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.

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.

scholarly journals Approximate number system task performance: Associations with domain-general and domain-specific cognitive skills in young children

2018 ◽  
Vol 4 (3) ◽  
pp. 590-612 ◽  
Author(s):  
Mary Wagner Fuhs ◽  
Kimberly Turner Nesbitt ◽  
Connor D. O’Rear
Keyword(s):  
Cognitive Skills ◽  
Visual Cues ◽  
Number System ◽  
Approximate Number System ◽  
Early Environment ◽  
Developmental Models ◽  
General Ability ◽  
Domain Specific ◽  
Research Findings ◽  
System Task

We investigated the associations between young children’s domain-general executive functioning (EF) skills and domain-specific spontaneous focusing on number (SFON) tendencies and their performance on an approximate number system (ANS) task, paying particular attention to variations in associations across different trial types with either congruent or incongruent non-numerical continuous visual cues. We found that children’s EF skills were strongly related to their performance on ANS task trials in which continuous visual cues were incongruent with numerosity. Novel to the current study, we found that children’s SFON tendencies were specifically related to their performance on ANS task trials in which continuous visual cues were congruent with numerosity. Children’s performance on ANS task trials in which children can use both congruent numerical and non-numerical continuous visual cues to approximate large quantities may be related to their unprompted tendency to focus on number in their early environment when there are not salient distractors present. On the other hand, children’s performance on incongruent ANS trials may be less a function of number-specific knowledge but more of children’s domain-general ability to inhibit salient but conflicting or irrelevant stimuli. Importantly, these effects held even when accounting for global math achievement and children’s cardinality knowledge. Overall, results support the consideration of both domain-specific and domain-general cognitive factors in developmental models of children’s early ability to attend to numerosity and provide a possible means for reconciling previous conflicting research findings.

Spontaneous Focusing on Numerosity Is Linked to Numerosity Discrimination in Children and Adults

2020 ◽  
Author(s):  
Mattan S. Ben-Shachar ◽  
Svetlana Lisson ◽  
Dalit Shotts-Peretz ◽  
Minna Hannula-Sormunen ◽  
Andrea Berger
Keyword(s):  
Number System ◽  
Fine Tuning ◽  
Developmental Pathways ◽  
Approximate Number System ◽  
Numerosity Discrimination ◽  
Stable Domain ◽  
Domain Specific ◽  
Mathematical Abilities ◽  
Academic Achievements ◽  
The Relationship

Spontaneous focusing on numerosity (SFON) is the tendency to spontaneously address exact numerosity in the environment without prompting. While previous studies have found children’s SFON to be a stable, domain-specific predictor of mathematical abilities throughout development, it is unclear whether SFON reflects individual differences in quantitative processing. This study examined the relationship between SFON and the acuity of the Approximate Number System (ANS) in children and adults. To measure adults’ SFON, we developed a numerosity bias task (NBT). In children and adults, better ANS acuity was related to higher tendency to spontaneously focus on numerosity. Additionally, in adults, SFON was related to higher mathematical academic achievements. These findings suggest an interplay between SFON and ANS acuity, indicating a mechanism where increased ANS acuity makes numerosity elements in the environment more salient, while early self-initiated numerical practice promotes fine-tuning of the ANS. Possible implications of these reciprocal developmental pathways are discussed.

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

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.

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.

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
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