Development of Arithmetic Skills and Knowledge in Preschool Children

Authored by: Jeffrey Bisanz , Jody L. Sherman , Carmen Rasmussen , Elaine Ho

Handbook of Mathematical Cognition

Print publication date:  December  2004
Online publication date:  August  2005

Print ISBN: 9781841694115
eBook ISBN: 9780203998045
Adobe ISBN: 9781135423667

10.4324/9780203998045.ch9

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Abstract

Children and adults “do arithmetic” in a variety of contexts. They compute prices, keep track of scores in games, calculate statistics, generate answers for tests of mathematics in school, and solve a host of practical and sometimes theoretical problems. Understanding and skill in arithmetic are demonstrated in many ways. A person’s proficiency might be judged by the accuracy of his or her answers, as in the case of achievement tests, but a much richer picture emerges when we examine how children and adults solve arithmetic problems. Sometimes they quickly remember arithmetic facts to generate answers, such as the value of 25, 9 × 8, or 3 + 4. When answers are not immediately apparent, children and adults sometimes create very sophisticated problem-solving procedures. Implicit in these procedures is knowledge about the symbol system used to represent problems and about an array of concepts such as cardinality (the amount represented by a number), ordinality (relations of more and less among numbers), and the many principles that define what is or is not legitimate in a system of arithmetical operations. Documenting the knowledge and skills that support arithmetic performance provides insights not only into how children and adults do arithmetic but also into the organization, coordination, and development of human cognition.

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