An investigative activity about polygons: reflection about unpredictabilities that promoted learnings

Abstract

The main objective of this text is to introduce a reflection about the unpredictability in Mathematics classes. The episode reported is part of an undergraduate final project of a Mathematics Teacher Education course from a public University, whose main objective was to characterize Mathematics class in which students were involved in situations of investigation, exploration and discoveries. This study is based on the works of Ponte (2003), Ponte, Brocardo and Oliveira (2016) that treat investigations in Mathematics classes and on the studies of Skovsmose (2000) with the concepts of landscape of investigation, risk zone and comfort zone. As a methodology, an exploration and investigation activity about polygons was implemented with 5th grade students from a public school in São Paulo. The development’s characterization of the activity was described after the class in an internship notebook. Considering the activity applied, it was possible to conclude that unpredictable situations place the teacher in a risk zone and it should not be avoided, because it can establish a collaborative way of work between teacher and students and also provide learnings to the teacher. In fact, it was what occurred to the teacher and the prospective teacher whose knowledge of the definition of polygons were increased. They could relish the encountered opportunities throughout the implementation of the activities and, therefore, discuss it with students.