Banca de DEFESA: MARCEL MUNIZ VILACA

DEVELOPMENT OF GEOMETRIC THINKING: ANALYSIS OF A DIDACTIC SEQUENCE EXPERIENCED IN GEOGEBRA TO APPROACH NOTABLE QUADRILATERS

Didactic Sequence; Notable Quadrilaterals; Geometric Thinking; GeoGebra.

The present research sought to analyze the contributions of a didactic sequence for the development of geometric thinking of 9th grade students in the final years of elementary school when working with quadrilaterals in GeoGebra. The investigation was divided into 3 stages: the first consisted of applying a diagnostic test with 20 students (divided into 10 pairs) of the 9th grade of a private school in the Metropolitan Region of Recife, which made it possible to identify evidence of the level of geometric thinking mobilized by each participant. The second moment consisted of the elaboration and experience of a didactic sequence involving the notable quadrilaterals and the use of GeoGebra. The third moment mobilized the application of a final diagnostic test that made it possible to identify the development of the geometric thinking of the research participants. In all stages, requests from the work of Pereira da Costa (2019) and his model of levels of development of geometric thinking were used to categorize and analyze the opportunities and evolutions acquired by the group of 20 students during the different stages of the research. The results obtained in the initial diagnostic test - TDI show that students do not consider the characteristics of quadrilaterals during their experiences and recognize them by their visual appearance (cerebral perceptual abstraction). This way, they were predominantly at level n of Pereira da Costa's (2019) model and were unable to use class inclusion criteria when addressing notable quadrilaterals. After the TDI, the activities of our didactic sequence were experienced in GeoGebra and then a final diagnostic test - TDF was applied. The main results show that the didactic sequence contributed to the development of the participants' geometric thinking by revealing that the students started to use class inclusion criteria when dealing with activities involving the notable quadrilaterals. The data obtained in the TDF show a significant increase in the amount of adequate answers, when compared with the results of the TDI and indicate that most students managed to advance from level where they were to n+1 and n+2. There was also an advance in predominantly mobilized geometric abstractions (perceptual) for analytical and descriptive ones. Among the main elements responsible for this increase, in addition to the activities structured in the light of the model by Pereira da Costa (2019), we highlight the dynamicity of GeoGebra by allowing students to establish relationships by “dragging” elements of the quadrilaterals by identifying the properties that remain unchanged and those that undergo modifications with these movements.