Proportional reasoning and strategies to solve problems of missing value and comparison

Abstract

This paper analyses strategies used by students in problem solving related to proportional reasoning. Twenty students from sixth degree of elementary school from a city of the state of Minas Gerais participated in the study and answered to questions in a pencil-and-paper test. The students answered correctly the missing value problems, and the vast majority employed covariaton relationship between the quantities involved; problems of simpler comparison were correctly answered through the settling of part-part relationships. There was great difficulty in more complex problems of comparison, considering that only four of them used the referential of half and only one used covariaton relationship. The results indicate that there was no parallel between strategies to the two kinds of problem, and the work suggests that differentiated situations should be offered to broaden conceptual field related to proportionality.