Variability signatures distinguish verbal from nonverbal counting for both large and small numbers

Cordes, Sara; Gelman, Rochel; Gallistel, C. R.; Whalen, J.

doi:10.3758/bf03196206

Cited by 382 publications

(399 citation statements)

References 38 publications

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“…Our two most important results were that (1) children cannot estimate the numerical size of sets beyond 4 without counting until 6 months after they have become cardinal-principle knowers (i.e., have mastered all of the counting principles) and (2) errors of application of "one" to "four" in estimation tasks do not show the noise signature of the analog magnitude system. We were eager to read Gallistel's thoughts on these data, for we obtained them with tasks and analyses that were modeled after his excellent studies of the mapping between numerals and analog magnitudes in adults (Cordes, Gelman, Gallistel, & Whalen, 2001;Whalen, Gallistel, & Gelman, 1999). Thus, we were greatly disappointed that he did not engage any part of our findings in his commentary, especially since they undermine the hypothesis he favors.…”

Section: The Nature Of Our Questions and The Logic Of Our Methodsmentioning

confidence: 99%

Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel

Corre

Carey

2008

Cognition

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Section: The Nature Of Our Questions and The Logic Of Our Methodsmentioning

confidence: 99%

Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel

Corre

Carey

2008

Cognition

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“…For example, if the magnitude of the ratio is large, for example, four dots versus eight dots (1:2 ratio), responses tend to be fast and precise, which indicates that a large ratio makes the comparison easy. If the magnitude of the ratio is small, for example, 15 dots versus 16 dots (15:16 ratio), responses tend to be slower than in the easy ratio condition, and the accuracy is typically lower (Barth, et al., 2003; Cordes, Gelman, Gallistel, & Whalen, 2001; Pica, Lemer, Izard, & Dehaene, 2004), indicating harder comparison. Converging evidence from developmental and comparative studies as well as studies with people whose languages do not have number words shows ratio‐dependent performance on nonsymbolic number comparison tasks suggesting a key feature of the ANS: independence from language (Cantlon, Brannon, Carter, & Pelphrey, 2006; Izard, Sann, Spelke, & Streri, 2009; Libertus and Brannon, 2009; Lipton & Spelke, 2003; Nieder, 2009; Pica et al., 2004; Xu & Spelke, 2000).…”

Section: Introductionmentioning

confidence: 99%

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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“…Further, unlike PI, AM places no upper limit on the size of sets that can be represented, and represents each set with a single magnitude. The ratio-limit signature of AM representations has been found in human adults, infants, rats, and various other species (Barth, Kanwisher, & Spelke, 2003;Brannon, Abbott, & Lutz, 2004;Brannon & Terrace, 1998;Brannon & Terrace, 2000;Cantlon & Brannon, 2006;Cordes, Gelman, & Gallistel, 2002;Gallistel, 1990;McCrink & Wynn, 2004;Platt & Johnson, 1971;Shettleworth, 1998;Whalen, Gallistel, & Gelman, 1999;Xu, 2003;Xu & Spelke, 2000;Xu, Spelke, & Goddard, 2005). Several studies document AM representations in rhesus monkeys (Brannon & Terrace, 1998, 2000Cantlon & Brannon, 2006;Flombaum, Junge, & Hauser, 2005).…”

Section: Introductionmentioning

confidence: 98%

“…the ratio between them (see Cordes, Gelman, Gallistel, & Whalen, 2001;Dehaene, 1997;Gallistel, 1990). Further, unlike PI, AM places no upper limit on the size of sets that can be represented, and represents each set with a single magnitude.…”

Section: Introductionmentioning

confidence: 99%

Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys

et al. 2008

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Set representations are explicitly expressed in natural language. For example, many languages distinguish between sets and subsets (all vs. some), as well as between singular and plural sets (a cat vs. some cats). Three experiments explored the hypothesis that these representations are language specific, and thus absent from the conceptual resources of non-linguistic animals. We found that rhesus monkeys spontaneously discriminate sets based on a conceptual singularplural distinction. Under conditions that do not elicit comparisons based on approximate magnitudes or one-to-one correspondence, rhesus monkeys distinguished between singular and plural sets (1 vs. 2 and 1 vs. 5), but not between two plural sets (2 vs. 3, 2 vs. 4, and 2 vs. 5).These results suggest hat set-relational distinctions are not a privileged part of natural language, and may have evolved in non-linguistic species to support domain general quantitative computations.3

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Variability signatures distinguish verbal from nonverbal counting for both large and small numbers

Cited by 382 publications

References 38 publications

Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel

Why the verbal counting principles are constructed out of representations of small sets of individuals: A reply to Gallistel

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

Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys

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