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The effect of instruction in modular arithmetic on the ability of grade 6 students to divide fractions and give a rational explanation of the process MacDonald, Alexander David

Abstract

The problem under investigation in this study was to find out what relationship a unit in modular arithmetic might have to Grade 6 pupils' skill in computing the division of fractions and to their understanding of the mathematical basis of the algorithm. It was hypothesized that a unit in modular arithmetic would aid in developing skill in computing and understanding of the algorithm. The study was conducted with a sample of 58 Grade 6 students from the same school. The subjects were assigned to two treatment groups. Both groups received a review of fraction concepts at the beginning of the study. Following this, one group was taught modular arithmetic while the other group reviewed adding and subtracting of fractions. Then both groups were taught multiplication and division of fractions. Following the instruction period, both groups were tested for ability to compute division of fractions. To test understanding of the division of fractions algorithm, an interview inventory test was administered to all subjects in both groups. A statistical analysis of the data from these tests revealed no support for the hypotheses. The conclusion was that teaching modular arithmetic to the Grade 6 pupils participating in the study did not appear to improve their ability to compute division of fractions nor their understanding of the mathematical basis of the division of fractions.

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