Investigative movements based on different lessons on the introduction to functions

Abstract

This article describes five lessons carried out by five residents as part of the Mathematics subproject of the Pedagogical Residency Program at a Federal University in the south of Minas Gerais, in a collaborative format, to address the introduction of the concept of function, under the guidance of the supervising and precepting teachers and the researcher from the Masters in Education at the same institution. The aim of this article, in addition to describing these lessons, is to analyze them, placing ourselves in the position of teachers who are researchers of our actions, highlighting the appropriation of Ole Skovsmose's theorizing on landscapes of investigation. To do this, we used the concepts of landscapes of investigation, dialog and the production of meanings as a theoretical framework for analysis, which were also discussed with the residents at the weekly team meetings to prepare their regencies. These meetings are part of the activities developed by the Mathematics subproject team and constitute a shared space for experiences. As a main result, we highlight that the different classes enable different ways of producing meanings based on the students' experiences with school content or experiences outside school and the team's production of meanings about the creation of landscapes of investigation in the classroom and the students' reading. The biggest difficulty the residents pointed out was establishing and maintaining a dialog and not providing answers to activities when they were asked. We believe that we have created investigative moments because at times there were landscapes of investigation and at others difficulties in maintaining them. The course on introduction to the role was fundamental for the other courses that took place afterwards, as this experience was decisive in proposing and trying to create new landscapes of investigation, taking into account the particularities of each class, and made the residents more attentive to the way they acted in the classroom.