Introduction

Descartes is the name of a highly configurable applet designed to present educational interactions involving numbers, functions and graphs. Descartes may be used by authors of educational Web pages to enrich their materials with a great variety of interactive mathematical models. This Web is dedicated to the presentation of the applet Descartes, its documentation and some applications.

Using Descartes a teacher may create interactive Web pages on several areas of mathematics. For example, this graph of a parabola is made with the applet Descartes.

The reader can modify the values of the parameter p (clicking the control arrows for p or actually writing in the text box and clicking intro) and see how the graph changes in response to these modifications. Each time that the parameter p changes, the graph is updated.  This way the user can check that the large values of p correspond to a more open parabola and the small values of p give rise to a more closed parabola. This first example is a typical application of the applet Descartes: a graph appears whose mathematical definition depends on a parameter and on changing the parameter, the graph is updated.

The applet Descartes allows practical viewing of all the graphs of functions of one variable and of equations in two variables which appear in secondary education.  However Descartes is not only useful for viewing graphs, but it also helps to understand the relationships between the equations, their graphs and the various elements of which they are composed.  The examples and the applications which are presented in this document illustrate the great variety of possible uses of Descartes.

Descartes is a work tool for math teachers who wish to create interactive lessons in the format of web pages, already for being put on an internet server or on a computer disk. The intention of the pages which form this document is to offer a guide to the teachers for learning how to use Descartes as a work tool and a complete technical documentation of this nippe.

The word nippe is formed from the initials of "núcleo interactivo para programas educativos" (interactive core for educatonal programmes). To know other nippes and the general ideas which give rise to this concept, it is suggested that the reader should consult the Proyecto Prometeo. For Descartes to be a nippe means that it is a piece of software which allows the creation of a wide variety of interactive educational programmes on Web pages.  Every application of Descartes is obtained by means of a particular configuration.

Technically speaking, the nippes are applets written in the Java language.  An applet is a program which can be included on Web pages.  Thus Descartes is an applet and thatīs why itīs various applications may be included in Web pages.  However, Descartes is not just any applet, it is a configurable applet.  Each configuration of Descartes gives rise to a different interactive program.

To create a configuration of Descartes it is necessary to know its fourteen tools (LANGUAGE, COLORS, SPACE, PARAMETERS, VARIABLES, FUNCTIONS, CONTROLS, EQUATIONS, POINTS, SEGMENTS, CURVES, ARCS, TEXTS and BUTTONS) and to learn how to configurate them.  These tools are configurated by means of a simple language which is explained in detail in the documentation included in this document.  However, it is not essential to study all this document to create applications with Descartes.  The language for configurating the tools is very simple and can be learnt by looking at the configurations in the examples.  Whatīs more, for creating an application, it is recommended that you start with an application which bears a certain resemblance to that which you wish to create, and modify it bit by bit until you achieve the desired result.   For this reason, before the examples and the technical documentation, it is suggested to the reader  to study the page named appetizer, in which it is explained how to modify a configuration to create another.

Contents of the document.

The main objective of this document is to teach the reader how to create applications with Descartes.  These applications will be educational programmes in which graphs will appear and the pupil-user will be able to modify certain parameters, move some controls and see the effect that these modifications and movements have on the graphs.

To achieve this objective the document has been organized in five parts.

The first is this introduction.

The second part is called appetizer and is a page which explains how to create Descartes applications from other applications.

The third part offers some simple examples which illustrate what can be done with Descartes. It is not claimed that these examples are educational applications on their own, for that they would have to be surrounded by explanations for the pupils and be organized in accordance with some study plan.  The object of these examples is solely to illustrate, by means of very simple examples, the way to configurate the various Descartes tools and to show some of their possibilities.

The fourth part is the technical documentation of nippe Descartes. In this part, it is explained how to configurate each one of the fourteen tools:  LANGUAGE, COLORS, SPACE, PARAMETERS, VARIABLES, FUNCTIONS, CONTROLS, EQUATIONS, POINTS, SEGMENTS, CURVES, ARCS, TEXTS and BUTTONS.

Finally the fifth part consists of some applications which can be useful as examples of educational Web pages in which the most is made of the nippe Descartes

 Ministerio de Educación, Cultura y Deporte. Aņo 2000