Situações de análise combinatória discutidas à luz da Teoria dos Campos Conceituais

Abstract

This qualitative work aims to analyze the operative invariants evoked by students enrolled in the 3rd year of elementary school of a private school in the municipality of Santarém-PA, when submitted to situations in the combinatorial field. As analyses aim to show the teacher the possibility of redirecting the teaching and learning process, based on the concepts and theorems-in-action evoked by the students in action. Data were collected during a meeting in the hybrid modality, where a list of problematic situations was applicationd and later a semi-structured interview was made with the class teacher. To support the discussion, the research makes use of Gérard Vergnaud's Theory of Conceptual Fields, which has conceptualization as the epicenter of the teaching and learning process. The research points out the concepts-in-action and theorems-in-action presented throughout the execution of the activity, besides evidencing the need for continuity of addition operations in contexts involving multiplication. The results showed that the students master the table, make use of the commutative property and can detect the data in the situation, whether explicit or not, in addition, they presented competence in proposing other possibilities of solution for the situations.