Previous work has shown that even young infants can “add” or “subtract” quantities of objects using the non-symbolic object tracking system. We asked how these non-symbolic addition skills may change as children learn to count. Thirty 3-year-old children completed a non-symbolic exact addition task, in which children saw an animal collect two sets of objects inside a container, and children were asked to choose the summed total from two alternatives. We also measured children’s knowledge of the count list and their working memory capacity. We found that children with higher count knowledge performed better in solving non-symbolic addition problems with small sets of objects (<3). However, even strong counters struggled when one of the operands exceeded working memory capacity (>=3). Our results suggested that non-symbolic addition skills in 3-year-old’s may be influenced by both their emerging number knowledge and the object tracking system.

Reasoning by exclusion allows us to infer properties of unobserved objects from currently observed objects, formalized by P or Q, not P, therefore Q. Previous work suggested that, by age 3, children can use this kind of reasoning to infer the location of a hidden object after learning that another location is empty (e.g. Mody & Carey, 2016). In the current study, we asked whether children could use reasoning by exclusion to infer the identities of previously unobserved occluded objects in a task that required them to track the locations of multiple occluded objects. Forty-nine 4-7-year-olds viewed animated arrays of virtual “cards” depicting images which were then hidden by occluders. The occluders then swapped locations during the maintenance period. Children were asked to select which card was hidden in a probed location. During the encoding period, we manipulated whether children saw all the card faces (Face-up block) or all but one of the card faces (Exclusion block), for which children had to reason by exclusion to infer the target in half of the trials. We found that all children succeeded in the Face-up block, but only 6-year-olds succeed in the Exclusion block when they had to deploy logical reasoning to identify a previously-unseen hidden target. Our results suggest that children’s ability to reason by exclusion to infer the identity of a hidden target while tracking multiple objects and locations may undergo protracted development.