Relationships between approximate number system acuity and early symbolic number abilities

Mussolin, Christophe; Nys, Julie; Leybaert, Jacqueline

doi:10.1016/j.tine.2012.09.003

Cited by 78 publications

(109 citation statements)

References 48 publications

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“…Although inconsistent with some previous findings where ANS accuracy predicted mathematics attainment (Bonny & Lourenco, 2013;Inglis et al, 2011;Libertus et al, 2011Libertus et al, , 2013Mussolin et al, 2012), the present results are consistent with a number of findings that have not found significant relations between tasks indexing the ANS and mathematics attainment (Göbel et al, 2014;Holloway & Ansari, 2009;Sasanguie, De Smedt et al, 2012;Sasanguie, van den Bussche et al, 2012). The pattern of our results (with the ANS supporting early calculation but not counting skills) suggests that the ANS has a differential influence on different number skills.…”

Section: Approximate Discriminationcontrasting

confidence: 92%

“…Individual differences in approximate quantity discrimination tasks have been found to relate concurrently, retrospectively and longitudinally to mathematical attainment (e.g. Bonny & Lourenco, 2013;Halberda, Mazzocco, & Feigenson, 2008;Inglis et al, 2011;Libertus et al, 2011Libertus et al, , 2013Mussolin, Nys, Leybaert, & Content, 2012). However, other studies have failed to identify this relationship (Göbel, Watson, Lervåg, & Hulme, 2014;Holloway & Ansari, 2009;Kolkman, Kroesbergen, & Leseman, 2013;Lonnemann, Linkersdorfer, Hasselhorn, & Lindberg, 2011;Sasanguie, De Smedt, Defever, & Reynvoet, 2012;Sasanguie, van den Bussche, & Reynvoet, 2012;Soltész, Szucs, & Szucs, 2010) or suggested that this relationship is inconsistent over development (Bonny & Lourenco, 2013).…”

Section: The Approximate Number System (Ans)mentioning

confidence: 99%

“…We chose to report accuracy as the index of children's ANS precision because it has been shown to be a stronger predictor of mathematics attainment than Weber fractions or RTs (Libertus et al, 2013), because Weber fractions have been shown to be highly correlated with percentage accuracy (Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013) and because the fit of the psychophysical model can be volatile in children (Mazzocco, Feigenson, & Halberda, 2011;Mussolin et al, 2012).…”

Section: Approximate Discriminationmentioning

confidence: 99%

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Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Soto-Calvo

Simmons

Willis

et al. 2015

Journal of Experimental Child Psychology

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The extent that phonological, visual-spatial STM and non-symbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4:8. Phonological awareness, visual-spatial STM and non-symbolic approximate discrimination predicted growth in early calculation skills. These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small non-symbolic quantity discrimination task (where the presented quantities were always within the subitising range) predicted growth in cardinal counting skills.These results suggest that the development of counting and calculation are supported by different cognitive abilities.

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Section: Approximate Discriminationcontrasting

confidence: 92%

Section: The Approximate Number System (Ans)mentioning

confidence: 99%

Section: Approximate Discriminationmentioning

confidence: 99%

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Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Soto-Calvo

Simmons

Willis

et al. 2015

Journal of Experimental Child Psychology

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“…Children who understood the exact meaning of the number words "one" to "six" at 3.5 years of age had significantly higher numerical preference scores in infancy than children who only understood a subset of those count words [t (38) = −2.70, P = 0.01], even though the groups did not differ in general intelligence (P > 0.2).…”

Section: Resultsmentioning

confidence: 99%

Number sense in infancy predicts mathematical abilities in childhood

Starr

Libertus

Brannon

2013

Proc. Natl. Acad. Sci. U.S.A.

317

272

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Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.analog magnitudes | approximate number system | cognitive development | mathematical cognition W here does the uniquely human capacity for abstract mathematical concepts come from? What are the ontological building blocks that scaffold our ability for representing number symbolically and performing exact arithmetic? One hypothesis is that the preverbal, nonsymbolic numerical capacities exhibited by human infants in the first year of life serve as a conceptual basis for learning to count and acquiring symbolic mathematical knowledge (1, 2). Although many cognitive abilities contribute to math achievement, including working memory, inhibition, and other executive functions (3, 4), symbolic mathematics is commonly thought to build on a domain-specific nonverbal numerical representation (5). This system, the approximate number system (ANS), is an evolutionarily and ontogenetically ancient system that allows approximate representation of number without the need to count or rely on numerical symbols (2, 6).Support for this hypothesis comes from a handful of studies that have shown a correlation between math ability and individual differences in ANS acuity. For example, ANS acuity in adolescence retroactively predicts math ability in elementary school (7) and ANS acuity in preschool-aged children correlates with their current and future math performance (8-12). In addition, children with dyscalculia, a severe deficit specific to math, have poorer ANS acuity than their typically developing peers (9, 11). These findings demonstrate that ANS acuity covaries with math ability, but the direction of this relationship remains unclear. One possibility is that ANS acuity guides the acquisition of the verbal counting system and symbolic math knowledge, such that children with greater ANS acuity learn t...

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“…Consistent with this, infants as young as 48 h are able to differentiate ratios of 3:1 but not 2:1 (20), and, as they age, children show increasingly precise abilities: at 6 mo, they can distinguish ratios of 2:1, and by 9 mo, ratios of 3:2 (21,22). They eventually reach competencies for ratios 4:3 by 3 y, 6:5 by 6 y, and 8:7 and more difficult ratios by adulthood (23)(24)(25)(26). Furthermore, the ability to discriminate nonsymbolic number in childhood is predictive of later numerical discrimination abilities (27,28).…”

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confidence: 99%

Numerosity representation is encoded in human subcortex

Collins

Park

Behrmann

2017

Proc. Natl. Acad. Sci. U.S.A.

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Certain numerical abilities appear to be relatively ubiquitous in the animal kingdom, including the ability to recognize and differentiate relative quantities. This skill is present in human adults and children, as well as in nonhuman primates and, perhaps surprisingly, is also demonstrated by lower species such as mosquitofish and spiders, despite the absence of cortical computation available to primates. This ubiquity of numerical competence suggests that representations that connect to numerical tasks are likely subserved by evolutionarily conserved regions of the nervous system. Here, we test the hypothesis that the evaluation of relative numerical quantities is subserved by lower-order brain structures in humans. Using a monocular/dichoptic paradigm, across four experiments, we show that the discrimination of displays, consisting of both large (5-80) and small (1-4) numbers of dots, is facilitated in the monocular, subcortical portions of the visual system. This is only the case, however, when observers evaluate larger ratios of 3:1 or 4:1, but not smaller ratios, closer to 1:1. This profile of competence matches closely the skill with which newborn infants and other species can discriminate numerical quantity. These findings suggest conservation of ontogenetically and phylogenetically lower-order systems in adults' numerical abilities. The involvement of subcortical structures in representing numerical quantities provokes a reconsideration of current theories of the neural basis of numerical cognition, inasmuch as it bolsters the crossspecies continuity of the biological system for numerical abilities.subcortex | numerical cognition | vision | development | phylogeny

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Relationships between approximate number system acuity and early symbolic number abilities

Cited by 78 publications

References 48 publications

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Number sense in infancy predicts mathematical abilities in childhood

Numerosity representation is encoded in human subcortex

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