
Contents
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An Aside: Why are There No ‘Five-Knowers’? An Aside: Why are There No ‘Five-Knowers’?
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Studies of Number-Knower Levels and Number-Concept Development Studies of Number-Knower Levels and Number-Concept Development
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Number-Knower Levels versus Counting or Estimation Number-Knower Levels versus Counting or Estimation
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Age Ranges for Each Knower Level Age Ranges for Each Knower Level
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Relation of Number-Knower Level to Vocabulary Development Relation of Number-Knower Level to Vocabulary Development
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Within-Child, Cross-Linguistic Consistency of Number-Knower Levels Within-Child, Cross-Linguistic Consistency of Number-Knower Levels
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Describing The Number Concepts Under Construction Describing The Number Concepts Under Construction
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Number is About Discrete Things, Not Continuous Substances Number is About Discrete Things, Not Continuous Substances
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Some Kinds of Actions Affect Number, Others Do Not Some Kinds of Actions Affect Number, Others Do Not
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Number Words are about Numerosity, Not Total Area or Other Properties of a Set Number Words are about Numerosity, Not Total Area or Other Properties of a Set
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Cardinality and The Successor Function Cardinality and The Successor Function
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Cardinality and Equinumerosity Cardinality and Equinumerosity
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Conclusions Conclusions
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Note Note
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References References
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16 How Counting Leads to Children’s First Representations of Exact, Large Numbers
Get accessBarbara W. Sarnecka, University of California, Irvine
Meghan C. Goldman, University of California, Irvine
Emily B. Slusser, San Jose State University
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Published:03 March 2014
Cite
Abstract
Young children initially learn to ‘count’ without understanding either what counting means, or what numerical quantities the individual number words pick out. Over a period of many months, children assign progressively more sophisticated meanings to the number words, linking them to discrete objects, to quantification, to numerosity, and so on. Eventually, children come to understand the logic of counting. Along with this knowledge comes an implicit understanding of the successor function, as well as of the principle of equinumerosity, or exact equality between sets. Thus, when children arrive at a mature understanding of counting, they have (for the first time in their lives) a way of mentally representing exact, large numbers.
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