Representations of numerical and non‐numerical magnitude both contribute to mathematical competence in children

Abstract

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

Spontaneous, modality-general abstraction of a ratio scale

“…The idea of a generalized magnitude system has often been invoked as an explanation for interactions between dimensions in adults and increasingly in infants and children (de Hevia, Izard, Coubart, Spelke, & Streri, 2014; Newcombe, Levine, & Mix, 2015; Lourenco & Bonny, 2016), but currently there is little evidence for specific, positive claims about candidate formats. The experiments presented in this paper fill in part of the hypothesis space by specifying and verifying one plausible type of representation, and thus represent an important step in building a more precise characterization of generalized magnitudes.…”

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

“…Overall accuracy has been suggested as a good measure of the ANS, showing good psychometric features (Inglis & Gilmore, 2014) and has been successfully used in previous studies (e.g. Lourenco & Bonny, 2017). Similarly, overall response times has also been used in previous studies (e.g.…”

“…The use of these measures is based on the idea that the more precise the ANS representations are, the higher the accuracy and the faster the responses in the task are in general (Dietrich, Huber, & Nuerk, 2015). Overall accuracy has been suggested as a good measure of the ANS, showing good psychometric features (Inglis & Gilmore, 2014) and has been successfully used in previous studies (e.g., Lourenco & Bonny, 2017). Similarly, overall RTs has also been used in previous studies (e.g., Halberda et al, 2012) and has been significantly associated with measures of math ability (Libertus, Feigenson, & Halberda, 2011).…”

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

“…There is mixed evidence regarding how well representational acuity of these three quantities correlates within the same individuals (e.g., time, space, and number: Agrillo et al, 2013;De Visscher, Noël, Pesenti, & Dormal, 2017;Odic, 2018;number and space: Geary & Vanmarle, 2016;Odic et al, 2013;time and number: Hamamouche et al, 2018;Odic et al, 2016;Young & Cordes, 2013). Although some studies have revealed similar representational acuity of these distinct quantities (DeWind & Brannon, 2012;Jang & Cho, 2016;Lourenco & Bonny, 2017), others have not found a correlation between tasks (e.g., Agrillo et al, 2013;2 Hamamouche et al, 2018;Odic et al, 2016). Although the ratios used in each task should not affect the likelihood of a correlation between tasks, it should be noted that those studies showing correlations tend to use the same ratios across quantities (see DeWind & Brannon, 2012;Jang & Cho, 2016;Lourenco & Bonny, 2017; but see Young & Cordes, 2013).…”