Young children's understanding of division: The relationship between division terms in a noncomputational task.

Abstract

The authors investigated development of the concept of division in young children. Experiment 1 examined whether children who can share are able to understand the inverse divisor-quotient relationship in partitive division tasks when asked to judge the relative size of 2 shared sets. Experiment 2 investigated whether young children understand the same inverse relation in quotitive tasks in which they were asked to judge the relative number of sets to be formed. The ability to compare share-outs and to take into account the inverse divisor-quotient relationship was present in approximately half of the 6-year-olds; age improvements were significant between 5 and 7 years. Partitive tasks, which are more similar to sharing, were easier than quotitive tasks, which seem to involve the coordination between sharing and part-whole concepts. This is evidence that children's initial understanding of division might be based on the action schema of sharing.