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 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.

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.

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.

The approximate number system represents rational numbers: The special case of an empty set

2021 ◽  
Vol 44 ◽  
Author(s):  
Michal Pinhas ◽  
Rut Zaks-Ohayon ◽  
Joseph Tzelgov
Keyword(s):  
Number System ◽  
Rational Numbers ◽  
Approximate Number System ◽  
Numerical Information ◽  
Special Case

Abstract We agree with Clarke and Beck that the approximate number system represents rational numbers, and we demonstrate our support by highlighting the case of the empty set – the non-symbolic manifestation of zero. It is particularly interesting because of its perceptual and semantic uniqueness, and its exploration reveals fundamental new insights about how numerical information is represented.

scholarly journals The Neurocognitive Bases of Numerical Cognition

2016 ◽  
Author(s):  
Francesco Sella ◽  
Charlotte Emily Hartwright ◽  
Roi Cohen Kadosh
Keyword(s):  
Experimental Psychology ◽  
Numerical Cognition ◽  
Relevant Literature ◽  
Short Review ◽  
Numerical Information ◽  
The Core ◽  
Code Model ◽  
Modes Of Representation ◽  
The Subject ◽  
The Relationship

Numerical Cognition describes the processes that one uses to assimilate, ascribe andmanipulate numerical information. This chapter is organised into two sections. The firstdraws heavily on data from Developmental and Experimental Psychology. We use this tooutline core findings related to processing numerical information in humans. In particular, wedescribe the trajectory of the acquisition of basic numerical skills. Starting in early infancy,we outline the processes that are believed to underlie non-symbolic representation. Next, wesummarise core studies that examine the representation of symbolic quantities (Arabicsystem). Lastly, we briefly report the relationship between basic numerical processing andmathematical achievement. The second part of the chapter explores evidence fromNeuropsychology and Neuroscience. The core methodological approaches used are brieflyoutlined with sign-posting to relevant literature. Next, we examine data from early lesionstudies, followed by a short review of one of the most influential models in the study ofNumerical Cognition, the Triple Code Model. Lastly, we look at the neurocognitive featuresof number, such as different modes of representation and the processing of quantity.Throughout, the core literature plus recent advances are summarised, giving the reader athorough grounding in the Neurocognitive Bases of Numerical Cognition.This preprint outlines a forthcoming chapter on the subject of ‘Numerical Cognition’ for inclusion in the forthcoming work tentatively entitled Stevens' Handbook of Experimental Psychology, Fourth Edition, Volume Three: Language & Thought (the “Work”), authored/edited by Sharon L. Thompson-Schill, due to be published by JOHN WILEY and SONS in 2017

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.

scholarly journals Is the ANS linked to mathematics performance?

2017 ◽  
Vol 40 ◽  
Author(s):  
Matthew Inglis ◽  
Sophie Batchelor ◽  
Camilla Gilmore ◽  
Derrick G. Watson
Keyword(s):  
Experimental Studies ◽  
Number System ◽  
Causal Link ◽  
Mathematics Performance ◽  
Curve Analysis ◽  
Approximate Number System ◽  
Evidential Value ◽  
And Mathematics

AbstractLeibovich et al. argue persuasively that researchers should not assume that approximate number system (ANS) tasks harness an innate sense of number. However, some studies have reported a causal link between ANS tasks and mathematics performance, implicating the ANS in the development of numerical skills. Here we report a p-curve analysis, which indicates that these experimental studies do not contain evidential value.

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