scholarly journals How to estimate how well people estimate: Evaluating measures of individual differences in the approximate number system

2015 ◽  
Vol 77 (8) ◽  
pp. 2781-2802 ◽  
Author(s):  
Dana Chesney ◽  
Par Bjalkebring ◽  
Ellen Peters
Author(s):  
Chris Donlan

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.


2020 ◽  
Vol 6 (3) ◽  
pp. 275-303
Author(s):  
Nuria Ferres-Forga ◽  
Justin Halberda

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.


2018 ◽  
Vol 81 (3) ◽  
pp. 621-636 ◽  
Author(s):  
Aaron Cochrane ◽  
Lucy Cui ◽  
Edward M. Hubbard ◽  
C. Shawn Green

2013 ◽  
Vol 55 (12) ◽  
pp. 1109-1114 ◽  
Author(s):  
Kerstin Hellgren ◽  
Justin Halberda ◽  
Lea Forsman ◽  
Ulrika Ådén ◽  
Melissa Libertus

Perception ◽  
2015 ◽  
Vol 45 (1-2) ◽  
pp. 44-55 ◽  
Author(s):  
Fanny Gimbert ◽  
Edouard Gentaz ◽  
Valérie Camos ◽  
Karine Mazens

2021 ◽  
Vol 44 ◽  
Author(s):  
José Luis Bermúdez

Abstract Against Clarke and Beck's proposal that the approximate number system (ANS) represents natural and rational numbers, I suggest that the experimental evidence is better accommodated by the (much weaker) thesis that the ANS represents cardinality comparisons. Cardinality comparisons do not stand in arithmetical relations and being able to apply them does not involve basic arithmetical concepts and operations.


2021 ◽  
Vol 44 ◽  
Author(s):  
Steven Gross ◽  
William Kowalsky ◽  
Tyler Burge

Abstract According to Clarke and Beck (C&B), the approximate number system (ANS) represents numbers. We argue that the ANS represents pure magnitudes. Considerations of explanatory economy favor the pure magnitudes hypothesis. The considerations C&B direct against the pure magnitudes hypothesis do not have force.


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