O jogo da senha numérica: uma proposta para o ensino dos princípios multiplicativo e aditivo baseada na teoria dos registros de representação semiótica

Abstract

This research sought to align three theoretical perspectives: games in Education, the concept of Research in Mathematics Education and Duval's Semiotic Representation Register Theory as forms of contribution to teaching the Multiplicative and Additive Principle of Combinatorial Analysis content for 8th grade classes. year of Elementary School. As for the methodology, the research is qualitative and descriptive in nature, in which a version of the MasterMind game, also known as the Numerical Password Game, and an investigative activity based on the game were developed and built, in search of a different way to teach proposed content. As a result, its development process was highlighted throughout the proposal, providing guidance for teachers who teach mathematics regarding the application of the game and the investigative task based on the game, in which the representation of data using tables, trees of possibilities and ordered lists, for example, they are resources that can make the student observe the statement of the question and, thus, choose a resolution method. These representations, that may be present in the combinatorial analysis content can be used in the context of TRRS. Thus, we can describe the different mathematical representations that are means of accessing mathematical objects. The game version, the development of the investigative sequence and the different representations of a possible password construction can open a way for students to explore the representation registers, promoting the construction of the concept of Multiplicative and Additive Principles. The Password Game version proved to be a good teaching resource that allows different possibilities for working on the content. These strategies highlighted a possible path to understanding for students.