Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children

Abstract

The process by which adults develop competence in symbolic mathematics tasks is poorly understood. Nonhuman animals, human infants, and human adults all form nonverbal representations of the approximate numerosity of arrays of dots and are capable of using these representations to perform basic mathematical operations. Several researchers have speculated that individual differences in the acuity of such nonverbal number representations provide the basis for individual differences in symbolic mathematical competence. Specifically, prior research has found that 14-year-old children's ability to rapidly compare the numerosities of two sets of colored dots is correlated with their mathematics achievements at ages 5-11. In the present study, we demonstrated that although when measured concurrently the same relationship holds in children, it does not hold in adults. We conclude that the association between nonverbal number acuity and mathematics achievement changes with age and that nonverbal number representations do not hold the key to explaining the wide variety of mathematical performance levels in adults.

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

“…If we assume that w correctly indexes ANS acuity, and if we only had recourse to this measure in our correlation analyses, we would be led to conclude that the data do not support the existence of a relationship between ANS acuity and arithmetic proficiency (as Castronovo & Göbel, 2012;Gilmore et al, 2011;Inglis et al, 2011;Price et al, 2012). On ASSESSING THE APPROXIMATE NUMBER SYSTEM the other hand, if we consider that CV is an adequate index of ANS acuity, we would have to conclude the opposite, as we found a significant correlation between CV and our arithmetic measure (as Mejias & Schiltz, 2013).…”

Sampling from the mental number line: How are approximate number system representations formed?

“…Several recent studies have shown that individuals' ANS acuities are correlated with achievement in symbolic mathematics (e.g. Gilmore, McCarthy & Spelke, 2010;Libertus, Feigenson & Halberda, 2011;Mazzocco, Feigenson & Halberda, 2011a, 2011b; but see Inglis, Attridge, Batchelor & Gilmore, 2011;Price, Palmer, Battista & Ansari, 2012), lending credence to the suggestion that the ANS is implicated in the development of symbolic mathematics competence.…”

“…When presenting numerical comparison tasks (where participants are shown two dot arrays and asked to determine which is more numerous), some researchers have permitted participants to decide how long to study the stimuli before reaching a judgement (e.g., Inglis et al, 2011;Pica et al, 2004), whereas others have displayed the stimuli for a fixed period. Among those who have used fixed stimuli durations, some have displayed stimuli for as little as 200ms (e.g., whereas others have used up to 2500ms (e.g., , and some researchers have used different stimuli durations for different participants within the same experiment (e.g., Mazzocco, Feigenson & Halberda, 2011b).…”

Indexing the approximate number system

“…Bonny & Lourenco, 2013;Castronovo & Göbel, 2012;Halberda, Ly, Willmer, Naiman, & Germine, 2012;Inglis et al, 2011;Libertus et al, 2011Libertus et al, , 2012Lyons & Beilock, 2011;Mazzocco et al, 2011a;Piazza et al, 2010;Price et al, 2012;Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013). It makes the INDEXING THE APPROXIMATE NUMBER SYSTEM 5 theoretical assumption that the ANS operates according to the Weber-Fechner law (e.g.…”