Didactical Engineering of the Second Generation: A Proposal of the Design and a Teaching Resource with the Support of the GeoGebra Software in Brazil

This article presents a partial excerpt from an ongoing master's research on the methodological theoretical aspects of problems related to the content of volumes, selected from the evaluations of the National High School Exam (ENEM). The Exam consists of a test proposed by the Brazilian federal government, which aims to assess the performance of students at the end of high school, in addition to being used as a selection criterion to enter higher education. In this way, a didactic situation is proposed in the context of ENEM structured in the Theory of Didactic Situations (TSD) and subsidized by the use of the GeoGebra software as a technological resource for the construction and resolution of the problem situation on the volume of a cylinder. The didactic session was consolidated in Didactic Training Engineering (EDF) and developed to design a didactic resource for teaching and training mathematics teachers. GeoGebra was used to carry out the didactic transposition of the problem, as it benefits the student to break the difficulties inherent in the understanding and appropriation of geometric concepts. This structure facilitates didactic mediation, in addition to giving a new meaning to the study and teaching of volumes in the context of ENEM assessments.