scholarly journals Numerical cognition needs more and better distinctions, not fewer

2021 ◽  
Vol 44 ◽  
Author(s):  
Hilary Barth ◽  
Anna Shusterman
Keyword(s):  
Numerical Cognition ◽  
Number System ◽  
Approximate Number System ◽  
The Way

Abstract We agree that the approximate number system (ANS) truly represents number. We endorse the authors' conclusions on the arguments from confounds, congruency, and imprecision, although we disagree with many claims along the way. Here, we discuss some complications with the meanings that undergird theories in numerical cognition, and with the language we use to communicate those theories.

Toward an integrative approach to numerical cognition

2017 ◽  
Vol 40 ◽  
Author(s):  
Tali Leibovich ◽  
Naama Katzin ◽  
Moti Salti ◽  
Avishai Henik
Keyword(s):  
Collaborative Research ◽  
Animal Studies ◽  
Numerical Cognition ◽  
Number System ◽  
Open Science ◽  
Integrative Approach ◽  
Approximate Number System ◽  
Suggested Model ◽  
Future Developments

AbstractIn response to the commentaries, we have refined our suggested model and discussed ways in which the model could be further expanded. In this context, we have elaborated on the role of specific continuous magnitudes. We have also found it important to devote a section to evidence considered the “smoking gun” of the approximate number system theory, including cross-modal studies, animal studies, and so forth. Lastly, we suggested some ways in which the scientific community can promote more transparent and collaborative research by using an open science approach, sharing both raw data and stimuli. We thank the contributors for their enlightening comments and look forward to future developments in the field.

Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too?

2021 ◽  
Vol 44 ◽  
Author(s):  
Edward M. Hubbard ◽  
Percival G. Matthews
Keyword(s):  
Numerical Cognition ◽  
Processing System ◽  
Number System ◽  
Rational Numbers ◽  
Approximate Number System ◽  
Access Points ◽  
Whole Numbers ◽  
Two Systems ◽  
Systems View

Abstract Clarke and Beck suggest that the ratio processing system (RPS) may be a component of the approximate number system (ANS), which they suggest represents rational numbers. We argue that available evidence is inconsistent with their account and advocate for a two-systems view. This implies that there may be many access points for numerical cognition – and that privileging the ANS may be a mistake.

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.

Probing the Neural Correlates of Number Processing

2016 ◽  
Vol 23 (3) ◽  
pp. 264-274 ◽  
Author(s):  
André Knops
Keyword(s):  
Computational Models ◽  
Numerical Cognition ◽  
Experimental Studies ◽  
Number System ◽  
Neural Correlates ◽  
Approximate Number System ◽  
Numerical Information ◽  
The Past ◽  
Code Model ◽  
Human Neuroimaging

The cognitive and neural mechanisms that enable humans to encode and manipulate numerical information have been subject to an increasing number of experimental studies over the past 25 years or so. Here, I highlight recent findings about how numerical information is neurally coded, focusing on the theoretical implications derived from the most influential theoretical framework in numerical cognition—the Triple Code Model. At the core of this model is the assumption that bilateral parietal cortex hosts an approximate number system that codes for the cardinal value of perceived numerals. I will review studies that ask whether or not the numerical coding within this system is invariant to varying input notation, format, or modality, and whether or not the observed parietal activity is number-specific over and above the parietal involvement in response-related processes. Extant computational models of numerosity (the number of objects in a set) perception are summarized and related to empirical data from human neuroimaging and monkey neurophysiology.

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.

Non-symbolic and symbolic number and the approximate number system

2021 ◽  
Vol 44 ◽  
Author(s):  
David Maximiliano Gómez
Keyword(s):  
Numerical Cognition ◽  
Number System ◽  
Rational Numbers ◽  
Approximate Number System ◽  
Symbolic Number

Abstract The distinction between non-symbolic and symbolic number is poorly addressed by the authors despite being relevant in numerical cognition, and even more important in light of the proposal that the approximate number system (ANS) represents rational numbers. Although evidence on non-symbolic number and ratios fits with ANS representations, the case for symbolic number and rational numbers is still open.

“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 Bilingualism and numerical cognition

2020 ◽  
Vol 24 (1) ◽  
pp. 340-360
Author(s):  
Carina da Silva Santos ◽  
Ingrid Finger
Keyword(s):  
Task Performance ◽  
Numerical Cognition ◽  
Language Background ◽  
Language History ◽  
Mathematical Problems ◽  
The One ◽  
The Relationship ◽  
The Way

The present study aimed to investigate the relationship between bilingualism and numerical cognition, more specifically, the way English-Portuguese bilinguals solve simple mathematical problems when these are presented in different formats (digits, English, and Portuguese) and whether their language history background has any effect on such behavior. The main results suggest that bilinguals are faster and more accurate in solving mathematical problems presented in digit format and in solving those problems presented in the written format when the language of the stimuli was the one in which they learned basic arithmetic. Also, the participants’ language background experience did not have any significance in their task performance.

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