Elementary algebra as a modelling tool: A plea for a new curriculum

Abstract

Elementary algebra is the foundation on which the entire modern mathematical edifice rises. But the algebraic curriculum fashioned by the process of didactic transposition for more than a century is no longer able to ensure this essential function. The present study focuses on the notion of formula and how its curricular evolution appears to be a witness and a cause of the degradation of taught algebra as a modelling tool. This examination involves careful analyses of curricular facts that seem not to have attracted the full attention of researchers, such as the deparametrization of algebra or the unplanned effects of its encounter with mathematical analysis. Drawing on the anthropological theory of the didactic (ATD), this allows to outline the perspective of an imperative reinvigoration of the algebraic curriculum.