Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

Abstract

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

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

“…Moreover, of studies that have examined the relation between AMS and SNS tasks at different timepoints, few if any include control for the outcome at time 1 (e.g., Libertus et al, 2011;Mazzocco et al, 2011;Wang et al, 2016). Inclusion of this control is crucial because it allows one to genuinely predict growth in the outcome.…”

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

“…For example, used displays of 2500ms for 3-year-olds, 1200ms for 4-, 5-and 6-year olds, and 750ms for adults, and Mazzocco et al (2011b) used display times of 1200ms and 2500ms for the two age groups in their study, combining the data into a single analysis. Our findings indicate that this analysis strategy may be flawed, and that Weber fractions derived from tasks with different display times are not comparable.…”

“…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). All these authors have assumed that these methods investigate the same underlying process, but if the formation of ANS representations is time dependent then it is questionable whether results from these studies are comparable.…”

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.…”