Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge.

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.