Children can manipulate non-symbolic representations of both small quantities of objects (about four or fewer, represented by the parallel individuation system) and large quantities of objects (represented by the analog magnitude system, or AMS). Previous work has shown that children can perform a variety of non-symbolic operations over AMS representations (like summing and solving for an unknown addend), but are not able to perform further operations on the derived solutions of such non-symbolic operations. However, while the computational capacity of AMS has been studied extensively in early childhood, less is known about the computational capacity of the parallel individuation system. In two experiments, we examined children’s ability to perform two types of arithmetic-like operations over representations of small, exact quantities, and whether they could subsequently perform novel operations on derived quantity representations. Four-6-year-old US children (n = 99) solved two types of non-symbolic arithmetic-like problems with small quantities: summation and unknown addend problems. We then tested whether children could use the solutions to these problems as inputs to new operations. Results showed that children more readily solved non-symbolic small, exact addition problems compared to unknown addend problems. However, when children did successfully solve either kind of problem, they were able to use those derived solutions to solve a novel non-symbolic small, exact problem. These results suggest that the parallel individuation system is computationally flexible, contrasting with previous work showing that the AMS is more computationally limited, and shed light on the computational capacities and limitations of representing and operating over representations of small quantities of individual objects.

Objects’ topological properties play a central role in object perception, superseding objects’ surface features in object representation and tracking from early in development. We asked about the role of objects’ topological properties in children’s generalization of novel labels to objects. We adapted the classic name generalization task of Landau et al. ( 1988 , 1992 ). In three experiments, we showed children ( n = 151; 3–8-year-olds) a novel object (the standard) and gave the object a novel label. We then showed children three potential target objects and asked children which of the objects shared the same label as the standard. In Experiment 1, the standard object either did or did not contain a hole, and we asked whether children would extend the standard’s label to a target object that shared either metric shape or topology with the standard. Experiment 2 served as a control condition for Experiment 1. In Experiment 3, we pitted topology against another surface feature, color. We found that objects’ topology competed with objects’ surface features (both shape and color) in children’s extension of labels to novel objects. We discuss possible implications for our understanding of the inductive potential of objects’ topologies for making inferences about objects’ categories across early development.