A computer program for the learning of algebra: description and first experiment
Résumé
We present APLUSIX, a computer system that helps students to learn algebra, available at http://aplusix.imag.fr. APLUSIX contains an advanced 2D editor of algebraic expressions that allows students to make the calculations (s)he wants, like in a paper-pencil context. The system verifies the student's calculations, by calculating the equivalence between two consecutives expressions, and shows the result to the student. It provides information concerning the progress of the resolution. Furthermore, the students can use commands like Reduce, Expand to ask the system to make some particular calculations. So APLUSIX combines features of a Microworld and of a CAS (Computer Algebra System) for education. This system has a lot of parameters allowing the teacher to choose the way it works. In particular, the teacher may active or not the verification of the equivalence between calculation steps, the progress indicators and the commands, to suit its own teaching strategy. We present also an experiment of the APLUSIX system realised in September 2002 with ten classes of 15 to 17 years old students (grade 9, 10, 11) on the following tasks: expand or factor polynomial expressions, solve equations, inequalities or systems of linear equations. We describe the influence of some parameters on the students' behaviour and statistics concerning the work of the ten classes. We have observed and analysed the resolutions of the students. The analysis was made by replaying their actions (they are recorded by the system). We present some results of this analysis. Last, we summarize an inquiry among the teachers who participated to the experiment
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