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UBC Theses and Dissertations

An experimental study to determine the effectiveness of group instruction use of certain manipulative materials in contributing to an understanding of decimal concepts. Greenaway, George James

Abstract

The increasing emphasis on teaching arithmetic meaningfully intensifies the search for materials of instruction which can effectively communicate arithmetical understandings to children. Though manipulative aids are widely approved as effective teaching media for achieving this purpose, most of the endorsements are subjective opinions rather than objective evaluations based on experimentation. This study is an attempt to determine the effectiveness of group instruction use of certain manipulative aids in teaching decimal fraction concepts to Grade VII pupils. The effectiveness was determined by comparing the achievement of two unselected groups, randomly assigned, on a test of understanding of the processes involved in decimal fractions. The two groups were given teaching treatments identical except in so far as the materials of instruction were concerned. One group used manipulative aids; the other used static representations of these aids. These materials were intended to differ only with respects to the characteristic of manipulability. Since manipulability of concepts is the most essential property of manipulative aids, it was isolated as the experimental variable. Because the groups were randomly assigned, analysis of covariance was selected to control statistically the initial differences between groups in the four variables considered likely to influence achievement on the criterion test: initial understanding of the processes involved in decimal fractions, computational ability in decimal fractions, mental ability, and reading ability. The data obtained from the investigation were analyzed and the following conclusions reached. 1. The pupils taught by means of group instruction with the manipulative aids used in this investigation did not acquire a significantly better understanding of decimal fractions than did the pupils taught with static representations of these aids. In other words, the manipulation of the concepts, performed by using the manipulative aids in group demonstrations, was not effective in contributing to the pupils’ understanding of these concepts. 2. A study of the correlations for both treatment groups between achievement on the criterion variable and achievement on each of the independent variables indicates that the manipulative aids proved to be neither more nor less effective than the static representations as media for conveying an understanding of decimal fractions to pupils of any particular ability in the areas represented by the independent variables. 3. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, used exclusively by the teacher for group demonstration purposes, would be applicable also to similar materials if they were used in a teaching procedure in which the pupils themselves, participated individually in the manipulative activity. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, which were used in a brief teaching assignment devoted exclusively to the rationalization of processes, would be applicable also to the same materials if they were used in a teaching assignment of longer duration, and/or a teaching assignment in which the emphasis on the WHY of the processes was taught concurrently with, or preceded, the emphasis on the HOW of the processes. 5. Independently of treatment groups, the achievement on the initial test of understanding of the processes involved in decimal fractions was the variable most predictive of achievement on the final test of understanding. Computational ability in decimal fractions and mental ability each shared approximately one-half the predictive capacity of the initial test of understanding. Reading ability was a negligible predictor of achievement on the final test of understanding.

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