Children’s mappings between number words and the approximate number system

Cognition ◽  
2015 ◽  
Vol 138 ◽  
pp. 102-121 ◽  
Author(s):  
Darko Odic ◽  
Mathieu Le Corre ◽  
Justin Halberda
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Words

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.

scholarly journals Estimation as analogy-making: Evidence that preschoolers’ analogical reasoning ability predicts their numerical estimation

2020 ◽  
Author(s):  
Joseph Alvarez ◽  
Monica Abdul-Chani ◽  
Paul Michael Deutchman ◽  
Kayla Dibiasie ◽  
Julia Iannucci ◽  
...  
Keyword(s):  
Cognitive Skills ◽  
Analogical Reasoning ◽  
Number System ◽  
Reasoning Ability ◽  
Approximate Number System ◽  
Numerical Estimation ◽  
Structure Mapping ◽  
Number Words ◽  
Number Systems ◽  
Linguistic Representations

All humans and many animals can represent approximate quantities of perceptual objects nonlinguistically by using the Approximate Number System (Dehaene, 1997/2011). Early in life, children in numerate societies also learn to describe this system using number words. How do linguistic representations of number become related to nonlinguistic representations of number? We hypothesize that the analogical process of structure mapping (Gentner, 1983) helps children to form mappings between the linguistic and nonlinguistic number systems on the basis of structural similarities between the two systems. To test this, we tested and analyzed 47 four-and-five year olds’ performance on estimation and analogy tasks. We found that analogical reasoning ability uniquely predicted several components of estimation performance, even when controlling for other domain-general cognitive skills. This provides strong evidence that analogical processes are uniquely related to the development of early estimation.

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

2016 ◽  
Vol 150 ◽  
pp. 207-226 ◽  
Author(s):  
Melissa E. Libertus ◽  
Darko Odic ◽  
Lisa Feigenson ◽  
Justin Halberda
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Words

scholarly journals Can you trust your number sense: Distinct processing of numbers and quantities in elementary school children

2020 ◽  
Vol 6 (3) ◽  
pp. 304-321
Author(s):  
Mila Marinova ◽  
Bert Reynvoet
Keyword(s):  
Elementary School Children ◽  
Developmental Change ◽  
Semantic Network ◽  
Number System ◽  
Early Age ◽  
Approximate Number System ◽  
Number Range ◽  
Number Words ◽  
Developmental Growth ◽  
Symbolic Number

Theories of number development have traditionally argued that the acquisition and discrimination of symbolic numbers (i.e., number words and digits) are grounded in and are continuously supported by the Approximate Number System (ANS)—an evolutionarily ancient system for number. In the current study, we challenge this claim by investigating whether the ANS continues to support the symbolic number processing throughout development. To this end, we tested 87 first- (Age M = 6.54 years, SD = 0.58), third- (Age M = 8.55 years, SD = 0.60) and fifth-graders (Age M = 10.63 years, SD = 0.67) on four audio-visual comparison tasks (1) Number words–Digits, (2) Tones–Dots, (3) Number words–Dots, (4) Tones–Digits, while varying the Number Range (Small and Large), and the Numerical Ratio (Easy, Medium, and Hard). Results showed that larger and faster developmental growth in the performance was observed in the Number Words–Digits task, while the tasks containing at least one non-symbolic quantity showed smaller and slower developmental change. In addition, the Ratio effect (i.e., the signature of ANS being addressed) was present in the Tones–Dots, Tones–Digits, and Number Words–Dots tasks, but was absent in the Number Words–Digits task. These findings suggest that it is unlikely that the ANS continuously underlines the acquisition and the discrimination of the symbolic numbers. Rather, our results indicate that non-symbolic quantities and symbolic numbers follow qualitatively distinct developmental paths, and argue that the latter ones are processed in a semantic network which starts to emerge from an early age.

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

Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge

2017 ◽  
Vol 29 (2) ◽  
pp. 191-205 ◽  
Author(s):  
David C. Geary ◽  
Kristy vanMarle ◽  
Felicia W. Chu ◽  
Jeffrey Rouder ◽  
Mary K. Hoard ◽  
...  
Keyword(s):  
Reading Achievement ◽  
School Readiness ◽  
Conceptual Understanding ◽  
Parental Education ◽  
First Grade ◽  
Number System ◽  
School Entry ◽  
Number Words ◽  
Education Levels ◽  
System Knowledge

We demonstrate a link between preschoolers’ quantitative competencies and their school-entry knowledge of the relations among numbers (number-system knowledge). The quantitative competencies of 141 children (69 boys) were assessed at the beginning of preschool and throughout the next 2 years of preschool, as was their mathematics and reading achievement at the end of kindergarten and their number-system knowledge at the beginning of first grade. A combination of Bayes analyses and standard regressions revealed that the age at which the children had the conceptual insight that number words represent specific quantities (cardinal value) was strongly related to their later number-system knowledge and was more consistently related to broader mathematics than to reading achievement, controlling for intelligence, executive function, and parental education levels. The key implication is that it is not simply knowledge of cardinal value but the age of acquisition of this principle that is central to later mathematical development and school readiness.

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
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