Symbolic Number Skills Predict Growth in Nonsymbolic Number Skills in Kindergarteners

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Abstract

There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial debate and study of the relationship between approximate, nonverbal (approximate magnitude system [AMS]) and exact, symbolic (symbolic number system [SNS]) representations of number. Here we examined several hypotheses concerning whether, in the earliest stages of formal education, AMS abilities predict growth in SNS abilities, or the other way around. In addition to tasks involving symbolic (Arabic numerals) and nonsymbolic (dot arrays) number comparisons, we also tested children’s ability to translate between the 2 systems (i.e., mixed-format comparison). Our data included a sample of 539 kindergarten children (M = 5.17 years, SD = .29), with AMS, SNS, and mixed-comparison skills assessed at the beginning and end of the academic year. In this way, we provide, to the best of our knowledge, the most comprehensive test to date of the direction of influence between the AMS and SNS in early formal schooling. Results were more consistent with the view that SNS abilities at the beginning of kindergarten lay the foundation for improvement in both AMS abilities and the ability to translate between the 2 systems. It is important to note that we found no evidence to support the reverse. We conclude that, once one acquires a basic grasp of exact number symbols, it is this understanding of exact number (and perhaps repeated practice therewith) that facilitates growth in the AMS. Though the precise mechanism remains to be understood, these data challenge the widely held view that the AMS scaffolds the acquisition of the SNS.

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