Seções cônicas: uma sequência didática no ensino médio utilizando o geogebra

Abstract

Conics are used as tools in various situations, both in mathematics and in other areas of knowledge (physics, engineering, architecture, astronomy, etc..). It's a rich topic in its constitution because it allows many practical applications. This work aims to provide the teacher of high school mathematics teaching sequence for teaching conic using the software GeoGebra. In this sense we construct this sequence considering theories Change Tables Régine Douady (1987) and the Didactic Transposition Yves Chevallards (1991) where we discuss the interactions between different frames, especially the algebraic and geometric, visualized with the software and also the use of the history of conic sections and their applications in other areas such as motivating factor for the students in this topic. The methodology was through literature, considering national and international works with special attention to the content conic, questionnaire design in order to diagnose whether students, the third year of high school, have studied the contents of analytic geometry that are required for the theme conic sections, covering also the point of view of these students about the importance of conic sections in other fields of knowledge. Furthermore, an analysis of four textbooks approved by the MEC in order to see how they bring to the classroom the conic sections as knowledge to be taught and how these applications work works in the daily contents of this and other areas knowledge. The research in the classroom was accomplished by applying the instructional sequence with students of the third year of high school in a public school in the interior of Alagoas, with the holding ten meetings scheduled for implementation. The results obtained allow us to state that this form of teaching this content can, in fact, contribute to effective learning. We hope to contribute to mathematics teachers to make the teaching of this subject more interesting.