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

Abstract

The objective of this study was to investigate, using a brain measure of approximate number system (ANS) acuity, whether the precision of the ANS is crucial for the development of symbolic numerical abilities (i.e., scaffolding hypothesis) and/or whether the experience with symbolic number processing refines the ANS (i.e., refinement hypothesis). To this aim, 38 children solved a dot comparison task inside the scanner when they were approximately 10-years old (Time 1) and once again approximately 2 years later (Time 2). To study the scaffolding hypothesis, a regression analysis was carried out by entering ANS acuity at T1 as the predictor and symbolic math performance at T2 as the dependent measure. Symbolic math performance, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. In order to study the refinement hypothesis, the regression analysis included symbolic math performance at T1 as the predictor and ANS acuity at T2 as the dependent measure, while ANS acuity, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. Our results supported the refinement hypothesis, by finding that the higher the initial level of symbolic math performance, the greater the intraparietal sulcus activation was at T2 (i.e., more precise representation of quantity). To the best of our knowledge, our finding constitutes the first evidence showing that expertise in the manipulation of symbols, which is a cultural invention, has the power to refine the neural representation of quantity in the evolutionarily ancient, approximate system of quantity representation.

Challenging the neurobiological link between number sense and symbolic numerical abilities

“…Mediation attempts to mathematically explain the mechanistic relation between outcome and predictor variables via a third construct, and these studies also suggest that the relation between number sense and math may be mediated by symbolic number processing . Along this line of inquiry, one recent neuroimaging study of 3rd to 8th grade children provides support for a refinement process that accompanies the development of symbolic number skills, whereby experience with symbolic quantities enhances the precision of a nonsymbolic number sense . In this longitudinal study, individual differences in arithmetic fluency at time 1 predict activation in the parietal lobe during the nonsysmbolic number comparison task at time 2 (2 years later).…”

“…Furthermore, regardless of the degree of representational overlap between symbolic and nonsymbolic number processing, enough previous literature has established that the two are linked in development that future models must explain this phenomenon. As we mentioned while explaining the details for a link between number sense and numerical abilities, development of symbolic number knowledge has frequently been shown to enhance nonsymbolic number acuity . Therefore, it may be the case that even if symbolic and nonsymbolic number formats are relatively distinct in their neural mechanisms, the acquisition of symbolic number could serve to enhance the perception of nonsymbolic number via attention mechanisms similar to those suggested in Challenge 3.…”

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

“…Although the replicability of these findings is unknown, this pattern of an influence of arithmetic on nonsymbolic numerical magnitude representation is counterintuitive to common beliefs held about the nature of numerical magnitude representation. These results by Suárez‐Pellicioni and Booth () emphasize the importance of designing studies to empirically test the direction of the relationship between nonsymbolic and symbolic numerical magnitude skills.…”

“…To our knowledge, few studies have examined bidirectionality in the relationship between symbolic arithmetic and nonsymbolic numerical magnitude representation. However, in one such study, Suárez‐Pellicioni and Booth () measured nonsymbolic numerical magnitude acuity and symbolic arithmetic in a group of 38 American 10‐year‐olds, and again 2 years later. Nonsymbolic numerical magnitude acuity was assessed both behaviorally, with a nonsymbolic comparison task, as well as neurally, through functional magnetic resonance imaging (fMRI) data collection during the nonsymbolic comparison task.…”

“…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. Despite this evidence for a relationship from symbolic to nonsymbolic numerical magnitude representation, there are further methodological considerations that need to be heeded when trying to establish longitudinal relationships of this nature.…”