Expressiveness and Abstraction with Computer Algebra Software

informatiques de calcul symbolique et apprentissage des mathématiques”, Rennes, France Twenty years ago, Seymour Papert put forth a vision for how computer software could transform the learning of mathematics: The idea of ‘talking mathematics ’ to a computer can be generalised to a view of learning mathematics in ‘Mathland’; that is to say, in a context which is to learning mathematics what living in France is to learning French*. (Papert 1980, page 6) When I first read this, in 1994, it connected very powerfully with my work at that time, which was developing new mathematics curriculum for undergraduate students based on the computer algebra system (CAS), Mathematica. Surely (I thought) a CAS is the closest one can get to “talking mathematics ” with a computer? Was I standing on the borders of Mathland? Well, six years later I am still excited by Papert’s vision, but, of course, still a long distance from a realisation of Mathland. In this paper, I describe two curriculum developments undertaken by myself and colleagues at Imperial College in London (the METRIC project, i.e. Mathematics Education Technology Research at Imperial College). Through these two examples, I want to explain the principles by which we attempted to realise Papert’s vision with CAS. These principles are neither new, nor of any great theoretical complexity, but they should, I believe, be much better known amongst the community of “didacticians ” concerned with CAS software and CAS-equipped calculators