Propostas de atividades de estudo e pesquisa para o estudo das funções trigonométricas seno e cosseno no âmbito de um curso de Licenciatura em Matemática

Abstract

The objective of this research was to analyze possibilities of Study and Research Activities that aim to enhance the learning process of the Sine and Cosine Trigonometric Functions. Thus, it was achieved through the validation of a Proposal for an Alternative Didactic Model and in the discussion and use of mathematical organizations planned for these activities, in addition to the emergence of others. The general objectives to achieve it were: to carry out the study of the historical and epistemological elements inherent to the Sine and Cosine Trigonometric Functions; to analyze the design of the Dominant Praxeological Model - MPD and its reflections in the scope of the Sine and Cosine Trigonometric Functions; and; to develop and analyze Study and Research Activities - AEP that aim to enhance the learning of the Sine and Cosine Trigonometric Functions. Thus, it was guided by Yves Chevallard's Anthropological Theory of Didactics - TAD and its methodology is at the core of the Study and Research Path Engineering - PEP and Study and Research Activities - AEP. The research was developed with students from the 1st and 2nd semesters of the Mathematics Degree course at the State University of Feira de Santana. Through the historical and epistemological study, an Epistemological Reference Model (ERM) was identified and it was noticed that the reason for studying the Sine and Cosine Trigonometric Functions had been lost due to social causes, which may be related to the difficulties in learning this knowledge. Thus, based on the Epistemological Reference Model and the Dominant Praxeological Model, which showed how knowledge is currently positioned, Study and Research Activities were developed for the study of the sine and cosine functions, integrated with the GeoGebra and Blooket software and manipulable materials, involving the elementary concepts of Trigonometry and periodic phenomena. These two models were analyzed to build the Alternative Didactic Model. Based on the results, the hypothesis “studying through Study and Research Activities – AEP integrated with manipulable materials and technologies favors the learning of Sine and Cosine Trigonometric Functions” was proven and the moments of constitution of the theoretical-technological environment referring to the technique and institutionalization and the dialectics of the individual and the collective and the media and the environments or of conjecture and proof were evidenced in the experiment.