This report from the Rational Number Project concerns the development of a quantitative concept of rational number in fourth and fifth graders. In a timed task, children were required to select digits to form two rational numbers whose sum was as close to 1 as possible. Two versions of the task yielded three measures of the skill. The cognitive mechanisms used by high performers in individual interviews were characterized by a flexible and spontaneous application of concepts of rational number order and fraction equivalence and by the use of a reference point. Low performers tended either not to use such cognitive mechanisms or to apply concepts in a constrained or inaccurate manner.
Merlyn J. Behr, Professor, Department of Mathematical Sciences, Northern Illinois Universiry, DeKalb, IL 60115