Approximate number sense correlates with math performance in gifted adolescents

Wang, Jinjing Jenny; Halberda, Justin; Feigenson, Lisa

doi:10.1016/j.actpsy.2017.03.014

Cited by 30 publications

(26 citation statements)

References 64 publications

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“…Despite the differences between the systems for representing symbolic and approximate number, symbolic number reasoning is thought by many to be rooted in the ANS, such that approximate number representations play a role even during symbolic mathematical computation (e.g., Dehaene, Dupoux, & Mehler, 1990). Consistent with this idea, individual differences in the ability to approximate the number of items in an array without counting predicts performance on standardized math tests such as the SAT and the Woodcock-Johnson (Bonny & Lourenco, 2013; Halberda, Mazzocco, & Feigenson, 2008; Libertus, Feigenson, & Halberda, 2011; Libertus, Odic, & Halberda, 2012; Lourenco, Bonny, Fernandez, & Rao, 2012; Wang, Halberda, & Feigenson, 2017; for review see Chen & Li, 2014; Feigenson, Libertus, & Halberda, 2013). Furthermore, individual differences in 6-month-old infants’ ability to visually discriminate approximate quantities predict symbolic number knowledge at 3.5 years of age (Starr, Libertus, & Brannon, 2013), and improving numerical approximation through specific forms of practice can temporarily boost symbolic math performance (Hyde, Khanum, & Spelke, 2014; Park & Brannon, 2013; Wang, Odic, Halberda, & Feigenson, 2016).…”

Section: Introductionmentioning

confidence: 90%

Numerical cognition is resilient to dramatic changes in early sensory experience

2018

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Humans and non-human animals can approximate large visual quantities without counting. The approximate number representations underlying this ability are noisy, with the amount of noise proportional to the quantity being represented. Numerate humans also have access to a separate system for representing exact quantities using number symbols and words; it is this second, exact system that supports most of formal mathematics. Although numerical approximation abilities and symbolic number abilities are distinct in representational format and in their phylogenetic and ontogenetic histories, they appear to be linked throughout development--individuals who can more precisely discriminate quantities without counting are better at math. The origins of this relationship are debated. On the one hand, symbolic number abilities may be directly linked to, perhaps even rooted in, numerical approximation abilities. On the other hand, the relationship between the two systems may simply reflect their independent relationships with visual abilities. To test this possibility, we asked whether approximate number and symbolic math abilities are linked in congenitally blind individuals who have never experienced visual sets or used visual strategies to learn math. Congenitally blind and blind-folded sighted participants completed an auditory numerical approximation task, as well as a symbolic arithmetic task and non-math control tasks. We found that the precision of approximate number representations was identical across congenitally blind and sighted groups, suggesting that the development of the Approximate Number System (ANS) does not depend on visual experience. Crucially, the relationship between numerical approximation and symbolic math abilities is preserved in congenitally blind individuals. These data support the idea that the Approximate Number System and symbolic number abilities are intrinsically linked, rather than indirectly linked through visual abilities.

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Section: Introductionmentioning

confidence: 90%

Numerical cognition is resilient to dramatic changes in early sensory experience

2018

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“…Better performance on this task has been found to be associated with higher mathematical competencies (Elliott, Feigenson, Halberda, & Libertus, 2019; Hawes, Nosworthy, Archibald, & Ansari, 2019; M. Schneider et al, 2017), even in older populations with higher achievement (J. Wang, Halberda, & Feigenson, 2017).…”

Section: Application Of the Tad Framework To Different Achievement Domentioning

confidence: 99%

“…Cardinality processing is typically assessed by means of number comparison tasks, in which children have to choose the larger of two numbers (presented either as Arabic digits or dot patterns). Better performance on this task has been found to be associated with higher mathematical competencies (Elliott, Feigenson, Halberda, & Libertus, 2019;Hawes, Nosworthy, Archibald, & Ansari, 2019;, even in older populations with higher achievement (Wang, Halberda, & Feigenson, 2017). The processing of ordinality information has been tested frequently by asking participants whether number triplets are in order (ascending or descending) or not.…”

Section: Mathematicsmentioning

confidence: 99%

Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research

Preckel

Golle

Grabner

et al. 2020

Perspect Psychol Sci

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Achievement in different domains, such as academics, music, or visual arts, plays a central role in all modern societies. Different psychological models aim to describe and explain achievement and its development in different domains. However, there remains a need for a framework that guides empirical research within and across different domains. With the talent-development-in-achievement-domains (TAD) framework, we provide a general talent-development framework applicable to a wide range of achievement domains. The overarching aim of this framework is to support empirical research by focusing on measurable psychological constructs and their meaning at different levels of talent development. Furthermore, the TAD framework can be used for constructing domain-specific talent-development models. With examples for the application of the TAD framework to the domains of mathematics, music, and visual arts, the review provided supports the suitability of the TAD framework for domain-specific model construction and indicates numerous research gaps and open questions that should be addressed in future research.

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“…There is also substantial evidence for a link between number sense and symbolic numerical abilities in typically developing populations. Many studies indicate that performance on the nonsymbolic number comparison task is related to earlier, concurrent, and later mathematics achievement in the typically developing range of mathematical abilities, a correlation that holds even among students gifted in mathematics and across development . Meta‐analyses estimate the effect size of the correlation to be around r = 0.20 ( k = 36) when considering only cross‐sectional correlations, or r = 0.24 ( k = 195) across cross‐sectional and longitudinal relations .…”

Section: The Case For a Link Between Number Sense And Symbolic Numerimentioning

confidence: 99%

Challenging the neurobiological link between number sense and symbolic numerical abilities

Wilkey

Ansari

2019

Annals of the New York Academy of Sciences

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A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

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Approximate number sense correlates with math performance in gifted adolescents

Cited by 30 publications

References 64 publications

Numerical cognition is resilient to dramatic changes in early sensory experience

Numerical cognition is resilient to dramatic changes in early sensory experience

Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research

Challenging the neurobiological link between number sense and symbolic numerical abilities

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