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Jean-Baptiste Lagrange
My involvement in research and development in the teaching and learning of advanced mathematical topics is at upper secondary level before university. In France, at this level, students have to consolidate their algebraic proficiencies in order to tackle pre-calculus.
The curriculum recommends non formal approaches of calculus concepts, but also that students should be introduced to abstraction and demonstration. It is then not easy to think of the role of algebraic techniques with regard to conceptualization. Rehearsing rote techniques certainly does not help, but it is important that students understand the equivalence of expressions and the benefit of algebraic transformations. They should also be able to perform basic transformations without too much difficulty in order to handle problems with inventiveness, intelligence and rigour.
My research group is developing and experimenting a Dynamic Geometry and Computer Algebra tool (Casyope). This tool can be described as a symbolic calculator of functions and it is also designed to help students deal mathematically with problems of geometrical dependencies (for instance the area of a figure against a length of a segment). We are currently experimenting on a series of lessons with this tool at 11th grade. We prepared specific tasks for helping students to develop algebraic techniques and reflect on these. We expect to learn about the role these development and reflection can play in students conceptualisation of advanced notions.
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