O campo conceitual multiplicativo: uma proposta de aprendizagem à luz da teoria das situações didáticas nos anos finais do ensino fundamental

Abstract

This research investigates the effects of a teaching approach based on the Theory of Didactic Situations on the performance of students in the Final Years of Elementary School in solving problem situations related to the Multiplicative Conceptual Field. The theoretical foundation used was Vergnaud's Theory of Conceptual Fields (1983, 1990), which examines knowledge construction through situations and representations mobilized by students during the teaching and learning process, and Brousseau's Theory of Didactic Situations (1996, 2008), which addresses learning through students' adaptation to the "milieu"—an environment that challenges their prior conceptions and promotes knowledge construction through direct interaction with problems and challenges, without direct and continuous intervention from the teacher. The main objective is to analyze the effects of this teaching approach on the performance of students in the Final Years of Elementary School in solving problem situations of the Multiplicative Conceptual Field. This study adopts a qualitative, exploratory, and descriptive approach, with a case study design. The research was conducted at the Federal University of Amazonas, within the project called Basic Mathematics School. Twenty-eight students from 6th, 7th, and 8th grades participated in the research. The results indicate a significant improvement in students' abilities to understand and apply multiplicative concepts in problem situations involving the Multiplicative Conceptual Field, suggesting that integrating the Theory of Didactic Situations and the Theory of Conceptual Fields facilitates deeper and more engaged mathematical learning. It is concluded that the pedagogical approach incorporating these theories not only helps to overcome conceptual difficulties in mathematics but also promotes more potentially meaningful and lasting learning.