Mapping Among Number Words, Numerals, and Nonsymbolic Quantities in Preschoolers

Abstract

In mathematically literate societies, numerical information is represented in 3 distinct codes: a verbal code (i.e., number words); a digital, symbolic code (e.g., Arabic numerals); and an analogical code (i.e., quantities; Dehaene, 1992). To communicate effectively using these numerical codes, our understanding of number must involve an understanding of each representation as well as how they map to other representations. In the current study, we looked at 3- and 4-year-old children’s understanding of Arabic numerals in relation to both quantities and number words. The results suggest that the mapping between quantities and numerals is more difficult than the mapping between numerals and number words and between number words and quantities. Thus, we compared 2 competing models designed to investigate how children represent the meanings of Arabic numbers—whether numerals are mapped directly to the quantities they represent or instead if numerals are mapped to quantities indirectly via a direct mapping to number words. We found support for the latter suggesting that children may first map numerals to number words (another symbolic representation) and only through this mapping are numerals subsequently tied to the quantities they represent. In addition, unlike both mappings involving quantity, the mapping between the 2 symbolic representations of number (numerals and number words) was not set-size-dependent, therefore providing further evidence that children may map symbols to other symbols in the absence of a quantity referent. Together, the results provide new insight into the important processes involved in how children acquire an understanding of symbolic representations of number.

View correction statement:

Correction

Acknowledgments

The research presented here was supported by a Postgraduate Scholarship from the Natural Science and Engineering Research Council of Canada to M. H., a National Science Foundation postdoctoral fellowship (#1203658) to U. A., and a Facilitating Academic Careers in Engineering and Science postdoctoral fellowship awarded to U. A. The authors would like to thank our museum partners, the Living Laboratory at the Museum of Science, Boston and the Boston Children’s Museum, and local preschools for their help with participant recruitment. We would also like to thank two anonymous reviewers for providing thoughtful insight on an earlier version of this manuscript.

Notes

¹ Although there is substantial debate about whether the symbolic representations are mapped to the approximate number system (ANS) or the object file system and how this mapping occurs (e.g., Gelman & Gallistel, 1978; Le Corre & Carey, 2007), we will remain agnostic about these claims and simply refer to “quantity,” which may be represented via either/both of these systems.

² Nine children completed tasks in a slightly different order. However, performance on each task was not significantly different between task orders (ps > .1).

³ Age was treated as a categorical variable for consistency within all the analyses. However, the pattern and significance of results are identical when age is treated continuously.