Proportional reasoning involves both qualitative and quantitative methods of thought. This study examined the relationship between qualitative and quantitative proportional reasoning of elementary school children. Two ratio types, velocity and thickness, were chosen. In the qualitative reasoning task, children were asked to determine the direction in which the numerator of the ratio would change (decrease, stay the same, or increase in value), when the denominator of the ratio changed and when the ratio was constant. In the quantitative reasoning task, children were given three components of two equal ratios and were asked to solve for the fourth component. These tasks were individually administered to thirty third-grade, twenty-nine fourth-grade, and thirty fifth-grade pupils. The results were as follows : 1) Qualitative reasoning preceded quantitative for each ratio type, while success rate on quantitative reasoning tasks increased with age. 2) Different ratio types, velocity and thickness, showed an effect only on qualitative reasoning in third graders. 3) Children's ability to reason qualitatively appeared to hare a strong impact on their performance on quantitative reasoning tasks.
