A learning path for rational numbers through different representations

In this paper, we aim to understand, in a context of teachers’ collaborative group, how emphasizing multiple representations can contribute to the learning of the rational numbers by elementary school students. We report part of a Design Based Research, within which a learning path for rational numbers was constructed and implemented in grade 3 classes. Data was collected through audio recordings of the collaborative group sessions, written records of the teachers’ and students’ interactions, as well as photo records of classroom work. We analyse two tasks focusing on students’ rational number learning of two classes, through discussion and reflection in the collaborative group. The results show that enactive and iconic representations, used as models in a recurrent way, support an intertwined understanding of symbolic representations. We conclude that the collaborative group work was essential to bring research into the classroom.