Learning circumference concepts from the didactical situations theory perspective

Abstract

The circumference study, as its importance, it is one of the most relevant contents in the Analytical Geometry curriculum. However, the complexity of related concepts to this theme linked to the content fragmentation, it difficulties the students thinking of transforming geometrical problems into equations solution, systems or inequations. Within, in this article we present a partial report of a master research work, of qualitative mode, which aimed to develop and to evaluate an alternative methodology by using musical parody composition to the teaching of Mathematics in trying to contribute to the circumference concepts learning process. For that, we carried out a case study with 36 third year high school students of a public school from the city of Campina Grande, Paraíba. The research work was based and discussed on Brousseau Didactical Situation Theory. It was chosen triangulation technique for the data analyses, collected from interviews, questionnaires and a list of mathematical exercises. We concluded that the parody composition resource allowed the students better understand the concepts of center, ratio, cord and the definition of the general circumference equation, as they were capable to identify the relative positions which a circumference assumes in relation to an equation of a straight line and between two circumferences in the various concepts that differentiated them. Thus, we can state that the musical parody composition as a didactical resource can contribute to the learning of mathematical contents.