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We report a study of 3- to 5-year-olds who performed a magnitude-comparison task. Stimuli were a series of pairs of arrays that sometimes differed in numerosity, and the children were asked to point to the more numerous array in each pair. The proportion of accurate responses was above chance for all age groups. However, error patterns were consistent with analog models of magnitude representation. Errors varied systematically with the ratio of stimulus pairs. Items with a 2:3 ratio were harder than items with a 1:2 ratio. Performance on posttests of verbal counting ability was variable, but did not predict performance on the numerical discrimination task. We argue that neither verbal counting nor nonnumerical perceptual strategies can explain these results. This study supports the hypothesis that adults and children share preverbal, analog representations of magnitude.

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Adults routinely use numbers to make precise references to amounts of substance (e.g. 5 liters of water), but the ontogenesis of this capability is poorly understood. We developed a new method for addressing this issue. This report focuses on children's ability to conceive of measuring substances by drawing on numerical information. Three-to 5-yearolds are unable to use even small differences of number to facilitate the quantitative comparison of small portions of sand. It is argued that children are biased to enumerate objects and to measure substances without counting.