A mental model for early arithmetic

The authors examined young children's ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier than verbal calculation ability but did not examine when it first appears. The authors propose that the ability to solve such problems involves domain-general symbolic processes similar to those involved in symbolic play and the use of physical models. Hence the ability to calculate should appear at about 2 years and should be related to overall level of intellectual competence. The authors show that the ability to reliably solve nonverbal calculation tasks emerges only after 2 years of age and that performance on nonverbal calculation problems is highly related to overall level of intellectual competence in children between 3 and 4 years of age. It is well known that children can carry out numerical transformations involving addition and subtraction by 5 or 6 years of age (e.g., Siegler & Shrager, 1984; Siegler &amp