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An investigation to determine the effectiveness of pictorial exposition versus symbolic exposition of tenth-grade incidence geometry Weinstein, Gerald P.

Abstract

The purpose of this investigation was to evaluate the effect of two modes of exposition of tenth-grade incidence geometry on logically evaluated problem solving ability. To achieve this purpose two classes of tenth-grade geometry students were chosen to be the experimental and control groups. The two treatments, which were of nine class hours duration per group, and were both taught by the investigator, involved the use of a set theoretic symbolic-nonrepresentational mode for the experimental group, and a pictorial-representational mode for the control group. The content of the treatments was Euclidean incidence geometry. At the termination of the treatment a criterion test was administered to both groups. The criterion test was composed of two types of problems- Type NR problems, which were believed to be most successfully solved by a symbolic-nonpictorial analysis, and Type R problems, which were believed to be most successfully solved by a pictorial analysis. Two hypotheses, of null form, were considered: that the mean scores of both groups on Type NR problems would be equal and that the mean scores of both groups on Type R problems would be equal. Both hypotheses were tested by means of an appropriate t-statistic at the .05 level of significance. Analysis of the data indicated that both null hypotheses were not to be rejected. A difference in means on Test NR of the control over experimental group was observed at the .20 level of significance. The implication of the analysis of the data and the restrictions imposed by the limitations of the study is that the pictorial-representational exposition was as effective as the experimental symbolic-nonrepresentational exposition for Type NR problems and for Type R problems. Since the pictorial-representational mode of exposition is generally considered standard practice in the teaching of tenth grade geometry it should be continued for the present.

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