

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In the previous report, we left the problem how the perception of a figure has effect on the thinking process in geometrical problem solving. The present study was undertaken for the purpose of clarifying this problem by three kind of experiments.<br>Method. Exp. I was planned to determine whether the drawing of assistance-line itself was related to the fundamental tendency of perception in geometrical problem solving. Exp. II was undertaken to clarify the factors which disturbed the finding of a specific figure (isosceles triangle) in the given geometrical figures. Exp. III, to study for the effects which the changes of the direction of geometrical figures or those of the length, size of their sides gave on the thinking process.<br>The Ss were 101V grade children of elementary school in Exp. I, 252 III, IV garde children in Ex. II, 120I grade students of junior high school who were divided into 8 homogeneous groups in Exp. III.<br>Results. (1) In some cases, drawing of assistance-line perpendicularly was easier than drawing of it horizontaly, and in other cases, drawing of it from left-up to right-down was easier than drawing of it from right-up to left-down. But there were no such tendencies mentioned above in the case of horizontal kite-quadrilateral (Exp. I).<br>(2) There were difficulties of finding isosceles triangle in some geometrical figures, but not in others. Generally the Ss felt more difficulty of finding two isosceles triangles which were disposed unsymmetrically up and down, than symmetrically, right and left (Exp. II).<br>(3) Generally, the changes of the direction of geometrical figures or those of the length, size of their sides gave pretty effects on the thinking process. They sometimes accelerated the recall of the referential theorem which was necessary for the solving, or inhibited it. In the case of inhibition they accerelated the recall of the other theorems (Exp. III).<br>(1) The difficulty of geometrical problem solving seemed not to be determined only by the difficulty of drawing the very assistance-line, or of finding the very figure as sub-goal, but chiefly by the degrees of sub-goal's being concealed by the problem-sentence and its figure-construction (Exp. I, II, III).

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