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The Child's Understanding of Correspondence Relations

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Irvin Sam Schonfeld at City College of New York
Irvin Sam Schonfeld
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A number of quantitative comparison tasks were designed to tap knowledge of injective and surjective correspondences, one-directional compositions (greater + greater yields greater), countervailing compositions (greater + lesser yields ?), and length-density relations in 4- to 7-year-olds. The results indicated that performance on the comparison tasks was related to performance on a number conservation test as well as to age. Nonconservers performed at better than chance levels on tasks that tapped an elementary knowledge of injective and surjective correspondences; concrete-operational children, however, tended to perform better on all tasks. Uncorrected and disattenuated correlation coefficients revealed considerable consistency across measures. Factor analyses, with and without age included, yielded a unitary factor. An explanation of the results based on perceptual salience was ruled out. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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... As anticipated in hypotheses three and four, the correlational and factor-analytical findings reveal consistency across measures and suggest that a unitary, developmental factor underlies performance differences. Consistent with Schonfeld (1990), the findings suggest that children's performance on comparison tasks improves in two ways: at advanced levels (1) the understanding of more complex functional relations emerges and (2) thinking becomes increasingly exact, facilitating improvement in cognitive performances in which the more advanced preoperational (i.e. OL-2) children demonstrate some preliminary competence (i.e. ...
... TPO items). The findings pertaining to the specific cognitive accomplishments of pre-operational children were consistent with results on cognate discrete-quantity tasks (Schonfeld, 1986Schonfeld, , 1990). The correlations among the liquid scales tended to be lower than the correlations among the discrete-quantity scales (median r=.52, median corrected r=.7O in Schonfeld, 1990; r= .68 for Scales 1 and 2, corrected r= .84 in Schonfeld, 1986). ...
... The most reasonable explanation for the difference is that the liquid scales had considerably less variance than the discrete-quantity scales. Each liquid scale comprised only three items and the discrete quantity scales included as many as 14 items (Schonfeld, 1990). The average size of the correlation coefficients among the liquid scales, however, was consistent with findings obtained by de Ribaupierre, Rieben & Lautrey (1985), who employed a different set of Piagetian tasks and a more conservative computational method. ...
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