Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults.

Abstract

Behavioral, neuropsychological, and brain imaging research points to a dedicated system for processing number that is shared across development and across species. This foundational Approximate Number System (ANS) operates over multiple modalities, forming representations of the number of objects, sounds, or events in a scene. This system is imprecise and hence differs from exact counting. Evidence suggests that the resolution of the ANS, as specified by a Weber fraction, increases with age such that adults can discriminate numerosities that infants cannot. However, the Weber fraction has yet to be determined for participants of any age between 9 months and adulthood, leaving its developmental trajectory unclear. Here we identify the Weber fraction of the ANS in 3-, 4-, 5-, and 6-year-old children and in adults. We show that the resolution of this system continues to increase throughout childhood, with adultlike levels of acuity attained surprisingly late in development.

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

“…Most other cognitive abilities, with the notable exception of face recognition ability (29), appear to peak earlier. This extends previous studies, which suggested developmental changes in w in smaller laboratory-based samples (9,10). The large overlap among interdecile ranges across the lifespan (Fig.…”

“…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)(9)(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)(16)(17)(18), a role that can be observed shortly after birth (19).…”

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

“…Studies using psychophysical techniques to quantify the coarseness of nonsymbolic number representations point to large individual differences in precision throughout the lifespan (21,22). Whereas some people have more noise associated with the ANS (i.e., more overlap in the Gaussian curves), others have less noise (i.e., less overlap in the Gaussian curves).…”

“…Additional evidence for a link between the ANS and symbolic arithmetic comes from individuals with dyscalculia, known as a specific disability in learning school-relevant math (17). Recent studies suggest that dyscalculia is also characterized by deficits in ANS processing such as nonsymbolic number comparison (18), with atypical IPS activation during both symbolic arithmetic (19) and approximate nonsymbolic comparisons (20).Studies using psychophysical techniques to quantify the coarseness of nonsymbolic number representations point to large individual differences in precision throughout the lifespan (21,22). Whereas some people have more noise associated with the ANS (i.e., more overlap in the Gaussian curves), others have less noise (i.e., less overlap in the Gaussian curves).…”

Reasoning strategies with rational numbers revealed by eye tracking

“…In general, children and adults are fairly accurate in comparing the approximate sizes of numerical magnitudes (Booth & Siegler, 2006;Halberda & Feigenson, 2008;McCrink & Wynn, 2004). Understanding of counting procedures develops later (Opfer & Siegler, 2012).…”