Tangram nos livros didáticos de matemática: um estudo à luz da teoria de registros de representação semiótica

Abstract

The purpose of this research is to investigate how the use of tangram can contribute to developing skills related to the visualization of a figure, considering that seeing a figure from a mathematical point of view is different from seeing any figure. It is a bibliographical and qualitative research, in which the purposes are reached from the analysis of activities that involve the tangram in three collections of Mathematics textbooks, from the final years of Elementary School. Based on Raymond Duval Theory of Semiotic Representation Records, categories aimed at geometrical views and apprehensions are organized, which guide the analysis of thirteen activities, distributed heterogeneously in the collections. The analysis shows that the highest incidence of activities involving the tangram is in the sixth grade, with few activities addressing the tangram in the other three school years. As for the geometric apprehensions, the perceptive and the operative stand out, and the heuristic and visualization properties are enhanced as the tangram pieces are reconfigured, that is, when the semiotic reconfiguration operation is performed, the main figural treatment operated on the same. With regard to looks, the iconic botanist look stands out, responsible for recognizing and differentiating shapes, followed by the inventor look. In general, the activities explore the tangram as a heuristic figure or as a didactic resource, and in both cases, they enabled the mobilization of different geometrical perspectives and apprehensions, meeting Duval proposal for the teaching of geometry.