Cardinal Equivalence of Small Number in Young Children

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Abstract
525 kindergarten and Grade 1 primary school children were given three types of equivalent cardination tasks in which the influence of the use of different stimulus configurations was assessed. The tasks were linear, linear-nonlinear, and nonlinear configurations, with a further differentiation in density in the linear-nonlinear tasks. Number reproduction tasks and evoked correspondence tasks were administered and the data compared with those on the linear cardination tasks. Nonlinear tasks were not more difficult than the linear ones and did not support Siegel's 1972 finding. If the elements in the sets of the cardination tasks were spaced apart, performance on the three tasks did not differ significantly. However, the density manipulation produced strong effects. The tasks, in which the elements were spaced closely together, were more difficult than those with elements spaced farther apart. This result does not confirm the work of Gelman and Gallistel and also not Brainerd's statement that the majority of children will judge a more dense set to contain more elements. This is a note-worthy result, because redundant, non-numerical cues (like target area, background area, and brightness) were eliminated in these equivalent-cardination tasks and only the density manipulation could be effective. Number reproduction and evoked correspondence tasks proved easier than the linear cardination tasks, perhaps because in these tasks the use of the one-to-one correspondence was evoked as a strategy to solve the tasks, whereas in the linear cardination tasks no attention was paid to the one-to-one correspondence in the instruction. Implications for understanding the cardination concept development are discussed.

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