Ensino de potenciação para o 6º ano do ensino fundamental: preparação de uma investigação baseada em design

Abstract

This research aims to describe and analyze the stage of preparation of a Design-Based Research (IBD) carried out collaboratively by a group of studies and researches and then elaborate conjectures for the teaching of Potentiation in the 6th year of elementary school. Preparation is the first step in an IBD cycle, which involves, in addition to preparation, the stages of conducting and retrospective analysis of a design experience. In the preparation, special attention is paid to the theoretical deepening on the subject to be investigated and the elaboration of conjectures (one in the dimension of content and the other in the didactic - pedagogical dimension) to be tested and improved during the investigation. Focusing on teaching Powering for the 6th year of elementary school, the research was carried out in the context of the remote meetings of the School Mathematics group: practices, research and studies, composed of 11 professors, linked to the Federal Technological Unive rsity of Paraná, which decided to collectively discuss the teaching and learning of Powerup, aiming at the preparation of an IBD. The data analyzed in the research were produced by recording eight meetings conducted by Google Meet, and: (i) four meetings were intended to elaborate the conjecture in the dimension of the content of Powering, so that principles can be established about what to teach, focusing on the students' learning objectives; (ii) two meetings were intended to discuss tasks for the elaboration of a Diagnostic Assessment capable of providing information about the starting point of students of the 6th year of elementary school, in terms of the knowledge that allows/favor the learning of the content of Potentiation; (iii) two meetings were intended to elaborate the conjecture in the didactic-pedagogical dimension, so that possibilities on how to approach the theme of teaching in the classroom are indicated. Each meeting was described and analyzed and as a result we elaborated the conjectures th at can be summarized as follows: in the dimension of the content, the theme Potentiation should be included in the broader context of algebraic thought, to the extent that the notation is a constituent part of the concept and considering that generalization is an important characteristic for its understanding; in the didactic-pedagogical dimension, the work with exploratory tasks allows students to work with identification of patterns of numerical sequences and generalization of these patterns, connecting it to the (new) notion of Potentiation, avoiding a teaching based on the presentation of the symbology and technical explanation of the operation. It is also concluded that a teaching approach that can favor work with exploratory tasks on Powering aimed at the development of algebraic thinking is Exploratory Teaching, since it offers students an opportunity to work with rich mathematical tasks and with an approach that requires sharing their ideas with other colleagues and with the teacher. In addition to the conjectures, at the end of the research an Educational Product was elaborated consisting of mathematical tasks that make up a Diagnostic Assessment, aiming to offer the teacher (researcher) tools to identify the students' previous knowledge in order to allow him to proceed to the next stages of realization and retrospective analysis of a design experience involving the teaching of Powering.