Interpolação e regressão polinomial: uma proposta para o ensino médio com auxílio do Geogebra

Abstract

This work aims to bring a proposal for teaching interpolation and polynomial regression for high school classes. In this way, every theoretical part has as reference the National Curriculum Parameters (PCN) and authors such as Biembengut (2014), Ruggiero (2000), among others. With this, the work will be based on interpolation methods such as Lagrange and Newton, error study, choice of the degree of the interpolator polynomial, Runge phenomenon, inverse interpolation and polynomial regression by the least squares method. In addition, the area of mathematical education will also enter into the foundation of work through history, model, modeling and modeling as a teaching method, together with the help of educational software in the teaching of mathematics, in this case, Geogebra. Finally, a sequence of examples that can be worked on, discussed, proposed in research projects and in interdisciplinary classes in high school classes will be presented, using and comparing concepts of interpolation and polynomial regression. In this case, the activities are summarized in current studies and problems in our daily lives, such as the contamination curve by Covid-19, problems with the increase in the prison population in Brazil, an estimate of the fuel consumption of a car and projections on the Brazilian demography.