O uso de materiais didáticos à luz da teoria dos registros de representação semiótica: abordagens para o ensino de tópicos da teoria de conjuntos e da geometria plana

Abstract

This research aimed to investigate possible uses of Concrete Manipulatives (CM) in light of the Theory of Registers of Semiotic Representation (TRSR) in the teachinglearning process of mathematics with the purpose of developing Didactic Sequences of topics from Set Theory and Plane Geometry that contemplate CM aligned with TRSR. To this end, a study of the aforementioned theory, proposed by Raymond Duval, was carried out based on his efforts to investigate mathematical learning taking into account a basis on representations in the area of Semiotics and based on cognitive studies of learning by Jean Piaget. In this context, semiotic representations refer to particular systems of signs, such as language, algebraic writing and Cartesian graphs. Semiotic representations of a given system can be converted into “equivalent” representations of another system, but they can also take on different meanings. Among the semiotic systems, those that allow three cognitive activities (formation, treatment, conversion) are exactly those in which the existence of different registers is possible. In light of this theoretical approach, the apprehension of a mathematical concept is only possible through coordination, that is, the use of several representation registers and the transition between different registers. For educational purposes, what is important is not the representations themselves, but the student’s ability to transition naturally between them. Therefore, in this research, the concrete manipulatives were adequately characterized, since they constitute the initial object of interest that resulted in the proposition of this undergraduate thesis. As objects, such manipulatives “incorporate” some characteristics of the concepts to be learned. Initial proposals for approaching mathematical concepts present in textbooks were explored and, as a result of this analysis, the concepts, registers and concrete manipulatives that guided the elaboration of the Didactic Sequences were delimited.