The approximate number system and its relation to early math achievement: evidence from the preschool years

Abstract

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.

Figure 1

Sample trial from the NDT (8 vs. 4 dots).

Figure 2

Accuracy on the NDT as measured by the mean percentage of trials in which children correctly chose the numerically larger array. Error bars reflect +/− 1 SEM. Collapsing across age, mean accuracy was above chance at each ratio (all ps < .001, Bonferroni corrected).

Figure 3

Scatterplot relating ANS precision on the NDT and mathematical ability (TEMA-3 scores) for children scoring above (right side of figure) versus below (left side of figure) the breakpoint. TEMA scores are centered to the breakpoint (i.e., individual score minus 113.4).