This study was undertaken to clarify what kind of effect the degree of figural generalization of a theorem had upon thinking process in geometrical problem-solving.
For the purpose of simplifying the experimental conditions, we took up only one theorem-the two basal angles of an isosceles triangle are equal to each other. The
Ss were first grade students of junior high school who had not yet learned geometry. For prior learning two steps of generalization of the theorem were set up by means of change in the shape and in the direction of an isosceles triangle in Exps. I and III, and in Exp. II four generalising steps were adopted in regard to two other isosceles triangles than one used in Exp. I. After prior learning, two experimental problems were used for this study.
The
Ss used in Exp. I were 16 girls who were divided into two groups homogeneous in terms of intelligence of T-Scores, those in Exp. II were 36 boys who were divided four homogeneous groups, and those in Exp. III were 160 students consisting of halves, highly and poorly scored in mathematics, who were divided into four homogeneous groups respectively.
Especially in Exp. III the analysis of variance of three factors: geneneralization, ability and orientation, was attempted. The results were as follows:
1) Generally the group who learned by higher-ordered generalization solved the problems more easily than the other groups. The nearer to the problem-figures the figures learned for generalization were, the easier their solving was (Exps. I, II).
2) The group who had prior learning in terms of lower generalization tended to make imperfect solutions and irrelevant responses and to be bothered by the problem-sentences (Exps. I, II).
3) Some of the
Ss who learned in terms of the lowest generalization could succeed in solving these problems. Their intelligence of T-Scores was not, however, the highest in every case, although above the average in general. When the difference between the highly and the poorly scored
Ss was great, the latter could not surpass the former, even if they had previously learned in terms of higher generalization than the others (Exps. I, II, III).
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