title: Non-symbolic division in childhood.
abstract: The approximate number system (ANS) underlies representations of large numbers of objects as well as the additive, subtractive, and multiplicative relationships between them. In this set of studies, 5- and 6-year-old children were shown a series of video-based events that conveyed a transformation of a large number of objects into one-half or one-quarter of the original number. Children were able to estimate correctly the outcomes to these halving and quartering problems, and they based their responses on scaling by number, not on continuous quantities or guessing strategies. Children's performance exhibited the ratio signature of the ANS. Moreover, children performed above chance on relatively early trials, suggesting that this scaling operation is easily conveyed and readily performed. The results support the existence of a flexible and substantially untrained capacity to scale numerical amounts.
authors.affiliation: Department of Psychology, Barnard College, Columbia University, New York, NY 10027, USA. Electronic address: kmccrink@barnard.edu.
authors.forename: Koleen
authors.initials: K
authors.lastname: McCrink
authors.affiliation: Department of Psychology, Harvard University, Cambridge, MA 02138, USA.
authors.forename: Elizabeth S
authors.initials: ES
authors.lastname: Spelke
mesh_terms: D002648:Child; D002675:Child, Preschool; D003071:Cognition / Q000502:physiology*; D005260:Female; D006801:Humans; D007600:Judgment / Q000502:physiology*; D008297:Male; D009483:Neuropsychological Tests; D011340:Problem Solving / Q000502:physiology*
keywords: Approximate number system; Cognitive development; Division; Number; Operational momentum; Scaling