Can I Bring My Calculator to the Exam? Some Reflections on the Abstraction Level of Computer Algebra Systems

Abstract

AbstractThe author began working with computer algebra systems (CAS) in the 80s to perform effective computations for his Ph.D Thesis in algebra. He thought at that moment that there would be an explosion in the use of CAS for research and teaching (at all levels of education). Surprisingly, its use in secondary education is still scarce. This article details some personal reflections on elementary mathematics questions (from both the mathematical and the computational points of view) and proposes a classification of such questions, illustrated with several examples. It is focused on some of the present impressive capabilities of CAS, underlining their abstraction levels in some eye-catching examples. The article is mainly aimed at mathematics teachers who are not experts in CA. Nevertheless, it may also be of interest to CAS experts, as it includes reflections on a topic not usually treated: the abstraction level achieved by CAS and its impact in teaching and assessment.