Mastery of the logic of natural numbers is not the result of mastery of counting: evidence from late counters.

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.