O ensino de funções trigonométricas através da resolução de problemas

Abstract

The Brazilian high school, particularly in São Paulo State, has as general objectives the deepening the concepts studied in elementary school, making the student able to continue their studies in higher education and / or vocational courses. In addition, objective the development of critical student's ability to use the mathematical knowledge / concepts studied to understand and solve real situations of their daily lives. However, it is common to see in our schools, students subjected only to the resolution of repetitive exercises, called by George Polya of "routine problems". Consequently, the development of their criticality and their logical / deductive reasoning are affected, not to say, forgotten as goals to be achieved. The research, at the level of Professional Master Degree, reported here was aimed at the "investigation of possible contributions to a methodology based on Problem Solving Theory may have towards the teaching and learning process of trigonometric functions, as well as with the development of mathematical reasoning students of the 2nd year of high school". To this end, it was formulated three issues to be investigated during the course of the research. Are they: (1st) What should be done to generalize the concept of trigonometric ratio (sine, cosine and tangent), studied in the right triangle to the trigonometric cycle? (2nd) How should the transition be held generalization preceded the trigonometric cycle for the study of trigonometric functions in the Cartesian plane in a logical and deductive way? (3rd) What is the contribution that this research brought to my teacher training in math, methodological and didactic perspectives? The investigation results show that the involvement of students in the search for solutions to the problems posed, increased understanding of mathematical concepts worked as well as their application in their everyday situations. Finally, from the my professional training perspective, the research has shown that, when driving the Teaching Process and Learning of Mathematics, from problems "non-routine" and contextualized, the chances of improvement in the understanding and application of mathematical concepts worked as well, interest and involvement of students increased significantly.