Tarefas exploratórias para o ensino de potenciação: manifestações do pensamento algébrico a partir de uma Investigação Baseada em Design

Abstract

The aim of this paper is to analyze manifestations of algebraic thinking of students in the 6th year of Elementary School when performing an exploratory task that aims to promote the construction of the potentiation operation. Assuming that working with patterns and generalization is central to the development of algebraic thinking, exploratory tasks were selected that allow students to recognize a pattern of growth and reach a close or distant generalization. The analyzed data were produced by audio recording of three classes based on Exploratory Teaching to introduce potentiation in the 6th year of Elementary School through an exploratory task. In the data analysis, it was possible to notice that the students reached a close generalization, as they discovered the next terms of the numerical sequence involving recursive relations, but they did not reach a distant generalization. We conclude that the task allows us to discuss the importance of power notation when writing large numbers.