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How counting represents number: what children must learn and when they learn it
Barbara W Sarnecka1, Susan Carey
1Department of Cognitive Sciences, SSPA 3151, University of California, Irvine, CA 92617-5100, USA. sarnecka@uci.edu
Cognition
|June 24, 2008
Summary
Children’s understanding of counting principles was assessed. Cardinal-principle-knowers, unlike subset-knowers, grasp that adding items means advancing numerically and understand the unit of change in counting.
Area of Science:
- Cognitive Development
- Child Psychology
- Number Cognition
Background:
- Early number understanding is crucial for mathematical development.
- Distinguishing between children who understand counting principles (cardinal-principle-knowers) and those who do not (subset-knowers) is key to characterizing this knowledge.
Purpose of the Study:
- To investigate the specific knowledge associated with understanding the cardinal principle of counting.
- To compare the reasoning of cardinal-principle-knowers and subset-knowers regarding number sets.
Main Methods:
- A comparative study involving 2- to 4-year-old children.
- Assessing children's responses to 'how many' questions and their understanding of numerical changes in sets.
Main Results:
- Many children incorrectly answer 'how many' based on the last number counted, irrespective of true understanding.
- Only children mastering the cardinal principle understand that adding/subtracting objects corresponds to moving forward/backward in the numeral sequence.
- Cardinal-principle-knowers, but not subset-knowers, comprehend that adding one object means advancing by one numeral word.
Conclusions:
- Understanding the cardinal principle is a distinct cognitive achievement in early number development.
- Subset-knowers demonstrate a superficial grasp of counting, lacking deeper conceptual understanding of quantity and numerical operations.
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