Semelhança matemática: significados a partir dos registros de representações semióticas

Abstract

The teaching of Geometry is essential for students' education and is a subject of debate in the field of Mathematics Education, as it can enhance competencies and skills related to visualization, observation, measurement, comparison, and abstraction of shapes and space within a context of inquiry and problem-solving exploration. Thus, this dissertation aims to analyze the understanding of Mathematical Similarity demonstrated by first-year high school students, based on the Theory of Registers of Semiotic Representations (TRRS). It provides brief considerations on the teaching and learning of Geometry in Basic Education, drawing from authors such as Pavanello (1996), Smole et al. (2000), Fonseca (2001), Huete and Bravo (2006), Eves (2011), Iezzi et al. (2015), Monteiro (2015), among others. The research is qualitative in a diagnostic modality, conducted with students from four (04) first-year high school classes in the city of Santa Luzia, in the interior of Paraíba. Data were collected in a single meeting, during which the research instrument was administered. This instrument included eleven (11) questions and considered the multiple ways in which students can approach and understand the concept of Similarity, aiming to promote a deeper understanding of Mathematics. The data analysis was grounded in TRRS. The students' responses were organized and analyzed, taking into account the three cognitive activities related to semiosis: the formation of an identifiable representation, processing, and conversion. After the data analysis, a didactic sequence was developed in light of TRRS, allowing for various representations of the concept of Mathematical Similarity, with the goal of contributing to a better grasp of the concept under study.