Desenvolvimento do pensamento algébrico por meio de tarefas exploratórias sobre potenciação

Abstract

This research aims to analyze manifestations of the algebraic thinking of students in the 6th year of Elementary School when carrying out tasks that aim to promote the construction of the potentiation operation. Considering Design-Based Research (IBD) as the research methodology, the data were produced over five classes held in a class with 35 students from the 6th year of Elementary School at a State College located in a city north of Paraná. Assuming that working with patterns and generalization is central to the development of algebraic thinking, two mathematical tasks were selected, worked from the perspective of Exploratory Teaching, which would allow students to recognize a pattern of growth and reach a close or distant generalization. The data analyzed was obtained from the students' written output and the audio recording of lessons designed to introduce potentiation to the class. In the analyses, it was possible to notice that the students reached a close generalization, as they discovered the following terms in the numerical sequence involving recursive relationships in the two tasks. Still, they did not reach a distant generalization. Despite this, it was concluded that the tasks allowed the teacher to introduce the potentiation operation based on wh at the students could develop and discuss in the classroom. Finally, a retrospective analysis was carried out, concluding the first cycle of IBD, commenting on the challenges of implementing Exploratory Teaching, especially for teachers who have never experienced this perspective in their practice. As a result of the research, an Educational Product is presented, aimed at teachers who teach Mathematics in Basic Education, with the planning of a didactic sequence aimed at teaching enhancement for the 6th year of Elementary School. This sequence was constructed with the two mathematical tasks analyzed in this research.