Matemática para o ensino: a construção do raciocínio funcional para os anos iniciais do ensino fundamental

Abstract

This research aimed to construct a mathematics for teaching in the early years based on the achievements of functional reasoning in different contexts. Based on related studies and ongoing training for elementary school teachers. To achieve the general objective, we assigned two specific objectives. The first was to construct a mathematics for teaching based on research related to functional reasoning. And the second was to construct a mathematics for teaching functional reasoning in ongoing training for elementary school teachers. The choice for qualitative research lies in the construction of the model through what is communicated as functional reasoning, whether by elementary school teachers in a training environment or through the scientific production of researchers. We used the investigative device of BrentDavis and Moshe Renert's Concept Study to identify the different uses of functional reasoning in the early years. This device was intertwined with the theoretical lenses of the work developed by researcher Anna Sfard, which constituted an analysis instrument and theoretical modeling strategy. The results of the study indicate a variability of functional reasoning achievements that were grouped into panoramas. Considering the related studies, the following panoramas were identified: generalization of patterns, proportionality and transformation machine. In the study with teachers, the following panoramas were identified: generalization of patterns, proportionality, algebraic expression and diagram.