Precocious thoughts on number: The long and the short of it.

Abstract

One hundred and sixty-three 3-, 4-, 5-, and 6-year-old children were tested on seven conservationlike number problems. Five were problems of inequivalence and two were problems of equivalance. All problems were presented in a static form so that the children did not see a transformation away from one-to-one correspondence. Few children made the correct numeric judgments on all problems. The youngest performed as well as the oldest on specific problems of inequivalence similar to one used by Mehler and Bever, but all ages performed similarly on the other problems of inequivalence and equivalence. The similarity between the oldest and youngest children does not seem to provide evidence of similarity in cognitive functioning. Rather the youngest appeared to be senstive to differences but not to relate them systematically, while the oldest children logically related differences in spatial properties to number. Three developmentally ordered models are proposed.

Heterogeneity and Spatial Factors as Determinants of Numeration Ability

“…These results support the analyses of Gelman (1972) and Pufall and Shaw (1972) of the development of number concepts in young children in which the child is assumed to gradually learn how to discriminate various dimensions (such as length and density) as irrelevant to number. The characteristics of the constituent members of the set, as opposed to their spatial relationships to each other, interfered with judgments of numerosity.…”

“…Previous research concerning the development of number concepts in young children (e.g., Gelman 1972;Pufall & Shaw 1972;Siegel 1972Siegel , 1973Wohlwill 1960;Zimiles 1966) has indicated that certain perceptual factors other than numerical size influence a child's perception of numerosity. Both heterogeneity of the constituents of a set and variations in the spatial arrangement of the set have been found to influence a child's perception of numerosity.…”

Numerical comparison processes

“…Qualitatively similar results have been obtained with children (Pufall & Shaw, 1972); performance is more accurate with congruent stimulus pairs than with incongruent stimulus pairs. Pufall and Shaw (1972) suggest that children often use length cues to make their numerical judgments. Thus, they will tend to make more errors when the numerically larger row is shorter.…”

“…For instance, young children make more errors with incongruent stimuli (in which the numerically larger row is shorter) than with congruent stimuli (Pufall & Shaw, 1972). Presumably, this effect occurs because length cues tend to be used to make the numerical comparison.…”

The Development of Time Concepts in Young Children: Reasoning about Duration

“…Similar quantitative analyses have already proven themselves to be of value in other cognitive areas (Bausano & Jeffrey 1975;Pufall & Shaw 1972). An analysis of the quantitative values of relevant and irrelevant cues (e.g., comparing problem difficulties of two pairs of cars whose speeds differ by 50% with pairs whose speeds differ by 100%) could cast light on the information processing involved in solving problems related to time concepts.…”