Recursos didáticos para números complexos na perspectiva da teoria dos registros de representação semiótica

Abstract

In this work, a study was developed with the objective of creating didactic resources for the teaching of complex numbers that allow the use of different types of semiotic representation. The dissertation is composed of an introduction, three independents chapters, final remarks and two educational products. In the first chapter, there is a bibliographic survey of dissertations and theses, together with the Theses Bank of the Coordination for the Improvement of Higher Education Personnel (CAPES), about alternatives for teaching complex numbers. In the second chapter, a didactic sequence (DS) was presented, composed of four thematic and interdisciplinary tasks for the teaching of complex numbers, for the third year of high school, evaluated by the author according to precepts that can characterize it as an Investigative Didactic Sequence (IDS). The third chapter discusses the potential of the Trincas Complexas game to understand the geometric meaning of addition, subtraction, multiplication and division operations with complex numbers in algebraic form and their respective conversions into graphical representations with vectors. Both the DS and the games created were based on the theoretical assumptions of the Theory of Semiotic Representation Registers (TSRR) - which consider that the teaching and learning of mathematics require work with a diversity of representations, and, in the stages of the Theory of Didactic Situations (TDS) - which seeks to promote reflection on the relationship between teaching content and educational methods. It is believed that both the SD composed of the tasks and the game have the potential to reduce learning gaps in the visualization of graphical representations of algebraic operations with complex numbers.