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.

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.

The Approximate Number System is not Predictive for Symbolic Number Processing in Kindergarteners

2014 ◽  
Vol 67 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Delphine Sasanguie ◽  
Emmy Defever ◽  
Bieke Maertens ◽  
Bert Reynvoet
Keyword(s):  
Number System ◽  
Number Processing ◽  
Approximate Number System ◽  
Symbolic Number

scholarly journals Developmental Change of Approximate Number System Acuity (Keenness) Reveals Delay

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Tayyaba Abid ◽  
Saeeda Khanum
Keyword(s):  
Number Sense ◽  
Developmental Change ◽  
Number System ◽  
Mathematics Performance ◽  
School Mathematics ◽  
Approximate Number System ◽  
Western Population ◽  
Cultural Variations ◽  
Numerical Acuity

The ability to process numbers approximately also called, approximate number system (ANS) is related and predictive of school mathematics performance. This system is functional since birth and continue to become more precise throughout the development. Developmental change of approximate number system over the growing years has not been investigated in Pakistan so the current study bridged this gap by investigating it from 261 participants ranging from 5 to 72 years of age. Panamath task being the robust measure of ANS acuity was administered. Results revealed that numerical acuity got precise with an increase in age. However, most sophisticated acuity has been shown around age 46-50 as compared to the western population showing its peak around 30 years of age. Delay in developing approximate number system acuity across the groups as compared to the trend reported in the western population raises many questions in terms of cultural variations and practices contributing to the development of number sense. The study has important implications for the development of number sense cross-culturally keeping in view the evidence from various cultures.

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 The relationship between children’s approximate number certainty and symbolic mathematics

2020 ◽  
Vol 6 (1) ◽  
pp. 50-65
Author(s):  
Carolyn Baer ◽  
Darko Odic
Keyword(s):  
Large Body ◽  
Number System ◽  
Math Performance ◽  
Approximate Number System ◽  
Mathematical Skills ◽  
Math Ability ◽  
Positive Correlations ◽  
Number Perception ◽  
The Relationship ◽  
Symbolic Number

Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.

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.

Relationships between approximate number system acuity and early symbolic number abilities

2012 ◽  
Vol 1 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Christophe Mussolin ◽  
Julie Nys ◽  
Jacqueline Leybaert ◽  
Alain Content
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Symbolic Number

scholarly journals Non-Symbolic Numerosity and Symbolic Numbers are not Processed Intuitively in Children: Evidence From an Event-Related Potential Study

2021 ◽  
Vol 6 ◽  
Author(s):  
Anne H. van Hoogmoed ◽  
Marije D. E. Huijsmans ◽  
Evelyn H. Kroesbergen
Keyword(s):  
Number System ◽  
Number Processing ◽  
Event Related Potential ◽  
Visual Features ◽  
Approximate Number System ◽  
Match To Sample ◽  
Potential Study ◽  
Symbolic Number

The approximate number system (ANS) theory and the ANS mapping account have been the most prominent theories on non-symbolic numerosity processing and symbolic number processing respectively, over the last 20 years. Recently, there is a growing debate about these theories, mainly based on research in adults. However, whether the ANS theory and ANS mapping account explain the processing of non-symbolic numerosity and symbolic number in childhood has received little attention. In the current ERP study, we first examined whether non-symbolic numerosity processing in 9-to-12-year-old children (N = 34) is intuitive, as proposed by the ANS theory. Second, we examined whether symbolic number processing is rooted in non-symbolic numerosity processing, as proposed the ANS mapping account. ERPs were measured during four same-different match-to-sample tasks with non-symbolic numerosities, symbolic numbers, and combinations of both. We found no evidence for intuitive processing of non-symbolic numerosity. Instead, children processed the visual features of non-symbolic stimuli more automatically than the numerosity itself. Moreover, children do not seem to automatically activate non-symbolic numerosity when processing symbolic numbers. These results challenge the ANS theory and ANS mapping account in 9-to-12-year-old children.

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