Acuity of the approximate number system and preschoolers' quantitative development.

The study assessed the relations among acuity of the inherent approximate number system (ANS), performance on measures of symbolic quantitative knowledge, and mathematics achievement for a sample of 138 (64 boys) preschoolers. The Weber fraction (a measure of ANS acuity) and associated task accuracy were significantly correlated with mathematics achievement following one year of preschool, and predicted performance on measures of children's explicit knowledge of Arabic numerals, number words, and cardinal value, controlling for age, sex, parental education, intelligence, executive control, and preliteracy knowledge. The relation between ANS acuity, as measured by the Weber fraction and task accuracy, and mathematics achievement was fully mediated by children's performance on the symbolic quantitative tasks, with knowledge of cardinal value emerging as a particularly important mediator. The overall pattern suggests that ANS acuity facilitates the early learning of symbolic quantitative knowledge and indirectly influences mathematics achievement through this knowledge.

Tracking and quantifying objects and non-cohesive substances.

The present study tested infants' ability to assess and compare quantities of a food substance. Contrary to previous findings, the results suggest that by 10 months of age infants can quantify non-cohesive substances, and that this ability is different in important ways from their ability to quantify discrete objects: (1) In contrast to even much younger infants' ability to discriminate discrete quantities that differ by a 1:2 ratio, infants here required a 1:4 ratio in order to reliably select the larger of two substance quantities. And (2), unlike with objects, infants required multiple cues in order to determine which of two quantities of substance was larger. Moreover, (3) although 14.5-month-olds were able to compare amounts of substance in memory, 10- to 12-month-olds were limited to comparing visible amounts of substance. These findings are discussed in light of the mechanisms that may underlie infants' quantification of objects and substances.