While many studies have investigated duration discrimination in human adults and in nonhuman animals, few have investigated this ability in infants. Here, we report findings that 6-month-old infants are able to discriminate brief durations, and, as with other animal species, their discrimination function is characterized by Weber's Law: proportionate difference rather than absolute difference between stimuli determined successful discrimination. Importantly, paralleling results found with nonhuman animals, the Weber function that we found for infants' discrimination of time is the same as that found for their discrimination of number. Infants discriminated durations of an audiovisual event differing by a 1:2 ratio, but not those differing by a 2:3 ratio, over a range of durations. This suggests that (a) in human as in nonhuman animals, the same mental mechanism may underlie the ability to measure duration as to represent number, and (b) we may share this mental mechanism with other animal species.

Recent research in vision science, infant cognition, and word learning suggests a special role for the processing of discrete objects. But what counts as an object? Answers to this question often depend on contrasting object-based processing with the processing of spatial areas or unbound visual features. In infant cognition and word learning, though, another salient contrast has been between rigid cohesive objects and nonsolid substances. Whereas objects may move from one location to another, a nonsolid substance must pour from one location to another. In the study reported here, we explored whether attentive tracking processes are sensitive to dynamic information of this type. Using a multiple-object tracking task, we found that subjects could easily track four items in a display of eight identical unpredictably moving entities that moved as discrete objects from one location to another, but could not track similar entities that noncohesively "poured" from one location to another-even when the items in both conditions followed the same trajectories at the same speeds. Other conditions revealed that this inability to track multiple "substances" stemmed not from violations of rigidity or cohesiveness per se, because subjects were able to track multiple noncohesive collections and multiple nonrigid deforming objects. Rather, the impairment was due to the dynamic extension and contraction during the substancelike motion, which rendered the location of the entity ambiguous. These results demonstrate a convergence between processes of midlevel adult vision and infant cognition, and in general help to clarify what can count as a persisting dynamic object of attention.

We demonstrate a link between preschoolers' quantitative competencies and their school-entry knowledge of the relations among numbers (number-system knowledge). The quantitative competencies of 141 children (69 boys) were assessed at the beginning of preschool and throughout the next 2 years of preschool, as was their mathematics and reading achievement at the end of kindergarten and their number-system knowledge at the beginning of first grade. A combination of Bayes analyses and standard regressions revealed that the age at which the children had the conceptual insight that number words represent specific quantities (cardinal value) was strongly related to their later number-system knowledge and was more consistently related to broader mathematics than to reading achievement, controlling for intelligence, executive function, and parental education levels. The key implication is that it is not simply knowledge of cardinal value but the age of acquisition of this principle that is central to later mathematical development and school readiness.

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One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.