Mathematical Modeling and semiotic representations: contributions to the development of algebraic thinking

Abstract

In this paper we propose to submit analyses and reflections on the
possibilities of incorporating modeling into mathematics, with a theory of
semiotic representations. Our analysis includes a proposal for primary schools,
dedicated to the development of algebraic thinking, mediated by mathematical
modeling, experienced among a group of teachers during a course held in
Faxinal do Céu, in the city of Pinhão, in the State of Paraná. We elected the stage
of mathematical modeling to solve the problems posed through themes, as we
knew we would need the knowledge of mathematical objects and their
conceptualizations as a consequence of the procedures and strategies listed in
solving the problems, and that the problems could not be solved without them.
We analyzed the solutions presented to the problems posed through themes and
we analyzed a theory of semiotic representations that contributes to the
conceptualization and the development of algebraic thinking, because the
different records of representation mobilize operations of cognitive training,
treatment and conversion, putting into play the phenomenon of semantic
congruence, responsible for a greater or lesser success of these
conceptualizations.