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

Abstract

What is the nature of the relationship between different lower‐level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for bidirectional relationships between symbolic and nonsymbolic numerical magnitude skill development is examined. Overall, present evidence is more indicative of an influence of symbolic numerical magnitude skills on the development of nonsymbolic numerical magnitude skills than vice versa. Looking forward, methodological issues pertinent to measuring the direction of such relationships are discussed. Also discussed is the important role that training studies need to play to further understand the complex relationships between basic number skills, and in turn their relationship with arithmetic. It is important that assumptions about relationships between lower and higher‐level cognitive skills are tested empirically and that seemingly counterintuitive relationships are given serious consideration.

Predictors of Children’s Early Numeracy: Environmental Variables, Intergenerational Pathways, and Children’s Cognitive, Linguistic, and Non-symbolic Number Skills

“…In typically-developing children, several studies have revealed a strict relationship between dot comparison – as a measure of ANS - and mathematics achievement ( Libertus et al, 2011 ; Mazzocco et al, 2011 ). However, there are contrasting results to this regard (for a review, see De Smedt et al, 2013 ), and some authors suggest that symbolic representation is more strictly related to mathematical achievements ( Göbel et al, 2014 ; Goffin and Ansari, 2019 ). This is in line with the strong relationship found between math skills and language development (e.g., Korpipää et al, 2019 ), supporting the idea that language competence may act as a scaffolding ability on which numerical development may rely ( Bonifacci et al, 2016 ).…”

Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures

“…We have carried out both null hypothesis significance testing and Bayesian analysis, the latter being able to quantify support for both the null and alternative hypotheses. Our study represents a strong test of recent theoretical and empirical models that have included domain-specific (ANS and SNC) and domain-general factors (WM) as predictors of mathematics achievement (Geary, 2013;Goffin & Ansari, 2019;Inglis, Attridge, Batchelor, & Gilmore, 2011).…”

Variation in early number skills and mathematics achievement: Implications from cognitive profiles of children with or without Turner syndrome

“…Numerical skills include nonsymbolic magnitude comparison (MC N ) skills that reflect an ability to represent and compare quantities, such as two sets of dot displays, independent of the words and symbols used to convey those quantities. Although there is considerable debate concerning what skills underlie performance on MC N tasks [ 27 – 29 ] and the influence of task demands on MC N task performance, there is general agreement that these skills differ from symbolic magnitude comparison skills that rely on digits and number words. Researchers also generally agree that symbolic magnitude comparison skills account for more variance in mathematics than do their nonsymbolic counterparts [ 30 ], particularly when predicting highly symbolic mathematics skills such as fractions [ 31 ].…”