Positing numerosities may be metaphysically extravagant; positing representation of numerosities is not

Scientific Ontology

Abstract Clarke and Beck (C&B) assume that approximate number system (ANS) representations should be assigned referents from our scientific ontology. However, many representations, both in perception and cognition, do not straightforwardly refer to such entities. If we reject C&B's assumption, many possible contents for ANS representations besides number are compatible with the evidence C&B cite.

Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

Journal of Educational Psychology ◽

10.1037/edu0000426 ◽

2020 ◽

Vol 112 (6) ◽

pp. 1167-1182 ◽

Cited By ~ 1

Author(s):

Stephanie A. Malone ◽

Kelly Burgoyne ◽

Charles Hulme

Keyword(s):

Number System ◽

Number Knowledge

“Approximate number system” training: A perceptual learning approach

Attention Perception & Psychophysics ◽

10.3758/s13414-018-01636-w ◽

2018 ◽

Vol 81 (3) ◽

pp. 621-636 ◽

Cited By ~ 3

Author(s):

Aaron Cochrane ◽

Lucy Cui ◽

Edward M. Hubbard ◽

C. Shawn Green

Keyword(s):

Perceptual Learning ◽

Number System ◽

Learning Approach ◽

Compromised approximate number system acuity in extremely preterm school-aged children

Developmental Medicine & Child Neurology ◽

10.1111/dmcn.12206 ◽

2013 ◽

Vol 55 (12) ◽

pp. 1109-1114 ◽

Cited By ~ 12

Author(s):

Kerstin Hellgren ◽

Justin Halberda ◽

Lea Forsman ◽

Ulrika Ådén ◽

Melissa Libertus

Keyword(s):

Number System ◽

School Aged Children ◽

Extremely Preterm

Children’s Approximate Number System in Haptic Modality

Perception ◽

10.1177/0301006615614448 ◽

2015 ◽

Vol 45 (1-2) ◽

pp. 44-55 ◽

Cited By ~ 3

Author(s):

Fanny Gimbert ◽

Edouard Gentaz ◽

Valérie Camos ◽

Karine Mazens

Keyword(s):

Number System ◽

Haptic Modality

The number sense does not represent numbers, but cardinality comparisons

Behavioral and Brain Sciences ◽

10.1017/s0140525x21001072 ◽

2021 ◽

Vol 44 ◽

Author(s):

José Luis Bermúdez

Keyword(s):

Experimental Evidence ◽

Number Sense ◽

Number System ◽

Rational Numbers ◽

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.

Supplemental Material for A Multilevel Meta-Analysis on the Causal Effect of Approximate Number System Training on Symbolic Math Performance

Journal of Experimental Psychology Learning Memory and Cognition ◽

10.1037/xlm0001087.supp ◽

2021 ◽

Keyword(s):

Causal Effect ◽

Meta Analysis ◽

Number System ◽

Math Performance ◽

Representation of pure magnitudes in ANS

Behavioral and Brain Sciences ◽

10.1017/s0140525x21001199 ◽

2021 ◽

Vol 44 ◽

Author(s):

Steven Gross ◽

William Kowalsky ◽

Tyler Burge

Keyword(s):

Number System ◽

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.