What Kinds of Computations Can Young Children Perform Over Non-Symbolic Representations of Small Quantities?

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.