Fragmentos de uma pesquisa – desafios geométricos, geogebra e "régua e compasso": estudando geometria por meio de construções de mandalas geométricas

Abstract

In this dissertation we bring text fragments that, as a whole, build the narrative of our research. Connecting fragments at this moment, after experiencing the serious health crisis caused by the COVID-19 pandemic, seemed to us the most sincere and honest way to report what we experienced. The interconnected fragments lead us to the research reported here, that observed the participation and movement of teachers, in continuing and/or initial training, involved with the teaching of mathematics in basic education, in the geometric construction workshops developed by us. The workshops were conceived before the pandemic and reformulated during it, according to the observations we have made and guided by the current sanitary conditions. From the face-to-face workshop to the workshop to be conducted remotely, we sought to maintain the founding concepts: to solve challenges, involving participants in exploratory and investigative processes that would trigger, in the course of the workshop, the mobilization of a list of knowing and knowledge (already acquired or under construction) about geometric constructions. The starting point was the Mandalas that could be decomposed into basic geometric constructions. The teaching methodological proposal bet on the complex-simple dialectic relationship – mandalabasic geometric objects – intrinsic in the construction of knowledge. The research aimed to observe and seek to understand the mobilization or not of knowing and knowledge by the participants of the workshops in solving the geometric challenges, combining Geometric Design with the use of traditional tools “ruler and compass” and GeoGebra software. This text brings together the processes in which the workshops were conceived, their initial formulation and reformulations and, finally, the observations of the researcher of the workshops in face-to-face and virtual formats. It is noteworthy that the experiments, face-to-face and virtual, even in different scenarios and with certain limitations managed to promote a collaborative learning environment where it was possible to provoke discussions and observe mobilization of knowledge about the geometric elements present in the construction of the structures. Mandalas. To publicize part of this work, we prepared a book, the educational resource, entitled Geodalas: Desafios Geométricos – Mandalas com régua, compasso e GeoGebra, where we gathered the Geometric Constructions of Mandalas, their resolutions and suggestions for Mathematics teachers.