Sistema de inequações do 1º grau: uma abordagem do processo ensino-aprendizagem focando os registros de representações - Traldi Júnior, Armando (2002)
In light of the emphasis that the term problem-solving has received in the mathematics education community as well as research results indicating the various difficulties students exhibit in solving problems, we embarked on this study. The study aims to investigate whether students, at the end of the Ensino Médio (High School) are able to resolve optimisation problems. For all of the problems investigated, it was possible to obtain the solution by applying concepts and procedures already studied by the students, among them, systems of inequalities of the first degree. To test our hypothesis that some students would experience difficulties in resolving these problems, we applied a diagnostic test to a group of 33 students. Analysis of students' responses indicated that none of the students were able to resolve the optimisation problems. Our next step was to investigate if, as proposed by Duval (1993), activities concerning the treatment, the conversion and the co-ordination between registers of representation of a certain object contribute to the processes of learning and teaching this object. To this end, we designed a didactic (teaching) sequence. After a second group of 10 students worked through the sequence, they completed a post-test. We conducted a comparative analysis between the responses of the first group to the diagnostic test and the post-test responses given by the second group of students. This analysis showed that, while the first group of students failed to solved the optimisation problems, all the students in the second group approached the problems and most were able to resolve them. These results suggest that the activities of treatment, conversion and co-ordination of registers of representation of the mathematical object system of inequality make an important contribution to the formation of the concept and its application in the resolution of optimisation problems