Learning Rational Numbers with Understanding through an Emergent Modeling Process

Abstract

The study presented in this paper focus on the role that representations assume as they are taken as models of a contextualized situation and reconstructed as models for reasoning, by primary school students (aged 8 to 10 years old). It regards rational numbers learning with an understanding framed by the development of a number sense perspective. Considering a learning trajectory that emphasizes initially the understanding of percentage, we analyzed four tasks of a teaching experiment that was developed, following the methodological procedures of a Design Based Research. Data were collected through participant observation, supported in a logbook, audio and video recorded lessons and students' productions at the classroom. The analysis highlights that the social construction of models from representations, initially associated with percentage, strengthens the interpretation of relations and facilitates the understanding of concepts related to rational numbers.

Keywords:
Rational Numbers; Number Sense; Representations; Emergent Modeling