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The relation of Piaget's three stages in number conservation development to achievement in grade I arithmetic Dennis, Isobel Gertrude

Abstract

Jean Piaget describes three stages in the development of that aspect of quantitative thinking which he named conservation of number. In the first stage, a child is quite unaware that one-to-one pairing of two sets implies equivalence of the sets. He is unable to make a correct one-to-one correspondence, and if presented with two sets of objects which have been matched unit for unit, believes that one set has become greater if its units are spread out, or smaller if they have been compressed. In the second stage, the child is able to make a correct correspondence, but does not believe in the continued equivalence of the sets when one is spatially rearranged. In the third stage, the child maintains that the matched sets remain equivalent even though the units of one set have been rearranged, that is, the child conserves number. Piaget postulates that conservation is a necessary condition of mathematical understanding. In this study, it was hypothesized that children who are in Stage 1 at the beginning of their Grade 1 year, and who are still in Stage 1 at the beginning of the second term show low achievement in arithmetic at the end of the school year. It was further hypothesized that each stage in conservation is associated with corresponding levels in terminal achievement in Grade 1 arithmetic. One hundred fifty-six children received an individual conservation test in October of their first grade year, and were thereby classified as being in Stage 1, Stage 2, or Stage 3 in conservation development. In January, those classified as Stage 1 received a second conservation test, and were again classified according to their stage in conservation development at that time. In May, the arithmetic sub-test of the Stanford Achievement Test, Primary I Battery was administered to all groups. A significant proportion of the Stage 1 group selected by the January conservation test had achievement scores which fell below the median for all subjects, while a significant proportion of the Stage 3 group selected by the October test had above-median achievement scores. Mean achievement scores for the two Stage 3 groups did not differ significantly from each other, but were higher than mean achievement scores for the Stage 1 and Stage 2 groups. No significant differences were found among mean achievement scores of Stage 1 and Stage 2 groups. The results were interpreted as being consistent with Piaget's theory. The superiority of the mean terminal achievement of early conservers over that of children who had not developed conservation by January appeared great enough to be of educational importance. Some individual scores showed marked deviation from the pattern derived from the group data, however, and caution in use of the conservation test as a predictive instrument was recommended. It was proposed that the conservation test could be a useful diagnostic procedure for the teacher.

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