Number sense across the lifespan as revealed by a massive Internet-based sample

Abstract

It has been difficult to determine how cognitive systems change over the grand time scale of an entire life, as few cognitive systems are well enough understood; observable in infants, adolescents, and adults; and simple enough to measure to empower comparisons across vastly different ages. Here we address this challenge with data from more than 10,000 participants ranging from 11 to 85 years of age and investigate the precision of basic numerical intuitions and their relation to students' performance in school mathematics across the lifespan. We all share a foundational number sense that has been observed in adults, infants, and nonhuman animals, and that, in humans, is generated by neurons in the intraparietal sulcus. Individual differences in the precision of this evolutionarily ancient number sense may impact school mathematics performance in children; however, we know little of its role beyond childhood. Here we find that population trends suggest that the precision of one's number sense improves throughout the schoolage years, peaking quite late at ∼30 y. Despite this gradual developmental improvement, we find very large individual differences in number sense precision among people of the same age, and these differences relate to school mathematical performance throughout adolescence and the adult years. The large individual differences and prolonged development of number sense, paired with its consistent and specific link to mathematics ability across the age span, hold promise for the impact of educational interventions that target the number sense.aging | analog magnitude | approximate number system | cognitive development | ensemble representation A lthough the particulars of our minds may differ from person to person, some aspects of cognition are close to our corethey are universally shared, present in the young, and actively engaged throughout our lifetimes (1, 2). Investigating developmental changes in these core systems may present us with a picture of how the mind transforms from infancy to senescence. Here we investigated change in the approximate number system (ANS), the cognitive system that gives rise to our basic numerical intuitions (3). The ANS generates nonverbal representations of numerosity in nonhuman animals (4, 5), infants (6, 7), school-aged children (8-10), and adults from mathematically fluent cultures (11,12) as well as cultures that do not practice explicit mathematics (13,14). In humans, imaging results suggest that these basic intuitions are supported by neurons in the intraparietal sulcus (15-18), a role that can be observed shortly after birth (19). Given the phylogenetically widespread occurrence of this primitive cognitive resource, the ANS might make little or no contact with the formal mathematical abilities that humans struggle to master and that no other animals acquire (20). Alternatively, this system may be a critical foundation upon which formal mathematical abilities are constructed (21,22). Although some evidence suggests a link between the ANS and formal mathemat...

Indexing the approximate number system

“…While some of these researchers have indexed ANS acuity using Weber fractions (e.g. Castronovo & Gobel, 2012;Halberda et al, , 2012Inglis et al, 2011;Libertus et al, 2012;Lyons & Beilock, 2011;Piazza et al, 2010;Price et al, 2012;Sasanguie et al, 2012), others have used NREs (e.g., Bugden et al, 2012;Holloway & Ansari, 2009;Lourenco et al, 2012;Merkley & Ansari, 2010;Price et al, 2012), and others accuracy (e.g. Fuhs & McNeil, 2013;Nys et al, 2013;Wei et al, 2012).…”

“…Bonny & Lourenco, 2013;Castronovo & Göbel, 2012;Halberda, Ly, Willmer, Naiman, & Germine, 2012;Inglis et al, 2011;Libertus et al, 2011Libertus et al, , 2012Lyons & Beilock, 2011;Mazzocco et al, 2011a;Piazza et al, 2010;Price et al, 2012;Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013). It makes the INDEXING THE APPROXIMATE NUMBER SYSTEM 5 theoretical assumption that the ANS operates according to the Weber-Fechner law (e.g.…”

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

“…The Approximate Number System (ANS) is believed to be a cognitive system that underlies this sense of number (Dehaene, 1997). Many researchers have shown that individuals with superior performance on tasks designed to measure ANS acuity also demonstrate more advanced mathematical abilities (Halberda, Ly, Wilmer, Naiman, & Germine, 2012;Halberda, Mazzocco, & Feigenson, 2008;Libertus, Feigenson, & Halberda, 2011;Libertus, Odic, & Halberda, 2012;Mazzocco, Feigenson, & Halberda, 2011a;Piazza et al, 2010, Piazza, Pica, Izard, Spelke, & Dehaene, 2013see Chen & Li, 2014 for a meta-analysis). This link has generated a great deal of interest from cognitive psychologists and education researchers, yet there are also many published studies which have failed to demonstrate this correlation (see De Smedt, Noël, Gilmore, & Ansari, 2013, for a review).…”

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

“…In recent years, many studies reported the existence of a relationship between arithmetic performance or math ability, and the value of the Weber fraction, both in children (e.g., Libertus, Feigenson, & Halberda, 2011;Inglis, Attridge, Batchelor, & Gilmore, 2011, experiment 1) and in adults (e.g., DeWind & Brannon, 2012;Guillaume, Nys, Mussolin, & Content, 2013;Halberda, Ly, Wilmer, Naiman, & Germine, 2012;Libertus, Odic, & Halberda, 2012;Nys & Content, 2012;Nys, Ventura, Fernandes, Querido, Leybaert, & Content, 2013). Notwithstanding these positive findings, contradictory results were also reported, with several studies failing to observe any significant correlation between ANS acuity (computed from such comparison tasks) and arithmetic competence in children Sasanguie, Göbel, Moll, Smets, Reynvoet, 2013;see also De Smedt, Noël, Gilmore, & Ansari, 2013, for a short review) or in adults (e.g., Castronovo & Göbel, 2012, experiment 1;Inglis et al, 2011, experiment 2;Price, Palmer, Battista, & Ansari, 2012).…”