Aprendizagem significativa: uma proposta para o ensino dos números racionais no sexta ano utilizando representação semiótica

Abstract

This research was developed based on an investigative study in the Master's degree course in Science and Mathematics Teaching of the Graduate Program in Science and Mathematics Teaching (PPGECM) at the University of Passo Fundo (UPF). The objective of this study is to develop, implement and apply a didactic sequence aimed at the sixth grade of elementary school, addressing rational numbers and their two representations, building solid concepts, establishing relationships between the different forms of representation with the aim of creating potentially meaningful material. The problem that generated the study reflects on the difficulty students have in understanding the representations of rational numbers, in which the same value can be represented in fractional, decimal, percentage and also in drawing form, requiring a good understanding of the concepts from the beginning in order to assimilate and transition between these forms of writing a quantity. Considering the importance of this understanding and its usefulness in our daily lives, we sought support from Raymond Duval's Theory of Semiotic Representation Registers (TRRS) and David Paul Ausubel's Theory of Meaningful Learning (TAS) to answer the following question: "How can a didactic sequence supported by the theory of semiotic representation registers constitute potentially significant material for the development of learning of rational numbers in the sixth year of Elementary School?" Thus, the TRRS was used to work on the different forms of representation of the same quantity and the TAS was used to construct significant learning in this process. This didactic sequence was applied to a sixth-grade class in a state school in the city of Passo Fundo/RS. The data used to analyze the material were divided into the following categories: subsumers, previous organizers, progressive differentiation and integrative reconciliation, student predisposition and application in new contexts. The nature of the research was classified as qualitative, since the evaluation of the potentially significant material was done through the activities of construction of materials by the students themselves and transition activities, thus identifying the signs of significant learning. The results obtained indicated that the didactic sequence consisted of potentially significant material, through the identification of the participants' subsumers, the connections between what was known and what was new through the previous organizers, the possibility of differentiating the concepts and then integrating them; consequently, they were interested in learning and applied the knowledge in new contexts. From this perspective, the study gave rise to support material for teachers, which consists of the educational product of this dissertation, which is available for download (http://educapes.capes.gov.br/handle/capes/746124).