Certainty in Numerical Judgments Develops Independently of the Approximate Number System

2019 ◽  
Author(s):  
Carolyn Baer ◽  
Darko Odic
Keyword(s):  
Recent Work ◽  
Number System ◽  
Approximate Number System ◽  
Older Children ◽  
Perceptual Features ◽  
General Ability ◽  
Number Discrimination ◽  
Age Related ◽  
System P ◽  
Child Friendly

Recent work has shown that the precision with which children reason about their ANS certainty improves with age: when making simple number discrimination decisions, like deciding whether there are more blue or yellow dots on the screen, older children are better able to differentiate trials that they answered correctly vs. incorrectly. Here, in two experiments, we examine whether the age-related improvement in ANS certainty is accounted for by children’s: (1) increasing ability to properly “calibrate” their certainty judgements (i.e., a reduction in over-confidence with age); (2) improving precision of the ANS representations themselves; and/or (3) the improvement of children’s ability to represent and reason about certainty in general. By testing children in a child-friendly “relative” certainty task, we find that 3-7 year-olds’ (N = 161) certainty in their ANS decisions develops independently of both ANS acuity and calibration abilities. These results hold even when non-numeric perceptual features, such as the density and cumulative area, are controlled for. We discuss these results in a broader context of children’s general ability to reason about certainty and confidence.

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.

scholarly journals Attentional bias induced by stimulus control (ABC) impairs measures of the approximate number system

2021 ◽  
Author(s):  
Marcus Lindskog ◽  
Leo Poom ◽  
Anders Winman
Keyword(s):  
Attentional Bias ◽  
Stimulus Control ◽  
Number System ◽  
Approximate Number System ◽  
Math Ability ◽  
Overt Attention ◽  
Number Discrimination ◽  
Presentation Time ◽  
Item Size ◽  
Individual Size

AbstractPervasive congruency effects characterize approximate number discrimination tasks. Performance is better on congruent (the more numerous stimulus consists of objects of larger size that occupy a larger area) than on incongruent (where the opposite holds) items. The congruency effects typically occur when controlling for nonnumeric variables such as cumulative area. Furthermore, only performance on incongruent stimuli seems to predict math abilities. Here, we present evidence for an attentional-bias induced by stimulus control (ABC) where preattentive features such as item size reflexively influence decisions, which can explain these congruency effects. In three experiments, we tested predictions derived from the ABC. In Experiment 1, as predicted, we found that manipulation of size introduced congruency effects and eliminated the correlation with math ability for congruent items. However, performance on incongruent items and neutral, nonmanipulated items were still predictive of math ability. A negative correlation between performance on congruent and incongruent items even indicated that they measure different underlying constructs. Experiment 2 demonstrated, in line with the ABC account, that increasing presentation time reduced congruency effects. By directly measuring overt attention using eye-tracking, Experiment 3 revealed that people direct their first gaze toward the array with items of larger individual size, biasing them towards these arrays. The ABC explains why the relation between performance on approximate number discrimination tasks and math achievement has been fragile and suggests that stimulus control manipulations have contaminated the results. We discuss the importance of using stimuli that are representative of the environment.

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 Structure and Implementation of Novel Task Rules: A Cross-Sectional Developmental Study

2018 ◽  
Vol 29 (7) ◽  
pp. 1113-1125 ◽  
Author(s):  
Frederick Verbruggen ◽  
Rossy McLaren ◽  
Maayan Pereg ◽  
Nachshon Meiran
Keyword(s):  
Developmental Study ◽  
Late Adolescents ◽  
Older Children ◽  
Learning And Development ◽  
Cross Sectional ◽  
Rule Based ◽  
Stimulus Response ◽  
Task Instructions ◽  
Age Related ◽  
Child Friendly

Rule-based performance improves remarkably throughout childhood. The present study examined how children and adolescents structured tasks and implemented rules when novel task instructions were presented in a child-friendly version of a novel instruction-learning paradigm. Each miniblock started with the presentation of new stimulus-response mappings for a go task. Before this mapping could be implemented, subjects had to make responses in order to advance through screens during a preparatory (“ next”) phase. Children (4–11 years old) and late adolescents (17–19 years old) responded more slowly during the next phase when the next response was incompatible with the instructed stimulus-response mapping. This instruction-based interference effect was more pronounced in young children than in older children. We argue that these findings are most consistent with age-related differences in rule structuring. We discuss the implications of our findings for theories of rule-based performance, instruction-based learning, and development.

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.

“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

scholarly journals Perceptual decision-making in children: Age-related differences and EEG correlates

2020 ◽  
Author(s):  
Catherine Manning ◽  
Eric-Jan Wagenmakers ◽  
Anthony Norcia ◽  
Gaia Scerif ◽  
Udo Boehm
Keyword(s):  
Decision Making ◽  
Drift Rate ◽  
Decision Time ◽  
Diffusion Models ◽  
Perceptual Task ◽  
Model Parameters ◽  
Older Children ◽  
Perceptual Decision Making ◽  
Boundary Separation ◽  
Age Related

Children make faster and more accurate decisions about perceptual information as they get older, but it is unclear how different aspects of the decision-making process change with age. Here, we used hierarchical Bayesian diffusion models to decompose performance in a perceptual task into separate processing components, testing age-related differences in model parameters and links to neural data. We collected behavioural and EEG data from 96 six- to twelve-year-olds and 20 adults completing a motion discrimination task. We used a component decomposition technique to identify two response-locked EEG components with ramping activity preceding the response in children and adults: one with activity that was maximal over centro-parietal electrodes and one that was maximal over occipital electrodes. Younger children had lower drift rates (reduced sensitivity), wider boundary separation (increased response caution) and longer non-decision times than older children and adults. Yet model comparisons suggested that the best model of children’s data included age effects only on drift rate and boundary separation (not non-decision time). Next we extracted the slope of ramping activity in our EEG components and covaried these with drift rate. The slopes of both EEG components related positively to drift rate, but the best model with EEG covariates included only the centro-parietal component. By decomposing performance into distinct components and relating them to neural markers, diffusion models have the potential to identify the reasons why children with developmental conditions perform differently to typically developing children - and to uncover processing differences inapparent in the response time and accuracy data alone.

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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