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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
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Numbers, numerosities, and new directions.

Sam Clarke1, Jacob Beck1

  • 1Department of Philosophy & Centre for Vision Research, York University, Toronto, ONM3J 1P3, Canada.spclarke@yorku.ca; http://www.sampclarke.netjbeck@yorku.ca; http://www.jacobbeck.org.

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Summary
This summary is machine-generated.

The number sense, encompassing the approximate number system (ANS), represents rational and natural numbers, not irrational ones. This response highlights future research directions in numerical cognition and representation.

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Area of Science:

  • Cognitive Science
  • Psychology
  • Neuroscience

Background:

  • The target article proposed that the number sense represents natural and rational numbers.
  • Commentaries raised questions about underlying assumptions and the nature of numerical representation.

Purpose of the Study:

  • To respond to 26 commentaries on the target article.
  • To outline new empirical and theoretical research directions.
  • To clarify the representation of numbers within the approximate number system (ANS).

Main Methods:

  • Theoretical discussion and synthesis of existing research.
  • Analysis of arguments concerning number sense and numerical representation.
  • Examination of the ANS's capacity for representing different number types.

Main Results:

  • The number sense is argued to represent natural and rational numbers.
  • The approximate number system (ANS) represents numerosities, not abstract numbers.
  • The ANS's representation is limited to rational, not irrational, numbers.

Conclusions:

  • The approximate number system (ANS) plays a crucial role in representing numerical quantities.
  • Further research is needed to explore the nuances of numerical representation in the brain.
  • Distinguishing between number and numerosity representation is key for understanding numerical cognition.