scholarly journals The relationship between numerosity discrimination and arithmetic skill reflects the approximate number system and cannot be explained by inhibitory control

2019 ◽  
Vol 184 ◽  
pp. 220-231 ◽  
Author(s):  
Stephanie A. Malone ◽  
Verena E. Pritchard ◽  
Michelle Heron-Delaney ◽  
Kelly Burgoyne ◽  
Arne Lervåg ◽  
...  
Keyword(s):  
Inhibitory Control ◽  
Number System ◽  
Approximate Number System ◽  
Numerosity Discrimination ◽  
Arithmetic Skill ◽  
The Relationship

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.

The Relationship Between Approximate Number System and Mathematics Competency in Indonesian Primary School Children

2018 ◽  
Vol 24 (8) ◽  
pp. 6259-6264
Author(s):  
Kevin Wijaya ◽  
Fransiskus X Ivan ◽  
Adre Mayza
Keyword(s):  
Response Time ◽  
Primary School ◽  
School Children ◽  
Weber Fraction ◽  
Number System ◽  
Primary School Children ◽  
Methodological Aspect ◽  
Approximate Number System ◽  
And Mathematics ◽  
The Relationship

The purpose of this study is to investigate the relationship between Approximate Number System (ANS), a cognitive system which represents and estimates the cardinality of a set, and mathematics competency of primary school children. Many findings on ANS and its relations with mathematics competency showed inconsistency. This research is the first of its kind in Indonesia. 318 fourth and fifth-grade primary school students were instructed to perform non-symbolic (dots) comparison task to measure their Weber fraction (w), accuracy (percentage correct), and response time (ms) which are the measurement for ANS acuity. Mathematics competencies of the students were taken from school’s report card and the data were standardized for each school separately. Correlation and regression linear analysis were conducted to find the relationship between ANS acuity and mathematics’ competency. Analysis showed there was a weak but significant (p < 0.05) correlation between two measurements of ANS acuity, namely the Weber fraction and accuracy, with mathematics competency, but not response time (p > 0.05). Further analysis with linear regression showed there was no relationship between the two variables and mathematics score, which disproves this correlation. This study shows that there is no relationship between children’s ANS acuity and mathematics competency. Intrinsic factors such as children’s attention, engagement, and motivation, also methodological aspect needed further consideration. Future studies are needed to investigate the methodological aspect related to the measurement of ANS and mathematics’ competency as there is no ‘gold standard’ yet to measure ANS.

scholarly journals Developmental differences in approaches to nonsymbolic comparison tasks

2018 ◽  
Vol 72 (3) ◽  
pp. 436-445 ◽  
Author(s):  
Sarah Clayton ◽  
Matthew Inglis ◽  
Camilla Gilmore
Keyword(s):  
Mathematics Achievement ◽  
Task Performance ◽  
Visual Information ◽  
Number System ◽  
Developmental Differences ◽  
Approximate Number System ◽  
Numerical Information ◽  
Formal Mathematics ◽  
Visual Characteristics ◽  
The Relationship

Nonsymbolic comparison tasks are widely used to measure children’s and adults’ approximate number system (ANS) acuity. Recent evidence has demonstrated that task performance can be influenced by changes to the visual characteristics of the stimuli, leading some researchers to suggest it is unlikely that an ANS exists that can extract number information independently of the visual characteristics of the arrays. Here, we analysed 124 children’s and 120 adults’ dot comparison accuracy scores from three separate studies to investigate individual and developmental differences in how numerical and visual information contribute to nonsymbolic numerosity judgements. We found that, in contrast to adults, the majority of children did not use numerical information over and above visual cue information to compare quantities. This finding was consistent across different studies. The results have implications for research on the relationship between dot comparison performance and formal mathematics achievement. Specifically, if most children’s performance on dot comparison tasks can be accounted for without the involvement of numerical information, it seems unlikely that observed correlations with mathematics achievement stem from ANS acuity alone.

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.

scholarly journals The measurement of approximate number system acuity across the lifespan is compromised by congruency effects

2018 ◽  
Vol 72 (5) ◽  
pp. 1037-1046 ◽  
Author(s):  
Jade Eloise Norris ◽  
Sarah Clayton ◽  
Camilla Gilmore ◽  
Matthew Inglis ◽  
Julie Castronovo
Keyword(s):  
Older Adults ◽  
Convex Hull ◽  
Surface Area ◽  
Visual Cues ◽  
Number System ◽  
Approximate Number System ◽  
Younger Adults ◽  
Numerosity Discrimination ◽  
Visual Cue ◽  
Valid Measurement

Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults’ ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.

scholarly journals Measuring the Approximate Number System

2011 ◽  
Vol 64 (11) ◽  
pp. 2099-2109 ◽  
Author(s):  
Camilla Gilmore ◽  
Nina Attridge ◽  
Matthew Inglis
Keyword(s):  
Numerical Cognition ◽  
Number System ◽  
Single System ◽  
Approximate Number System ◽  
Methodological Issues ◽  
Educational Benefits ◽  
Adult Participants ◽  
Typical Performance ◽  
The Relationship

Recent theories in numerical cognition propose the existence of an approximate number system (ANS) that supports the representation and processing of quantity information without symbols. It has been claimed that this system is present in infants, children, and adults, that it supports learning of symbolic mathematics, and that correctly harnessing the system during tuition will lead to educational benefits. Various experimental tasks have been used to investigate individuals' ANSs, and it has been assumed that these tasks measure the same system. We tested the relationship across six measures of the ANS. Surprisingly, despite typical performance on each task, adult participants' performances across the tasks were not correlated, and estimates of the acuity of individuals' ANSs from different tasks were unrelated. These results highlight methodological issues with tasks typically used to measure the ANS and call into question claims that individuals use a single system to complete all these tasks.

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