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 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.