Análise dos níveis do pensamento geométrico dos estudantes ingressantes em um Curso de Licenciatura em Matemática na perspectiva de Van Hiele

Abstract

It is not new that Mathematics is considered by many to be difficult and abstract, and geometry stands out among the dreaded contents of mathematics, whether due to the difficulties of teachers in teaching them or by students in understanding them. The teaching of geometry has been the subject of research for over 30 years, and remains current, being the object of study to understand the development of geometric thinking or addressed through digital technologies, methodologies and differentiated resources. Thus, the present research aimed to investigate the level of geometric thinking of students entering the first year of the Bachelor's Degree in Mathematics at a Public University of Paraná, with Van Hiele's Theory as its theoretical foundation. For this purpose, students' own cell phones were used to carry out activities developed with the GeoGebra application for Android. This research has a qualitative approach of exploratory nature and was developed through the participation of academics in the development of 19 activities divided into 4 levels: level 0 (visualization), level 1 (analysis), level 2 (informal deduction) and level 3 (formal deduction) and the corresponding skills indicated in the theoretical framework. From the analysis carried out with the data collected from the activity resolutions, it can be concluded that the participants reached level 1, with the graphic skill being the most developed and the logic needing to be improved. For levels 2 and 3, the number of activities delivered by the two classes was well below expectations and due to the low representativeness of the sample, the inferences pointed out at these levels cannot be generalized to the classes. The results regarding the skills of levels 2 and 3 more and less developed seem to remain the same as the previous levels. In this small sample, academics show the skills partially developed in relation to levels 2 and 3 of the development of geometric thinking, but it is noteworthy that in level 3, the logical ability was zeroed. The results presented are worrisome because these lags can harm students in future content and even in future classes that these academics will teach. Finally, we highlight the importance of developing studies that use Van Hiele's Theory, as it enables a better understanding of students' geometric thinking and thus facilitates decision making in the classroom, with a focus on learning the concepts in Geometry.