Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

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 non-symbolic (dot arrays) number comparisons, we also tested children's ability to translate between the two systems (i.e., mixed-format comparison). Our data included a sample of 539 Kindergarten children (mean=5.17yrs, SD=0.29yrs), 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 two systems. Importantly, we found no evidence to support the reverse. We conclude that, once one acquires a very 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.

Fluency in symbolic arithmetic refines the approximate number system in parietal cortex

“…Lyons and colleagues (2017) designed a study to investigate the relationship between ANS acuity and symbolic processing with a different approach: besides assessing children’s symbolic and non-symbolic abilities at each time point, they also measured their ability to translate between the two systems and studied how those abilities changed over time. Namely, they used a comparison task including: only numeral (e.g.…”

“…On the other hand, the refinement hypothesis, claiming that symbols refine the ANS acuity, would not necessarily assume a strong association between the symbolic and the non-symbolic systems, what would imply a higher cost of mixing symbolic and non-symbolic inputs early in development. With increasing experience with symbols, the non-symbolic quantities representations would be “increasingly understood in symbolic terms” and therefore the link between the two systems would be stronger over time (Lyons, Bugden, Zheng, De Jesus, & Ansari, 2017). …”

“…Despite the advances made by well-designed longitudinal studies in recent years, this research is still in an early stage and the mechanisms by which symbols refine the ANS remain, to date, unknown (Ansari, 2008; Feigenson, Libertus, & Halberda, 2013; Lyons et al, 2017; Matejko & Ansari, 2016). However, several possible mechanisms have been suggested.…”

How Are Symbols and Nonsymbolic Numerical Magnitudes Related? Exploring Bidirectional Relationships in Early Numeracy

“…Instead, findings from Toll et al () provide evidence for a bidirectional relationship between symbolic and nonsymbolic numerical magnitude representation. However, Kolkman et al (), Matejko and Ansari (), Mussolin, Nys, Content, and Leybaert (), Lyons et al (), Shusterman et al () and Vanbinst et al () suggest a unidirectional relationship in the direction opposite to that predicted by most theories: that development of symbolic numerical magnitude representation impacts processing of nonsymbolic numerical magnitude. Additionally, although there is a lack of research examining the relationship between higher‐level symbolic skills (i.e., arithmetic) and nonsymbolic numerical magnitude representation, Suárez‐Pellicioni and Booth () found evidence that symbolic arithmetic may actually refine later nonsymbolic numerical magnitude skills, as opposed to the reverse.…”

“…Many published longitudinal studies could not assess potential bidirectional relationships because the predictor and outcomes measures were not measured at all time points. Recent evidence using the same measures taken at multiple time points suggests bidirectionality between the development of symbolic and nonsymbolic numerical magnitude representation (Kolkman, Kroesbergen, & Leseman, ; Lyons, Bugden, Zheng, De Jesus, & Ansari, ; Matejko & Ansari, ; Mussolin, Nys, Content, & Leybaert, ; Toll, Van Viersen, Kroesbergen, & Van Luit, ).…”