Descartes is an applet (a program written in Java) which can be configured. It has been designed to present educational interactive tasks with numbers, functions and graphs. Descartes can be used by creators of educational Web pages as a means of supplementing their material with a wide variety of interactive mathematic models.

Teachers can use Descartes to produce their own interactive Web pages, which cover a wide variety of subject areas within mathematics. For example, the following parabola graph has been created using the Descartes applet.

The values of parameter p can be changed, by using the p control arrows or writing the new value in the space and pressing the enter key. Note how the graph changes as it responds to these new values. Every time the parameter p is altered, the graph changes. In this way, we can see how greater values of p produce a more open-shaped parabola , whereas smaller values of p produce a more closed-shape graph. This first example is a typical Descartes applet application: a graph whose mathematical definition is dependant on a parameter and whose appearance changes when this parameter is altered.

Virtually all graphs of functions with one variable and of equations with two variables, which are covered during compulsory and post-compulsory secondary education, can be illustrated with the Descartes applet. However, Descartes is not just a way of illustrating graphs. It is also a way of helping students to understand the relation between equations, their graphs and their component parts. The applications included in this document show the great variety of possible uses that Descartes has.

Descartes is a work tool for mathematics teachers who want to create interactive lessons in Web page format. These lessons can be put onto an Internet server or onto the computer hard disk. The aim of the pages in this document is to act as a guide for teachers who want to learn how to use Descartes as a work tool and offer detailed technical information about this nippe.

The word nippe is formed with the initial letters of "núcleo interactivo para programas educativos" ( interactive nucleus for educational programs). More information about other nippes and general information about the idea of nippes can be found by consulting Proyecto Prometeo. Descartes is a nippe which means that it is a piece of software which can be used to create a wide variety of educational, interactive programs in Web page format. Each Descartes application is produced using a particular configuration.

Technically speaking, nippes are applets written in Java. An applet is a program which can be included on a Web page.  Descartes is an applet and its numerous applications can therefore form part of Web pages. However, Descartes is not just any old applet. It is an applet which can be configured. Each Descartes configuration produces a different interactive program, which is known as a window.

There is a detailed explanation of the tools needed to configure these windows in the information included with this document. However, it is not necessary to study all the information in this document in order to create applications with Descartes.

Configuring the tools is very straight forward and much can be learnt simply by looking carefully at the configuration in the examples given. Furthermore, in order to produce you own application, we recommend starting with a similar-looking application which can be adapted little by little until you reach the required result. For this reason, we suggest that the reader first consults the page appetizer, which explains how to adapt one configuration in order to create another, before going to the examples and technical information.

  José Luis Abreu León
Spanish Ministry of Education, Social Afairs and Sport. Year 2003