Individual differences in non-verbal number acuity correlate with maths achievement

Abstract

Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.

Verbal interference suppresses exact numerical representation

“…However, it is also possible that the English speakers' differential cultural experience with mathematics and other uses of exact numerosity led to their relatively more precise representation of analog magnitude. Although our current data do not directly speak to this possibility, it is an intriguing avenue for further research (Halberda et al, 2008).…”

Evidence of the impact of visuo-spatial processing on magnitude representation in 22q11.2 microdeletion syndrome

“…Later on, the influence of parallel surface processing decreases (Rousselle & Noël, 2008) but even adults continue to be sensitive to perceptual dimensions in their numerical judgments (Gebuis & Reynvoet, 2012a, 2012bSzucs, Nobes, Devine, Gabriel, & Gebuis, 2013). Even if the majority of studies currently try to control the influence of perceptual variables when assessing non-symbolic magnitude processing Halberda, Mazzocco, & Feigenson, 2008;Mazzocco, Feigenson, & Halberda, 2011;Piazza et al, 2010;Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004), the visual stimulus properties (e.g., surface, density) cannot be controlled for in each individual trial (Gebuis & Reynvoet, 2011, 2012a.…”

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

“…Individual differences in mathematics achievement have been related to both symbolic (Durand, Hulme, Larkin, & Snowling, 2005;Holloway & Ansari, 2009) and non-symbolic (Halberda, Mazzocco, & Feigenson, 2008;Mundy & Gilmore, 2009) numerical magnitude comparison tasks and to number line estimation tasks (Booth & Siegler, 2006;Ramani & Siegler, 2008), which are all considered to be reliable indicators of children's understanding of numerical magnitudes (Laski & Siegler, 2007). Most interestingly, Booth and Siegler (2008) demonstrated that children's representations of magnitude, as measured by a number line estimation task, were uniquely predictive of their learning of answers to novel addition problems and of the errors on them.…”