Abstract
The approximate number system (ANS) is widely considered to be a foundation for the acquisition of uniquely human symbolic numerical capabilities. However, the mechanism by which the ANS may support symbolic number representations and mathematical thought remains poorly understood. In the present study, we investigated two pathways by which the ANS may influence early math abilities: variability in the acuity of the ANS representations, and children’s’ ability to manipulate ANS representations. We assessed the relation between 4-year-old children’s performance on a non-symbolic numerical comparison task, a non-symbolic approximate addition task, and a standardized symbolic math assessment. Our results indicate that ANS acuity and ANS manipulability each contribute unique variance to preschooler’s early math achievement, and this result holds after controlling for both IQ and executive functions. These findings suggest that there are multiple routes by which the ANS influences math achievement. Therefore, interventions that target both the precision and manipulability of the ANS may prove to be more beneficial for improving symbolic math skills compared to interventions that target only one of these factors.
Highlights
Math ability when a child first enters schooling is the strongest predictor of later math and overall academic achievement (Duncan et al, 2007)
Planned paired t-tests confirmed that children were both more accurate and responded more quickly on the 1:4 ratio trials compared to the 1:2 ratio trials in the approximate addition task [accuracy: t(144) = 8.63, p < 0.001; RT: t(144) = −4.90, p < 0.001], which suggests that this task engaged the approximate number system (ANS)
The first model (Model 1) examined the variance in symbolic math achievement predicted by ANS acuity, ANS manipulability, and IQ
Summary
Math ability when a child first enters schooling is the strongest predictor of later math and overall academic achievement (Duncan et al, 2007). Many cognitive and socioeconomic factors are known to contribute to individual differences in math achievement. One of these factors is an evolutionarily ancient system for representing approximate quantities. Humans use linguistic symbols to represent number, we possess a system for representing number in an approximate, non-symbolic fashion. This system, termed the approximate number system (ANS), emerges independent of exposure to language or formal schooling and is present in a wide variety of non-human species, and emerges early in human development (e.g., Gallistel and Gelman, 1992; Dehaene, 1997; Hubbard et al, 2008)
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