Fostering Transit between Real World and Mathematical World: Some Phases on the Modelling Cycle

This study shows how, in the initial training of mathematics teachers, it is possible to promote processes of abstraction and mathematisation through modelling a real situation with the support of auxiliary material to mediate understanding. By adapting elements of the theoretical and methodological framework called Abstraction in Context (AiC), participants’ discussions while building a mathematical model—in a nested epistemic actions—are analysed. Two specific points are discussed in this paper. The first aims to identify how different types of knowledge emerge when an individual is faced with a modelling task. The second is regarding the use of auxiliary material as a means of metaphorising a situation. It was evidenced how the material favours the construction of a mathematical model through the simplification and idealisation that it brings. The meaning constructed for the model is supported in recognising a decreasing behaviour as a part of a whole.