Abstract
Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.
Highlights
Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown
A Greenhouse-Geisser corrected repeated-measures analysis of covariance (ANCOVA) with Ratio as the independent variable (IV) and Age as a covariate showed that accuracy on this task was ratio-dependent, F(3.31, 231.98) = 35.23, p < .001, ηp2 = .34, and that children were more accurate with age, F(1, 70) = 17.65, p < .001, ηp2 =
What factors explain the observed relationship between individual differences in children’s intuitive number sense and symbolic mathematics? Here, we tested whether non-symbolic/ANS numerical metacognition—that is, the sensitivity of children’s ability to decide when they can discriminate between ANS trials—might mediate the reported relationship between ANS precision and performance on a standardized test of symbolic mathematics (TEMA-3)
Summary
Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. An emerging body of work suggests that individual differences in ANS precision—the smallest ratio that observers can reliably discriminate without counting—predict scores on standardized and non-standardized math assessments in both children and adults (Chen & Li, 2014; Dehaene, 2009; Feigenson et al, 2013; Halberda et al, 2008; Schneider et al, 2017; Szkudlarek & Brannon, 2017) While these results have frequently been a topic of fierce debate (e.g., Gilmore et al, 2013; Lindskog & Winman, 2016; Sasanguie, Defever, Maertens, & Reynvoet, 2014; Szűcs & Myers, 2017), ANS precision has been shown to predict mathematics ability concurrently (Libertus, Feigenson, & Halberda, 2011; Libertus, Odic, & Halberda, 2012), retrospectively (Halberda et al, 2008), and predictively (Starr, Libertus, & Brannon, 2013). Individual differences in children’s ability to detect differences in certainty are at least partly independent of ANS precision itself and may constitute a kind of domain-general currency of perceptual confidence that can be used across many different domains (Baer et al, 2018; Baer & Odic, 2019; see De Gardelle, Le Corre, & Mamassian, 2016; De Gardelle & Mamassian, 2014)
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