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 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 Ontogenetic origins of human integer representations

2019 ◽  
Author(s):  
Susan Carey ◽  
David Barner
Keyword(s):  
Number Word ◽  
Second Phase ◽  
Word Meanings ◽  
Hume’S Principle ◽  
Number Words ◽  
Number Representations ◽  
Exact Counting ◽  
Counting Algorithms ◽  
Numerical Magnitudes ◽  
Two Phases

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children’s understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume’s principle (that 1-to-1 correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.

Spatial–numerical associations: Shared symbolic and non-symbolic numerical representations

2019 ◽  
Vol 72 (10) ◽  
pp. 2423-2436 ◽  
Author(s):  
Stefan Buijsman ◽  
Carlos Tirado
Keyword(s):  
Theoretical Perspective ◽  
Number System ◽  
Snarc Effect ◽  
Approximate Number System ◽  
Symbolic Processing ◽  
Shared Representations ◽  
Theoretical Perspectives ◽  
Number Representations ◽  
Neuroimaging Data ◽  
Numerical Representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial–numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

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

Mechanisms Underlying Transfer from Domain-Specific and Domain-General Cognitive Training to Children’s Math Skills

2021 ◽  
Author(s):  
Andrew David Ribner ◽  
Melissa Libertus
Keyword(s):  
Math Achievement ◽  
Skill Training ◽  
Later Life ◽  
Number System ◽  
Approximate Number System ◽  
Life Outcomes ◽  
Math Skills ◽  
Domain Specific ◽  
Number Representations ◽  
Symbolic Number

Math achievement is one of the strongest predictors of later life outcomes, and much of what comprises later math is decided by the time children enter kindergarten. Individual differences in precision of approximate representations of number and mapping between non-symbolic and symbolic number representations predict math achievement and honing these representations improves math skills. The goal of this registered report is to disentangle potential mechanisms of transfer. Approximately 324 preschool-aged children will be assigned to one of three, 5-week computerized, teacher-facilitated training conditions to target their approximate number system, symbolic number skills, and executive function to better understand whether changes in approximate number system acuity, mapping between number representations, or attention to number underlie successful transfer of skill training.

Ordinal structure of the symbolic number system mediates refinement of the approximate number system

2020 ◽  
Author(s):  
Christian Peake ◽  
Carolina Briones ◽  
Cristina Rodríguez
Keyword(s):  
Developmental Psychology ◽  
Number System ◽  
First Year ◽  
Approximate Number System ◽  
Parallel Development ◽  
School Year ◽  
System P ◽  
Underlying Mechanisms ◽  
The Relationship ◽  
Symbolic Number

Interest in the relationship between the Approximate Number System (ANS, an early cognitive system to process non-symbolic quantities) and the Symbolic Number System (SNS, learned through instruction or intense exposure) is currently growing among researchers in developmental psychology. This research contrasted the two main hypotheses regarding the issue: the traditional mapping account, which states that the ANS underlies the learning of numerical symbols; and the parallel development account, which argues that the SNS develops independently from the ANS and, in fact, serves to refine it during mapping between them, as the ANS is approximate in nature. Moreover, this study focused on the underlying mechanisms that mediate the relationship between the ANS and the SNS. A sample of 200 children in first year of preschool (4 to 5 years old) were followed over the course of the school year. Symbolic and non-symbolic comparison tasks and estimation tasks where applied at the beginning (T1) and end (T2) of the school year. A cardinality task was administered at T1 and an ordinality task at T2. This allowed us to run two serial multiple mediator models to test both hypotheses with multiple longitudinal mediators. Results showed a bidirectional causal relationship between the ANS and the SNS that was interpreted as supporting the parallel development account. Importantly, ordinality mediated the relationship between the SNS at T1 and the ANS at T2, even when controlling for the development of translation skills from the SNS to the ANS and cardinality. This is the first evidence that knowledge of the relationship between number symbols, addressed in terms of their ordinal structure, is the cognitive mechanism that underlies the refinement of the ANS. As such, it supports the idea that the two systems develop independently, although they may impact each other at early stages of learning.

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).

Number Representations and their Relation with Mathematical Ability

2014 ◽  
Author(s):  
Titia Gebuis ◽  
Bert Reynvoet
Keyword(s):  
Number System ◽  
Neural Representation ◽  
Approximate Number System ◽  
Developmental Models ◽  
Domain Specific ◽  
Mathematical Abilities ◽  
Number Representations ◽  
The One ◽  
Insight Into ◽  
Symbolic Number

In this chapter we review research on the processes that underlie the development of mathematical abilities. It is proposed that numerical deficiencies might arise from domain specific problems. The approximate number system that supports reasoning with non-symbolic numbers, on the one hand, and the symbolic number system on the other hand were put forth as possible candidates. To gain insight into the two different systems, we will describe the development of non-symbolic and symbolic number processing and introduce the two main theories about numerical deficiencies: the approximate number system and the access deficit hypothesis. The paradigms used to study both accounts differ in several ways and are of importance for research on the relation between non-symbolic and symbolic number and mathematical abilities. Then, we will review how the studies investigating both accounts relate to two different sets of developmental models that describe the neural representation of number.

scholarly journals Neural basis of approximate number system develops independent of visual experience

2019 ◽  
Author(s):  
Shipra Kanjlia ◽  
Lisa Feigenson ◽  
Marina Bedny
Keyword(s):  
Visual Experience ◽  
Human Life ◽  
Number System ◽  
Approximate Number System ◽  
Neural Basis ◽  
Neuronal Populations ◽  
Number Representations ◽  
Population Codes ◽  
Congenitally Blind ◽  
Blind Individuals

AbstractThinking about numerical quantities is an integral part of daily human life that is supported by the intraparietal sulcus (IPS). The IPS is recruited during mathematical calculation and neuronal populations within the IPS code for the quantity of items in a set. Is the developmental basis of IPS number representations rooted in visual experience? We asked if the IPS possesses population codes for auditory quantities in sighted individuals and, critically, whether it does in the absence of any visual experience in congenitally blind individuals. We found that sequences of 4, 8, 16 and 32 tones each elicited unique patterns of fMRI activity in the IPS of both sighted and congenitally blind individuals, such that the quantity a participant heard on a given trial could be reliably predicted based on the pattern of observed IPS activity. This finding suggests that the IPS number system is resilient to dramatic changes in sensory experience.

scholarly journals Grammatical morphology as a source of early number word meanings

2013 ◽  
Vol 110 (46) ◽  
pp. 18448-18453 ◽  
Author(s):  
A. Almoammer ◽  
J. Sullivan ◽  
C. Donlan ◽  
F. Marusic ◽  
R. Zaucer ◽  
...  
Keyword(s):  
Number Word ◽  
Word Meanings ◽  
Grammatical Morphology ◽  
Early Number
Sign in / Sign up

Export Citation Format

Share Document