GeoGebra as learning tool for the search of the roots of functions in numerical methods

Abstract

Physics is capable of describing, through equations, phenomena on a micro and macroscopic scale. However, most of these equations are non-linear and the identification of their roots requires the use of approximation methods, with numerical methods being a proposal based on a systematic and iterative process, that conclude only when a pre-established tolerance is satisfied. Traditional teaching of numerical methods involves the memorization of algorithms. However, this hinders student's ability to understand the important aspects and then apply them for solving applied problems in subjects such as kinematics, dynamics, electromagnetism, etc. Therefore, this work proposes the use of GeoGebra, as a didactic tool to illustrate the functioning of single root searching algorithms. By using the dynamical graphic's view of GeoGebra, a series of abstract and applied problems where solved by engineering students taking a numerical methods course. The scores of this test group was then compared to a test group, taught trough algorithm memorization. Results show can improve their understanding of how the bisection, false position, secant, and Newton-Raphson methods are able to find approximated solutions to polynomial and trigonometric equations. The results are compared against traditional learning, based on memorizing the steps of the algorithm for each method and the representation of the convergence of successive roots by numerical tables.