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Conscious and Non-conscious Representations of Emotional Faces in Asperger's Syndrome

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Ontogenetic Origins of Human Integer Representations.

Susan Carey¹, David Barner²

¹Department of Psychology, Harvard University, Cambridge, MA 02138, USA.

Trends in Cognitive Sciences

|August 24, 2019

Summary

Children learn number words by first associating them with small sets and then mastering counting logic, not by linking them to perceptual magnitudes. Approximate number representations are not foundational to developing integer concepts.

Keywords:

conceptual change counting language magnitudes number

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Area of Science:

Cognitive Science
Developmental Psychology
Philosophy of Mathematics

Background:

Recent research suggests approximate numerical magnitudes are key to developing integer concepts in children.
This perspective posits a foundational role for perceptual magnitude estimation in early number understanding.

Purpose of the Study:

To challenge the view that approximate number representations are foundational for children's integer concept development.
To propose an alternative two-phase model for how children acquire number word meanings.

Main Methods:

Theoretical argumentation against the sufficiency of approximate number representations.
Proposal of a two-phase developmental model for number word acquisition.

Main Results:

Approximate number representations are insufficient, both empirically and theoretically, to explain the content of integer concepts.
Children's understanding of number words develops in two distinct phases.

Conclusions:

The first phase involves learning small number words through association with discrete sets.
The second phase involves mastering exact counting principles (successor function, one-to-one correspondence) for larger number words.
Approximate number representations do not play a foundational role in either phase of number word acquisition.