scholarly journals Parallel individuation supports numerical comparisons in preschoolers (in press)

2017 ◽  
Author(s):  
Pierina Cheung
Keyword(s):  
Word Learning ◽  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Numerical Comparisons ◽  
Subject Design ◽  
Tentative Evidence ◽  
Numerical Operations

While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities (< 4) or exclusively large numerosities (> 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003).

scholarly journals Parallel individuation supports numerical comparisons in preschoolers

2018 ◽  
Vol 4 (2) ◽  
pp. 380-409 ◽  
Author(s):  
Pierina Cheung ◽  
Mathieu Le Corre
Keyword(s):  
Word Learning ◽  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Numerical Comparisons ◽  
Subject Design ◽  
Tentative Evidence ◽  
Numerical Operations

While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities (< 4) or exclusively large numerosities (> 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003; https://doi.org/10.1111/1467-7687.00313).

scholarly journals Electrophysiological Evidence for the Involvement of the Approximate Number System in Preschoolers' Processing of Spoken Number Words

2014 ◽  
Vol 26 (9) ◽  
pp. 1891-1904 ◽  
Author(s):  
Michal Pinhas ◽  
Sarah E. Donohue ◽  
Marty G. Woldorff ◽  
Elizabeth M. Brannon
Keyword(s):  
Number System ◽  
Number Word ◽  
Word Knowledge ◽  
Approximate Number System ◽  
Word Comprehension ◽  
Number Words ◽  
Visual Objects ◽  
Number Representations ◽  
Word Onset ◽  
Neural Underpinnings

Little is known about the neural underpinnings of number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3- to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory number word was incongruent with the number of visual objects on half the trials and congruent on the other half. Children's number word comprehension predicted their ERP incongruency effects. Specifically, children with the least number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high number word knowledge showed an enhanced, negative polarity incongruency response (Ninc) over centroparietal sites from 200 to 500 msec after the number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (Pinc) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most number word knowledge showed ratio dependence in the Pinc (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the Pinc from 700 to 800 msec was found in children with intermediate number word knowledge. These results provide the first neural correlates of spoken number word comprehension in preschoolers and are consistent with the view that children map number words onto approximate number representations before they fully master the verbal count list.

scholarly journals Do children's number words begin noisy?

2018 ◽  
Author(s):  
Katherine Wagner ◽  
Junyi Chu ◽  
David Barner
Keyword(s):  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Word Meanings ◽  
Number Words ◽  
System P ◽  
Number Representations ◽  
Lively Debate ◽  
Early Number ◽  
Made In

How do children acquire exact meanings for number words like three or forty-seven? In recent years, a lively debate has probed the cognitive systems that support learning, with some arguing that an evolutionarily ancient “approximate number system” drives early number word meanings, and others arguing that learning is supported chiefly by representations of small sets of discrete individuals. This debate has centered around findings generated by Wynn’s (1990, 1992) Give-a-Number task, which she used to categorize children into discrete “knower level” stages. Early reports confirmed Wynn’s analysis, and took these stages to support the “small sets” hypothesis. However, more recent studies have disputed this analysis, and have argued that Give-a-Number data reveal a strong role for approximate number representations. In the present study, we use previously collected Give-a-Number data to replicate the analyses of these past studies, and to show that differences between past studies are due to assumptions made in analyses, rather than to differences in data themselves. We also show how Give-a-Number data violate the assumptions of parametric tests used in past studies. Based on simple non-parametric tests and model simulations, we conclude that (1) before children learn exact meanings for words like one, two, three, and four, they first acquire noisy preliminary meanings for these words, (2) there is no reliable evidence of preliminary meanings for larger meanings, and (3) Give-a- Number cannot be used to readily identify signatures of the approximate number system.

Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

2020 ◽  
Vol 112 (6) ◽  
pp. 1167-1182 ◽  
Author(s):  
Stephanie A. Malone ◽  
Kelly Burgoyne ◽  
Charles Hulme
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Knowledge

“Approximate number system” training: A perceptual learning approach

2018 ◽  
Vol 81 (3) ◽  
pp. 621-636 ◽  
Author(s):  
Aaron Cochrane ◽  
Lucy Cui ◽  
Edward M. Hubbard ◽  
C. Shawn Green
Keyword(s):  
Perceptual Learning ◽  
Number System ◽  
Learning Approach ◽  
Approximate Number System

scholarly journals Compromised approximate number system acuity in extremely preterm school-aged children

2013 ◽  
Vol 55 (12) ◽  
pp. 1109-1114 ◽  
Author(s):  
Kerstin Hellgren ◽  
Justin Halberda ◽  
Lea Forsman ◽  
Ulrika Ådén ◽  
Melissa Libertus
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
School Aged Children ◽  
Extremely Preterm

Children’s Approximate Number System in Haptic Modality

Perception ◽  
2015 ◽  
Vol 45 (1-2) ◽  
pp. 44-55 ◽  
Author(s):  
Fanny Gimbert ◽  
Edouard Gentaz ◽  
Valérie Camos ◽  
Karine Mazens
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Haptic Modality

The number sense does not represent numbers, but cardinality comparisons

2021 ◽  
Vol 44 ◽  
Author(s):  
José Luis Bermúdez
Keyword(s):  
Experimental Evidence ◽  
Number Sense ◽  
Number System ◽  
Rational Numbers ◽  
Approximate Number System

Abstract Against Clarke and Beck's proposal that the approximate number system (ANS) represents natural and rational numbers, I suggest that the experimental evidence is better accommodated by the (much weaker) thesis that the ANS represents cardinality comparisons. Cardinality comparisons do not stand in arithmetical relations and being able to apply them does not involve basic arithmetical concepts and operations.

Representation of pure magnitudes in ANS

2021 ◽  
Vol 44 ◽  
Author(s):  
Steven Gross ◽  
William Kowalsky ◽  
Tyler Burge
Keyword(s):  
Number System ◽  
Approximate Number System

Abstract According to Clarke and Beck (C&B), the approximate number system (ANS) represents numbers. We argue that the ANS represents pure magnitudes. Considerations of explanatory economy favor the pure magnitudes hypothesis. The considerations C&B direct against the pure magnitudes hypothesis do not have force.

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