# Teaching Basic Calculus Using SAGE

Katerina Tsarava (University of Macedonia, Greece), Spyros T. Halkidis (University of Macedonia, Greece & Model Experimental School of the University of Thessaloniki, Greece), Pantelis Venardos (Model Experimental School of the University of Thessaloniki, Greece) and George Stephanides (University of Macedonia, Greece)
DOI: 10.4018/978-1-4666-4233-1.ch014

## Abstract

This chapter presents an attempt to review basic calculus concepts to high school students with the help of a Computer Algebra System, namely SAGE. A review lesson on limits and derivatives as well as an introduction of the bisection method for finding roots of continuous functions is presented. The evaluation of the lesson by the students is analyzed. The aim of this chapter is to examine the power of SAGE in reviewing basic calculus concepts, presenting the advantages and disadvantages of SAGE compared to other Computer Algebra Systems, as well as the benefit from using a computer system in making concepts such as the squeeze theorem for computing limits of functions more clear.
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## Literature Review

The use of Computer Algebra Systems in Modern Education is commonplace nowadays. A lot of research has been devoted to examining the impact of these systems in the learning process of mathematics in the classroom.

Meagher (2005) has examined in his Ph.D. thesis the learning process of factoring, solving equations, multiplying polynomials, taking derivatives and calculating limits using Mathematica.

Vlachos and Kehagias (2000) have evaluated the teaching of business calculus using MathCAD.

Kramarski and Hirsh (2003) have tested the process of solving equations in junior high school using traditional teaching an compared it to teaching using a computer algebra system.

Dana-Picard and Kidron (n.d.) describe a pedagogical process for examining the learning techniques assisted by a Computer Algebra System in the first year foundation courses of an Engineering College.

Brown (n.d.) provides us with an evaluation of teaching algebra in high school using a TI 92 mathematical computer.

Finally, Fuchs (2001) gives a restricted overview of the influence of Computer Algebra Systems in Mathematics Education.

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## Selection Of The Course Material And Justification

The course material selected included limits of functions, derivatives of functions and the bisection method, based on the Bolzano theorem (Apostol 1967).

The basic reason for selecting the specific material was that this material was already taught in a conventional course.

One basic reason for selecting limits and derivatives of functions for the course was the ability of SAGE to present illustrative plots of functions. Although a plot does not provide us with a proof that a mathematical function has a specific limit and/or a specific derivative, it can give us some intuition about this issue. The functions that were selected for illustration were functions that do not encompass smooth behavior and therefore plots of these functions may prove useful.

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