Ladrilhamento no plano : uma experiência de engenharia didática

Abstract

This work is linked to the project entitled “Mathematical and Interdisciplinary Investigations in Learning Projects” and aims to show the experience of undergraduate mathematics students in the tiling technique through the phases of Didactic Engineering. This research reports the development of a course conceived during the COVID19 pandemic and, for this reason, structured in a virtual environment, with remote activities in Geogebra Book software and synchronous in Google Meet. The purpose of the course is to encourage ways to explore principles and generalization of patterns from the composition of polygons in the plane through the technique of tiling. The target audience is made up of academics from the undergraduate mathematics course, enrolled in the sixth and eighth semester of the course. The objective of the course is to analyze the virtual learning environment with 4 students when submitted to a tiling activity through a didactic engineering. The theoretical-methodological conceptual conception is Didactic Engineering, through which the following phases were developed: previous analyses; design and a priori analysis; experimentation, a posteriori analysis and validation. The results showed that E.D. contributed to the expansion and construction of geometric mathematical knowledge, as it was possible to detect that academics understand in a contextualized way the relationship between elements of a regular polygon and their application in the tiling technique, as well as were able to carry out conjectures and representable generalizations through of statements and formulas.