Imagine you have a magical calculator that can perform arithmetic-like operations without symbols or numbers. That’s similar to what young children with limited knowledge of formal mathematics are capable of! But how exactly do these nonsymbolic arithmetic operations work? A group of researchers conducted experiments with children to investigate if there are function-like rules guiding these operations, similar to how symbolic arithmetic works. The children were given nonsymbolic arithmetic problems and then asked to determine which solution should be added to a smaller set of objects to make them ‘about the same’ as another set. The researchers hypothesized that if nonsymbolic arithmetic shares function rules with symbolic arithmetic, then children should be able to use the solutions from one nonsymbolic problem as inputs for another one. Surprisingly, the results showed that children were unable to consistently do so, suggesting that nonsymbolic computations may not function independently from each other. This implies that nonsymbolic and symbolic arithmetic are algorithmically distinct, which could limit children’s ability to transfer their nonsymbolic arithmetic skills to formal mathematics education. If you want to dig deeper into this fascinating research, check out the full article!

Abstract
Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like structure, like symbolic arithmetic. Children (n = 74 4- to -8-year-olds in Experiment 1; n = 52 7- to 8-year-olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them “about the same.” We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.

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