Synthese 198 (Suppl 5):1001-1018 (2015)

Abstract
This article focuses on how young children acquire concepts for exact, cardinal numbers. I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey. In this framework, the counting list and the counting routine form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information that they had no way of representing before.
Keywords Children  Young children  Early childhood  Number  Numbers  Preschool  Counting  Bootstrapping  Concepts  Conceptual development  Conceptual change  Exact equality  Number-knower levels  Math  ANS  Successor  Cardinality  Subset-knower  CP-knower  Education  SES  Interventions
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DOI 10.1007/s11229-015-0854-6
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References found in this work BETA

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Core Systems of Number.Stanislas Dehaene, Elizabeth Spelke & Lisa Feigenson - 2004 - Trends in Cognitive Sciences 8 (7):307-314.
The Number Sense: How the Mind Creates Mathematics.Stanislas Dehaene - 1999 - British Journal of Educational Studies 47 (2):201-203.

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Citations of this work BETA

Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology 12 (4):1-24.
Situated Counting.Peter Gärdenfors & Paula Quinon - 2021 - Review of Philosophy and Psychology 12 (4):721-744.

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