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UBC Theses and Dissertations

Investigation into the use of physical devices in teaching a unit of geometry. MacLean, Charles Fairbanks


This study was an attempt to determine the effect of the use of models in learning the volume and total surface area of various polyhedra. It was hypothesized that the classes who were allowed, to construct models of various space figures would achieve significantly better results on a test of the work covered than would those classes who were taught the same material by sketches and notes on the chalkboard. It was further hypothesized that the classes which had utilized the models would score significantly higher on a retest which was held approximately two weeks after the initial test. Five teachers and eight classes were involved in the study. Two teachers taught a control group and an experimental group of grade seven students while a third teacher had a control group and an experimental group of grade six students. The fourth teacher taught one control group of grade seven students and the fifth teacher taught one experimental group of grade seven students. Mental age, previous mathematical achievement (teachers' Easter grades) and scores on the geometry unit test and retest were recorded for ninety-four control group students and ninety-seven experimental group students. Any student who had not attended eighty percent of the teaching periods or for whom no mental age or previous mathematical achievement was available were not included for purposes of this study. The geometry unit, which was, of two weeks duration, was followed by a multiple-choice test of twenty-five items and a retest two weeks later. The usual correction factor was applied to offset the effect of guessing by the examinees. A covariate analysis was then done in which the two independent variables, previous mathematical achievement and mental age were partialled out and the adjusted means for the test and retest were recorded. The results Indicated that there was no significant difference in the mean scores obtained by the two groups on the initial test - 14.647 for the control group and 14.6822 for the experimental - but that there was a significant difference in the mean scores obtained by the two groups on the retest held two weeks later. The mean score of the experimental group was 14.4124 as compared to 13.9255 for the control group. Although this difference was significant at the .005 level it was recognized that, for all practical purposes, a difference of half a point in a total of twenty-five items must be considered unimportant for the practising teacher. A superficial examination of the data indicated two questions that might be answered by further related study: (1) Would a longer period between the test and the retest show a greater difference in the mean scores, of the two groups? and (2) Would the use of models be of greater benefit to a particular age group or i to a homogeneous group of high or low achievers? The results obtained by this and other related studies seems to militate against any definitive conclusions as to the merit of using models in the teaching of mathematics as a whole. It appears that if any significant ,benefit is to be derived from their use it will be in particular subject areas that will be determined only through carefully designed research.

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