Students' improper proportional reasoning: The case of area and volume of rectangular figures

Abstract

In this paper, we investigate the predominance of the linear model in 12-13 year old Cypriot students, while solving non-proportional word problems involving area and volume of rectangular figures. Using three different kinds of tests related to the context of the word problems presented we attempt to identify a differentiation in students’ responses. The results reveal students’ tendency to apply proportional reasoning in problem situations in which this kind of reasoning is not suited. This tendency appears to decrease in the second phase of the study when the context of the problems was changed. The data also suggest that students are not able to detect the common non-linear character of area and volume tasks and therefore, deal with them in a different way.