title: Mastery of the logic of natural numbers is not the result of mastery of counting: evidence from late counters.
abstract: To master the natural number system, children must understand both the concepts that number words capture and the counting procedure by which they are applied. These two types of knowledge develop in childhood, but their connection is poorly understood. Here we explore the relationship between the mastery of counting and the mastery of exact numerical equality (one central aspect of natural number) in the Tsimane', a farming-foraging group whose children master counting at a delayed age and with higher variability than do children in industrialized societies. By taking advantage of this variation, we can better understand how counting and exact equality relate to each other, while controlling for age and education. We find that the Tsimane' come to understand exact equality at later and variable ages. This understanding correlates with their mastery of number words and counting, controlling for age and education. However, some children who have mastered counting lack an understanding of exact equality, and some children who have not mastered counting have achieved this understanding. These results suggest that understanding of counting and of natural number concepts are at least partially distinct achievements, and that both draw on inputs and resources whose distribution and availability differ across cultures.
authors.affiliation: Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, USA.
authors.forename: Julian
authors.identifier: http://orcid.org/0000-0002-6167-1647
authors.initials: J
authors.lastname: Jara-Ettinger
authors.affiliation: Department of Brain & Cognitive Sciences, University of Rochester, USA.
authors.forename: Steve
authors.initials: S
authors.lastname: Piantadosi
authors.affiliation: Department of Psychology, Harvard University, USA.
authors.forename: Elizabeth S
authors.initials: ES
authors.lastname: Spelke
authors.affiliation: Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, USA.
authors.forename: Roger
authors.initials: R
authors.lastname: Levy
authors.affiliation: Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Gibson
mesh_terms: D002648:Child; D002657:Child Development / Q000502:physiology*; D002675:Child, Preschool; D003210:Concept Formation / Q000502:physiology*; D005260:Female; D006801:Humans; D007858:Learning / Q000502:physiology; D008128:Logic; D008297:Male; D008433:Mathematics