Individual Differences

2015 ◽  
Author(s):  
Chris Donlan
Keyword(s):  
Individual Differences ◽  
Primary School ◽  
Strong Evidence ◽  
Number System ◽  
Basic Number ◽  
Number Processing ◽  
Approximate Number System ◽  
Identification Task ◽  
Comparison Task ◽  
Primary School Mathematics

This article discusses the results of three studies that have attempted to identify the factors underlying individual differences in mathematics. Holloway and Ansari (2009), explored the relation between basic number processing and attainment in primary school mathematics. Mazzocco et al. (2011) used a non-symbolic comparison task as an indicator of a preschool child’s Approximate Number System (ANS). Goebel et al. (2014), who tested the number knowledge of 173 six-year olds using a number identification task. All three studies tested specific hypotheses by making use of individual differences and associations between them. They also strongly validate two fundamental principles: that correlational models are limited by the measurements they contain, and that evidence consistent with a particular hypothesis does not necessarily constitute strong evidence in its favour. This article concludes by providing an overview of the topics covered in this book concerning individual differences in mathematics.

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

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 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.

scholarly journals Approximate number system discrimination training for 7-8 year olds improves approximate, but not exact, arithmetics, and only in children with low pre-training arithmetic scores

2020 ◽  
Vol 6 (3) ◽  
pp. 275-303
Author(s):  
Nuria Ferres-Forga ◽  
Justin Halberda
Keyword(s):  
Individual Differences ◽  
Discrimination Training ◽  
Specific Effect ◽  
Training Group ◽  
Number System ◽  
Control Group ◽  
The Novel ◽  
Approximate Number System ◽  
Exact Arithmetic ◽  
Arithmetic Performance

We investigated whether training the Approximate Number System (ANS) would transfer to improved arithmetic performance in 7-8 year olds compared to a control group. All children participated in Pre- and Post-Training assessments of exact symbolic arithmetic (additions and subtractions) and approximate symbolic arithmetic abilities (a novel test). During 3 weeks of training (approximately 25 minutes per day, two days per week), we found that children in the ANS Training group had stable individual differences in ANS efficiency and increased in ANS efficiency, both within and across the training days. We also found that individual differences in ANS efficiency were related to symbolic arithmetic performance. Regarding arithmetic performance, both the ANS training group and the control group improved in all tests (exact and approximate arithmetics tests). Thus, the ANS training did not show a specific effect on arithmetic performance. However, considering the initial arithmetic level of children, we found that the trained children showed a higher improvement on the novel approximate arithmetic test compared to the control group, but only for those children with a low pre-training arithmetic score. Nevertheless, this difference within the low pre-training arithmetic score level was not observed in the exact arithmetic test. The limited benefits observed in these results suggest that this type of ANS discrimination training, through quantity comparison tasks, may not have an impact on symbolic arithmetics overall, although we cautiously propose that it could help with approximate arithmetic abilities for children at this age with below-average arithmetic performance.

scholarly journals Cognitive control in number processing: new evidence from task switching

2020 ◽  
Author(s):  
Andreas Schliephake ◽  
J. Bahnmueller ◽  
K. Willmes ◽  
K. Moeller
Keyword(s):  
Cognitive Control ◽  
Task Switching ◽  
Numerical Cognition ◽  
Basic Number ◽  
Number Processing ◽  
Input Output ◽  
Problem Size ◽  
Comparison Task ◽  
Specific Stimulus ◽  
Magnitude Comparison

Abstract Recently, it was demonstrated that even basic numerical cognition such as the processing of number magnitude is under cognitive control. However, evidence so far primarily came from adaptation effects to stimulus characteristics (e.g., relative frequency of specific stimulus categories). Expanding this approach, we evaluated a possible influence of more active exertion of cognitive control on basic number processing in task switching. Participants had to perform a magnitude comparison task while we manipulated the order of compatible and incompatible input–output modalities (i.e., auditory/vocal input–visual/manual output vs. auditory/visual input–manual/vocal output, respectively) on the trial level, differentiating repeat vs. switch trials. Results indicated that the numerical distance effect but not the problem size effect was increased after a switch in input–output modality compatibility. In sum, these findings substantiate that basic number processing is under cognitive control by providing first evidence that it is influenced by the active exertion of cognitive control as required in task switching.

scholarly journals Processing symbolic numbers: The example of distance and size effects

2020 ◽  
Author(s):  
Attila Krajcsi ◽  
Petia Kojouharova ◽  
Gabor Lengyel
Keyword(s):  
Size Effects ◽  
Alternative Model ◽  
Numerical Cognition ◽  
Number System ◽  
Approximate Number System ◽  
Comparison Task ◽  
Semantic System ◽  
Simple Representation

According to the dominant view in the literature, several numerical cognition phenomena are explained coherently and parsimoniously by the Approximate Number System (ANS) model, which model supposes an evolutionarily old, simple representation behind many numerical tasks. We offer an alternative model, the Discrete Semantic System (DSS) to explain the same phenomena in symbolic numerical tasks. Our alternative model supposes that symbolic numbers are stored in a network of nodes, similar to conceptual or linguistic networks. The benefit of the DSS model is demonstrated through the example of distance and size effects of comparison task.

Can Dyscalculics Estimate the Results of Arithmetic Problems?

2016 ◽  
Vol 50 (1) ◽  
pp. 23-33 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Number System ◽  
Chance Level ◽  
Approximate Number System ◽  
Comparison Task ◽  
Strategy Analysis ◽  
Developmental Dyscalculia ◽  
Exact Answer ◽  
Reference Number ◽  
Multiplication Problem

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than controls, their performance was well above chance level. The performance of controls but not of those with developmental dyscalculia (DD) improved consistently for smaller problem sizes. The performance of both groups was superior when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, both of which are considered to be the markers of the approximate number system (ANS). Strategy analysis distinguished between an approximated calculation strategy and a sense of magnitude strategy, which does not involve any calculation but relies entirely on the ANS. Dyscalculics used the latter more often than controls. The present results suggest that there is little, if any, impairment in the ANS of adults with DD and that their main deficiency is with performing operations on magnitudes rather than with the representations of the magnitudes themselves.

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