The Child's Representation of Number: A Multidimensional Sealing Analysis

MILLER, KEVIN, and GELMAN, ROCHEL. The Child's Representation of Number: A Multidimensional Scaling Analysis. CHILD DEVELOPMENT, 1983, 54, 1470-1479. In order to describe developments in children's conceptions of number, judgments of similarities between numbers were solicited from children in grades kindergarten, 3, and 6 as well as from adults. Analysis of the resulting data by clustering and nonmetric multidimensional scaling techniques suggested that children become sensitive to an expanding set of numerical relations during this period, although even kindergartners appear to understand the importance of magnitude as a basis for judging similarity between numbers. Results implicate the acquisition of numerical skills and operations such as counting, addition, and multiplication in this broadening of the concept of number. A second study was conducted with a group of kindergartners in which letters replaced numbers as stimuli, and an explicit criterion based on closeness between stimuli in the alphabet was given to subjects as the basis for judging similarity. These results suggest that the numbersimilarity judgments of kindergartners, and to a lesser extent of older children, are based on counting distance. Implications of this research for the distinction between defining features of number (such as one-to-one correspondence) and numerical operations in children's reasoning about numbers are discussed.