Children's Understanding of the Principles of Covariation and Compensation in Part-Whole Relationships

Interviews were held with 107 children, aged 4 through 7, to ascertain their understanding of compensation and covariance in part-whole relationships. They were questioned about uncounted quantities, counted quantities, and numerical equations. The results showed that 4-year-old children could usual...

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Bibliographic Details
Published in:Journal for research in mathematics education 1996-01, Vol.27 (1), p.25-40
Main Author: Irwin, Kathryn C.
Format: Article
Language:English
Subjects:
Age groups
Buttons
Causal covariation
Children
Cognitive Structures
Covariance
Dolls
Elementary School Students
Foreign Countries
Interviews
Mathematics education
New Zealand
Number Concepts
Preschool Children
Primary Education
Ratios (Mathematics)
Seriation
Toffees
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Summary:Interviews were held with 107 children, aged 4 through 7, to ascertain their understanding of compensation and covariance in part-whole relationships. They were questioned about uncounted quantities, counted quantities, and numerical equations. The results showed that 4-year-old children could usually predict the effect of changes to one or more parts of an uncounted whole, but were less competent in predicting changes to counted quantities. The ability to predict changes to counted quantities and give reasons for the change increased with age. Some 6-year-old children were able to give reasons for these relationships that went beyond direct observation. Only 7-year-old children were able to use covariance and compensation in a purely numerical context, that of derived equations. These results have implications for teaching young children.
ISSN:0021-8251
1945-2306
DOI:10.2307/749195