Generalising principles in spite of procedural differences: Children's understanding of division

Abstract

Between ages 5 and 7, children are known to be quite good at sharing discrete quantities but very bad at sharing continuous quantities. Our aim was to find whether they can transfer their understanding of logical relations from discrete to continuous quantities though the procedures used in sharing these quantities are markedly different. Two samples of 5- to 7-year-olds participated in two studies. In the first study, the items involved partitive division; in the second, quotitive division tasks. In both studies, the children solved tasks with discrete and continuous quantities. Performance varied significantly across age level and logical principle (equivalence between different rounds of sharing versus inverse relation between the divisor and the quotient) but not across type of quantity (discrete versus continuous). There was a very strong relation between performance across type of quantity. We conclude that children can generalise reasoning principles in division across type of quantity in spite of the difference in sharing procedures.