The development of children's understanding of proportions

To determine whether the understanding of proportions develops before formal operations, children in grades 1, 3, and 5 and college students were given a variety of judgment tasks contrasting the comparison of quantity with the comparison of proportions. Results for the most difficult tasks indicated that a majority of fifth graders still lacked a full understanding of proportion. Results were interpreted as consistent with Inhelder and Piaget's contention that the comprehension of abstract relations requires formal operations. In grades 3 and 5, boys scored significantly higher than girls.