Construct a Sum: A Measure of Children's Understanding of Fraction Size

Abstract

The question of how children perceive the "bigness" of rational numbers is of importance. Addition of fractions like1/3 and 3/5 does not make sense to a child without a quantitative notion of each addend. In order for children to perceive the size of a fraction, it seems necessary that they perceive the ordered pair such as 3/4; as one conceptual entity. This note describes, and summarizes results from several tasks the Rational Number Project has used to investigate children's perception of fractions, and especially of the size of a fraction. The Rational Number Project has involved fourth- and fifth-grade children in extensive teaching experiments. The teaching milieu of these experiments is especially manipulative rich, concept oriented, and involves small groups of children.