Is Nonsymbolic Arithmetic Truly “Arithmetic”? Examining the Computational Capacity of the Approximate Number System in Young Children

Author:

Cheng Chen1,Kibbe Melissa M.2

Affiliation:

1. Division of Social Science Hong Kong University of Science and Technology

2. Department of Psychological and Brain Sciences Boston University

Abstract

AbstractYoung 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.

Funder

National Science Foundation

Publisher

Wiley

Subject

Artificial Intelligence,Cognitive Neuroscience,Experimental and Cognitive Psychology

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