Extensions praxémiques liées aux ensembles de nombres : des complexes aux relatifs

Abstract

This paper focuses on the learning and teaching of negative numbers. This topic has been intensively studied using, among others, theoretical frameworks stemming from psychology - we give a summary of those researches in the first part of the paper. It is our aim to point out the peculiarities of a purely didactical approach. We do so using didactic concepts and most notably that of a praxemic extension. This concept will be put to use to bring to light the kind of problems and/or debates teachers and students have to face when dealing with extension of sets of numbers. This is made possible by contrasting negative numbers with complex numbers – hence the title. Lastly we expose the main lines of two didactic engineerings, closely related to the praxemic extensions analyzed above, and show what kind of shape they display when they are cast in contrasting curricular settings.