A construção do conceito de número racional no sexto ano do ensino fundamental

Abstract

This work was developed from the preparation, implementation and analysis of a didactical sequence aimed to promoting the learning of concept of rational number by students in the sixth year of elementary school. We used the concept of zone of proximal development by Vygotsky and the treatment and conversion concepts developed by Duval. It is believed, in accordance with Duval, that the concept can only occur when the student is able do the treatments and the conversions of mathematical objects and, in accordance to Vygotsky, that the process of teaching and learning should be geared to the needs of individuals. This research is theoretically and methodologically basad the Didactic Engineering, methodology aimed to studying the work in the classroom by internal validation, that is, comparing what the student knew before having contact with an educational tool to learn what he achieved after the completion of the work. The didactical sequence proposed could provide students with the appropriation of the concept of rational number, that is, they managed to make the treatments and conversions with the following forms of representation of rational numbers: natural language, decimal, fractional and figural. This form, assisting them in performing daily activities that involve on mathematical object.