Putting counting to work: preschoolers’ understanding of cardinal extension

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that...

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Bibliographic Details
Published in:International journal of educational research 2003, Vol.39 (7), p.695-718
Main Authors: Muldoon, Kevin, Lewis, Charlie, Freeman, Norman H.
Format: Article
Language:English
Subjects:
Arithmetic
Cardinality
Computation
Counting
Error-detection
Mathematics Instruction
Mathematics Skills
Number Concepts
Numeracy
Preschool Children
Preschoolers
Problem Solving
Reasoning
Teaching Methods
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Summary:Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two experiments we found that although counting proficiency was necessary to solve these types of arithmetical problems, the best predictor of success was the ability to detect and reason about someone else's miscounts. We argue that these data suggest that a breakthrough in connecting counting with arithmetical problem solving is associated with an explicit representation of the rules governing cardinality and how they are applied correctly or incorrectly. We propose that teaching 4-year-olds to compare sets should include tasks where they judge another's counting proficiency, giving them the opportunity to conceptualise miscounts.
ISSN:0883-0355
1873-538X
DOI:10.1016/j.ijer.2004.10.006