Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities

Abstract

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the present study we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of two years. Additionally, at the last time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3; Ginsburg & Baroody, 2003). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned, non-symbolic system of quantity representation and the system of mathematical reasoning that children come to master through instruction.

The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

“…We further replicated a divergence in the relation between w and formal versus informal math abilities. Consistent with the findings of Libertus and colleagues (2013b), we found that w significantly related to informal math abilities even when controlling for age (r s = −.36, p < .05; Figure 5a), but w showed no significant relation to formal math abilities (r s = −.06, p = .71; Figure 6a). This asymmetry motivated us to probe for a similar divergence in the link between informal versus formal math abilities and their relation to verbal number estimation.…”

“…In a recent study, Libertus, Feigenson, and Halberda (2013b) found that 3- to 7-year-old children’s ANS precision predicted their informal but not their formal math abilities up to two years later. In adults, Lourenco and colleagues (2012) showed that ANS precision correlated with performance on the Woodcock-Johnson (WJ) calculation subtest and KeyMath geometry subtest, but not with the WJ math fluency, applied math problems, or quantitative concepts subtests (but see Inglis, Attridge, Batchelor, & Gilmore, 2011, for a failure to find a link between any WJ math subtest and ANS acuity in adults).…”

How do different aspects of spatial skills relate to early arithmetic and number line estimation?

“…In prior research, findings about the importance of the ANS in mathematical development remained inconclusive (De Smedt, Noël, Gilmore, & Ansari, 2013;Halberda et al, 2008;Kolkman et al, 2013;Libertus, Feigenson, & Halberda, 2011, 2013a, 2013bSasanguie, Göbel, Moll, Smets, & Reynvoet, 2013). Our results corroborate prior findings (Kolkman et al, 2013;Sasanguie et al, 2013) showing that as soon as symbolic skills are mastered, non-symbolic skills lose their predictive value for mathematics.…”

Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement

“…This is the default setting on the Panamath software 5 , and this type of control has been used in multiple studies of the ANS (e.g. Halberda et al, 2012;Hellgren, Halberda, Forsman, Ådén, & Libertus, 2013;Libertus et al, 2011;Libertus et al, 2012;Libertus, Feigenson, & Halberda, 2013a, 2013bMazzocco et al 2011a;Mazzocco, Feigenson, & Halberda, 2011b;Odic, Libertus, Feigenson, & Halberda, 2013;Odic, Hock, & Halberda, 2014).…”