The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

Libertus, Melissa E.; Odic, Darko; Feigenson, Lisa; Halberda, Justin

doi:10.1016/j.jecp.2016.06.003

Cited by 64 publications

(66 citation statements)

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“…Previous studies found that large quantities are likely to be underestimated (Izard & Dehaene, 2008; Krueger, 1982, 1984; Libertus et al., 2016; Odic et al., 2015). We replicate this underestimation bias in the behavioral nonsymbolic number estimation task.…”

Section: Discussionmentioning

confidence: 99%

“…The reference dot quantity either contained 25, 30, or 39 dots, which correspondingly induced overestimation, linear‐like estimation, and underestimation in participants' performance (Izard & Dehaene, 2008). Third, there are individual differences in the underestimation bias in adults (Izard & Dehaene, 2008; Odic et al., 2015) and young children who have acquired symbolic number knowledge (Libertus, Odic, Feigenson, & Halberda, 2016). Altogether, these behavioral findings suggest that people are able to map between the ANS and SNS, but that this mapping is not precise and is subject to a systematic underestimation bias.…”

Section: Introductionmentioning

confidence: 99%

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The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

et al. 2018

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IntroductionAdults can represent numerical information in nonsymbolic and symbolic formats and flexibly switch between the two. While some studies suggest a strong link between the two number representation systems (e.g., Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004 Neuron, 44(3), 547), other studies show evidence against the strong‐link hypothesis (e.g., Lyons, Ansari, & Beilock, 2012 Journal of Experimental Psychology: General, 141(4), 635). This inconsistency could arise from the relation between task demands and the closeness of the link between the two number systems.MethodsWe used a passive viewing task and event‐related potentials (ERP) to examine the temporal dynamics of the implicit integration between the nonsymbolic and symbolic systems. We focused on two ERP components over posterior scalp sites that were found to be sensitive to numerical distances and ratio differences in both numerical formats: a negative component that peaks around 170 ms poststimulus (N1) and a positive component that peaks around 200 ms poststimulus (P2p). We examined adults' (n = 55) ERPs when they were passively viewing simultaneously presented dot quantities and Arabic numerals (i.e., nonsymbolic and symbolic numerical information) in the double‐digit range. For each stimulus, the nonsymbolic and symbolic content either matched or mismatched in number. We also asked each participant to estimate dot quantities in a separate behavioral task and observed that they tended to underestimate the actual dot quantities, suggesting a need to adjust the match between nonsymbolic and symbolic information to reflect the perceived quantity of the nonsymbolic information.ResultsUsing this adjustment, participants showed greater N1 and P2p amplitudes when perceived dot quantities matched Arabic numerals than when there was a mismatch. However, no differences were found between the unadjusted match and mismatch conditions.ConclusionOur findings suggest that adults rapidly integrate nonsymbolic and symbolic formats of double‐digit numbers, but evidence of such integration is best observed when the perceived (rather than veridical) dot quantity is considered.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

et al. 2018

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“…Figure shows an example of dot arrays from the Panamath instrument. Developed by Halberda and colleagues, this instrument is widely used by neuropsychologists to index students' ANS acuity for non‐symbolic numerical comparison tasks (e.g., Halberda et al, ; Libertus, Odic, Feigenson, & Halberda, ; Price, Palmer, Battista, & Ansari, ) and has demonstrated inter‐test reliability across other ANS assessments (DeWind & Brannon, ). The Panamath was reliable with a Cronbach's alpha of 0.97 for the sample population.…”

Section: Methodsmentioning

confidence: 99%

“…The Panamath, designed to index students' ANS acuity, was scored for accuracy. While there has been considerable debate about the scoring mechanisms employed for indexing ANS acuity (Libertus et al, ; Price et al, ), Inglis and Gilmore () found that accuracy (the number of correct responses) was an adequate means of indexing the measure. Students earned one point for selecting the color of dots (blue or yellow) that were more numerous and earned zero points for selecting the incorrect color.…”

Section: Methodsmentioning

confidence: 99%

Next generation crosscutting themes: Factors that contribute to students' understandings of size and scale

et al. 2018

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This study examined the degree to which individual differences in students' (N = 232) concepts of size and scale are explained by factors such as students' innate sense of number, out‐of‐school science experiences, exposure to size and scale instruction, gender identities, and racial/ethnic identities. There is increasing emphasis being placed on the use of crosscutting concepts to promote deep learning in science. A multiple linear regression indicated students' racial/ethnic identities, experiences with scale outside of school, and exposure to size and scale instruction significantly added to the prediction model. Results from this study can both inform the movement toward incorporating crosscutting concepts into pedagogy as well as inform educators, administrators, and other stakeholders of the factors that may shape students' understanding of the cross‐cutting concept of scale, proportion, and quantity.

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“…Further, according to the mapping account, the ability to translate between ANS and SNS representations would be seen as the progress through which symbolic numerals are being affixed on ANS representations (e.g., Libertus, 2015;Libertus, Odic, Feigenson, & Halberda, 2016). The mapping account would view tasks that involve solely the SNS (e.g., symbolic number comparison) and tasks that invoke both ANS and SNS (e.g., mixed-format comparison) similarlythat is, both tasks would draw on the semantic knowledge afforded by the ANS and performance would be dependent on the quality of the mapping between the SNS and ANS.…”

Section: The Mapping Accountmentioning

confidence: 99%

Kindergarteners’ Symbolic Number Abilities Predict Non-Symbolic Number Abilities and Math Achievement in Grade 1

Lau¹,

Merkley²,

Tremblay³

et al. 2019

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Research has shown that two different, though related ways of representing magnitude play foundational roles in the learning of classroom math abilities: a non-verbal, approximate number system (ANS) and an exact, symbolic number system (SNS). While there have been a multitude of studies suggesting that the ANS and SNS are important predictors of math achievement (MA), there has recently been substantial debate regarding whether and how these basic numerical competencies may be developmentally interrelated. Specifically, there has been discussion on whether children’s ANS abilities predict later SNS abilities (the mapping account) or children’s SNS abilities predict later ANS abilities (the parallel development account). We modelled and contrasted multiple theoretical predictions posited by these two developmental accounts using multiple longitudinal path models. Our sample included 622 kindergarten children (M = 62 months, SD = 3.5), whose ANS, SNS and mixed-comparison skills were assessed over three time points and MA assessed over four time points. Results were most consistent with the parallel development account, suggesting that earlier SNS abilities are consistently the strongest predictor of ANS abilities, mixed-comparison abilities, and MA. Notably, our results demonstrated that, when individual models are examined in isolation, model fit either reached or approached adequate fit for all models tested. This highlights the need for future research to contrast competing accounts, as our results suggest that the examination of any one account in isolation may lead to misleading theoretical conclusions. In sum, our results are consistent with the view that children’s SNS abilities predicts later ANS abilities.

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The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

Cited by 64 publications

References 95 publications

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

Next generation crosscutting themes: Factors that contribute to students' understandings of size and scale

Kindergarteners’ Symbolic Number Abilities Predict Non-Symbolic Number Abilities and Math Achievement in Grade 1

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