Método de Newton-Raphson e raízes de funções polinomiais utilizando tecnologias em uma sequência didática no ensino médio

Abstract

The study of polynomial functions and their roots is very present and important in the final years of Elementary School, as well as in High School. However, the study of their behavior, graphs, and roots is usually quite limited to polynomial functions of degree 1 and 2. The present work presents a didactic sequence elaborated and applied in a second year of high school class of a public school of the State Education Network of Bahia, and uses the Newton-Raphson Method to obtain the approximation of roots of polynomial functions of different degrees. The didactic sequence was elaborated and applied with the objective of re-presenting the basic knowledge of functions, highlighting the polynomials of grades 1 and 2, previously known by the students. In addition, expand the field of studies to higher degree polynomials, using the technological tools and knowledge about the Newton-Raphson Method. As tools to assist in this endeavor, some Digital Technologies in Education were used, through the Geogebra software and Microsoft Excel spreadsheets, as well as their respective applications for the construction of graphs and spreadsheets (GEOGebra and Excel). The use of apps is highly feasible due to students' greater accessibility to mobile devices than computers. Throughout the development of the didactic sequence, it is possible to perceive a significant improvement in student engagement, as well as a greater ability to solve problem situations without the need for frequent teacher intervention. With the insertion of technological tools, it is noticeable how much the interest of students increases, especially in relation to the possibilities within Excel and its application. Thus, it can be seen that the use of Didactic Sequences in mathematics classes, in this work specifically in the study of the roots of polynomial functions and Newton's Method, is an enriching and satisfying teaching possibility. It is also noticed that the use of educational technologies is a strong ally in the resolution of several mathematical problems, enabling studies of contents a little more advanced than those regularly presented in High School, as in the present work.