Denis Bouhineau

Mixing Microworld and Cas Features in Building Computer Systems that Help Students Learn Algebra

We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these calculations. This requires an advanced editor for algebraic expressions, an editor for algebraic reasoning and an algorithm that calculates the equivalence of two algebraic expressions. A second feature typical of microworlds is the ability to provide students information about the state of the problem in order to help them move toward a solution. A third feature comes from the CAS (Computer Algebra System) paradigm, consisting of providing commands for executing certain algebraic actions; these commands have to be adapted to the current level of understanding of the students in order to only present calculations they can do without difficulty. With this feature, such a computer system can provide an introduction to the proper use of a Computer Algebra System. We have implemented most of these features in a computer system called aplusix for a sub-domain of algebra, and we have done several experiments with students (mainly grades 9 and 10). We had good results, with positive feedback from students and teachers. aplusix is currently a prototype that can be downloaded from http://aplusix.imag.fr. It will become a commercial product during 2004.

The Aplusix-Editor: A New Kind of Software for the Learning of Algebra

The first part of the paper presents our conception of a new kind of software for helping students to learn algebra. Such software has three main characteristics. First it includes an advanced editor that allows the student to build easily algebraic expressions. Second it reifies the students reasoning as a tree. Third it verifies the students calculations. In the second part, we present the Aplusix-Editor, a system of that kind that we have realised, and we describe the first tests of this system.

Helping teachers generate exercises with random coefficients

First, we propose two taxonomies concerning software designed for teaching mathematics, which we call Technology Enhanced Learning (TEL) environments, the first one concerns the teachers place and role in TEL environments, the second one concerns the activities which are foreseen and provided by TEL environments. Second, we consider TEL environments which provide teachers with tools for building patterns of exercises used in the TEL environment to generate randomly and dynamically exercises or lists of exercises. Our approach is compared to classical approaches (based on standards like IMS-QTI or on Computer Algebra Systems).