As decisões didáticas do professor de matemática na perspectiva do desenvolvimento do pensamento algébrico

Abstract

This study, developed in the field of Mathematics Didactics of French origin, aims to investigate the factors that influence the didactic decisions made by a Mathematics teacher in the (re)construction of a didactic sequence involving patterns and regularities, aimed at developing the algebraic thinking of high school students. To this end, we initially discussed some aspects that we consider important about the teaching of Algebra and then we anchored ourselves in the theoretical field of Didactic Decisions, a theory proposed by Margolinas (2002, 2005) that presents the Model of Levels of Teacher Activity, and in the Model of Decisional Factors proposed by Bessot (2019). Our methodology consists of a qualitative approach and is based on the case study of a mathematics teacher participating in the high school working group in the PRIPINT Project. The procedure for producing the research data occurred in three phases: Phase 1 – The production of didactic sequences (versions 1 and 2) based on the task “The matchsticks”; Phase 2 - Comparison of the versions of the didactic sequence; Phase 3 - Preparation and implementation of an interview with the teacher. Data analysis was inspired by the content analysis proposed by Bardin (2016), which comprises the following phases: Pre-analysis; Exploration of the material; and Treatment of results, inference and interpretation. Based on the analyses performed, we infer that the decisions made by the teacher to reconstruct the didactic proposal emerged from the direct influence of a combination of epistemic and didactic history factors, with a predominance of the former, especially those linked to the teacher's personal relationship with pedagogy and the teacher's personal relationship with the knowledge to be taught. We believe that the predominance of these two subtypes of epistemic factors is directly related to the teacher's conceptions about the mathematical knowledge to be taught and about the pedagogy that guides this teaching.