# LEARNING MATHEMATICS WITH EXCEL

M. Oliveira^{1},

S. Nápoles^{2},

E. Ralha^{3}^{ 1}Escola E.B. 2,3 Piscinas Lisboa; Member of the Mathematics Center at Minho University (PORTUGAL)

^{ 2}Dep de Matemática, Faculdade de Ciências, Universidade de Lisboa Collaboration in the mathematics communication area with CAUL and CMAF Univ. Lisboa. (PORTUGAL)

^{ 3}Dep de Matemática, Cmat, University of Minho (PORTUGAL)

The technological development of our society has not only lead to a significant evolution in methods that allow us to use the results of the existing mathematical theories but it has given place to new areas of application and new fields of research in mathematics. Hence, it becomes evident that, just as mathematics and its applications, mathematics communication cannot be indifferent to the fast technological growth of modern societies integrating new mathematical models and procedures.

In this perspective, mathematics communication must be continuously updated demanding new computational means which make easier and more efficient the process of teaching and learning mathematics, starting from classical models and integrating new ones.

The work we have been developing in collaboration with Universidade do Minho aims to show that, in the same way that the understanding of an algorithm of an operation is important for its use, certain mathematical problems can be better understood when a computational program is developed to analyze it. In spite of the existing animated modules currently available in commercial circuits, which can be advantageous for the understanding of mathematics, we sustain the hypothesis that there are more benefits when these computational modules are constructed by the end user as a result of mastering of the mathematical concepts acquired.

In this presentation, we provide a brief description of an IT project that has been implemented in a public school in Lisbon, Portugal - “Dynamic Mathematics”.

This project was developed during the last school year with two seventh grade classes.

MS-Excel and in few cases Geogebra (freeware) were the computer programs chosen to develop this project. They can be used across the mathematics curriculum resulting in no need to use different software when teaching different concepts for different school levels.

The "Matematica Dinâmica" project remains focused on the students, and on improving their understanding of mathematics by directly developing applets manipulating software. Another objective of this project is to guide students to learn mathematics on their own, by using sketches to explore properties, comprehend features of mathematical objects, and understand theorems.

The examples presented as well as the whole work developed throughout the school year in the scope of this project, including the applications developed by the students, are placed on the website:www.matematicadinamica.com.

To further illustrate our goals, we present two examples that can be used in different school contexts adjustable to the level of the students we are teaching.

The aim of the first example is to build an application in Excel which provides the study of the convergence of the sequence of the areas of regular polygons inscribed and circumscribed to the circle, inspired on the process Archimedes used to calculate a approximate value to Pi.

The second example concerns the study of the oscillatory motion of a pendulum to illustrate the important role of differential equations in mathematical modeling of physical phenomena and the interest of the development of computational modules using a spreadsheet, an excellent tool to support structural modeling and analysis of results.