Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities

Ana M Martín-Caraballo,Ángel F Tenorio-Villalón

doi:10.29333/iejme/291

Abstract

This paper exemplifies the potential of GeoGebra as didactic resource for teaching Mathematics not only in High School but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative) methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position) method and the tangent (or Newton-Raphson) method, this last as example of fixed-point methods.

Highlights

Pablo de Olavide University (UPO) has been developing its teaching activities according to the framework of European Higher Education Area (EHEA) for the last six years
Bermudo et al (2006) proposed a planning and organizational model for Mathematics and Statistics courses. This model was based on students’ autonomous work by using several techniques and tools to asses and to monitor students’ academic activities. They emphasized that teachers should be considered as advisors and managers for students’ knowledge, since students turn into leading actors in their education and training, following recommendations in official documents about degree implementation in Spain – see ANECA (2005) and MECD (2003)
We show one of the uses given to Information and Communication Technology (ICT) in our courses: the application of GeoGebra as a didactic resource which allows us to explain some notions to students by manipulation of concepts and problems which makes easier their subsequent assimilation

Summary

INTRODUCTION

Pablo de Olavide University (UPO) has been developing its teaching activities according to the framework of European Higher Education Area (EHEA) for the last six years. This model was based on students’ autonomous work by using several techniques and tools to asses and to monitor students’ academic activities They emphasized that teachers should be considered as advisors and managers for students’ knowledge, since students turn into leading actors in their education and training, following recommendations in official documents about degree implementation in Spain – see ANECA (2005) and MECD (2003). Despite the existence and use of these digital resources, students must learn to correctly apply traditional problemsolving algorithms, but not with problems involving to spend more time than necessary and consisting in computation-based exercises These latter do not allow us to check and assess if students have assimilated the notions and procedures or if they can modelize real-world problems as mathematical problems, translating mathematical solutions into real-world solutions. We show one of the uses given to ICT in our courses: the application of GeoGebra as a didactic resource which allows us to explain some notions (about numerical analysis) to students by manipulation of concepts and problems which makes easier their subsequent assimilation

USING ICT IN OUR MATHEMATICS COURSES

Bisection method

Secant method

Using GeoGebra to teach numerical methods

CONCLUSIONS