Ratios comparison problems: an evaluation of proportional reasoning of sixth degree students

Abstract

This paper compares strategies of solving two comparison problems utilized by students from sixth degree of elementary school in two distinct moments: before and after a didactic intervention applied with the objective of introducing the concepts of ratio and proportion. The subjects were 15 students of a private school. The intervention was planned in the context of professional master’s degree and applied during the classes in normal period. The analysis indicated that, although a considerable number of students already had covariation and invariance schemes before the didactic intervention, this factor didn’t facilitate the solving of the first problem. After intervention, several students presented the schemes in such a way that they were recomposed and enriched in symbolic language, but not all of them gave the correct answer to the problem nor justified it. According to Gérard Vergnaud perspective, this investigation reveals that the process of acquiring the concepts of ratio and proportion has a very complex nature, and many situations are required so that those concepts and the procedures necessary to problem solving get an effective meaning to the student.