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Summary of Reference

Author:
Irwin, Kathryn C

Title:
Children’s Understanding of the Principles of Covariation and Compensation in Part-Whole Relationships

Bibliographic data:
Irwin, K.C.  (1996). Children’s understanding of the principles of covariation and compensation in part-whole relationships, Journal for Research in Mathematics Education, 27 (1), 25-40.

Summary: 
Teachers often have trouble determining the level of mathematical understanding of new school entrants. In New Zealand mathematics textbooks make the assumption that children need to be taught about relationships between uncounted things yet practical experience with young children leads us to believe that they certainly know when they have lost an item from a toy collection.

This paper reports on a study of the understanding held by children between the ages of four and seven of the relationships between parts and wholes when changes were made in one or both of the parts. The evidence shows that most four year old children (in meaningful circumstances) could demonstrate an understanding of the effect on the whole of changes to uncounted parts before they could predict this relationship for counted quantities.

The result has implications for the New Zealand school curriculum as well as for other countries where schools have programmes that do not introduce part-whole relationships of quantities until children are seen to understand seriation.

There are two possible negative effects in ignoring the children’s understanding of mathematical concepts until the curriculum is ready to teach them. One is that the children’s time is being wasted and the other is that children learn that there is a clear demarcation between the knowledge they bring to school and that which they learn in school.