Numerical ordering ability mediates the relation between number-sense and arithmetic competence

Lyons, Ian M.; Beilock, Sian L.

doi:10.1016/j.cognition.2011.07.009

Cited by 295 publications

(371 citation statements)

References 31 publications

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“…It entails counting to twenty and back or counting upwards and backwards from an arbitrary starting point (Jordan and Levine 2009;Lipton and Spelke 2005), knowing that each number occupies a fixed position in the sequence of all numbers (Griffin 2004). Counting skills underpin arithmetical competence in general (Gersten et al 2005;Passolunghi et al, 2007;Stock et al, 2010) and mental arithmetical competence in particular (Lyons and Beilock 2011).…”

Section: Systematic Countingmentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed.

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Section: Systematic Countingmentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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“…Then, when assessed on the basis of the psychophysical model (Pica et al, 2004;Barth, La Mont, Lipton, Dehaene, Kanwisher, & Spelke, 2006), w and CV evaluate the exact same characteristic, based on the scalar variability of mental number representations. Actually, measures of w and CV in Western adult samples converge on similar figures, around 0.15 (w: Inglis & Gilmore, 2013, experiment 1;Lyons & Beilock, 2011;Pica et al, 2004;CV: Castronovo & Göbel, 2012, experiments 3 & 4;Frank, Fedorenko, Lai, Saxe, & Gibson, 2012;.…”

mentioning

confidence: 71%

“…Additionally, we investigated whether w and CV were related to arithmetic performance, expecting both measures to be correlated with arithmetic scores. We also assessed symbolic number processing in order to investigate whether the two non-symbolic measures were equally associated to symbolic processing, as the latter is suspected to constitute a crucial mediator variable between non-symbolic numerosities and math ability (Lyons & Beilock, 2011). We therefore conducted an experiment in which participants received a numerical estimation task, a non-symbolic comparison task, a symbolic comparison task, and an arithmetic test.…”

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confidence: 99%

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

Guillaumé

Gevers

2015

Psychological Research

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Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate.The findings reported in the literature are actually inconsistent; some studies emphasised the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the Coefficient of Variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and nonnumerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.Abstract word count: 243 words.

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“…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).…”

Section: Price Et Al (2012) Calculated Immediate Test-retest Reliabimentioning

confidence: 99%

“…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.…”

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confidence: 99%

Indexing the approximate number system

2014

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Much recent research attention has focused on understanding individual differences in the Approximate Number System, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the Numerical Ratio Effect has poor testretest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or Numerical Ratio Effects.

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Numerical ordering ability mediates the relation between number-sense and arithmetic competence

Cited by 295 publications

References 31 publications

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

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

Indexing the approximate number system

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