This research compares the differences between the effective methods used by two specialised teachers working in IME (Instituts médicaux-éducatifs = Mental Retardation Institutes) with handicapped teenagers. The goal is to determine if these two teachers display specific lines of conduct, and to localise some of the aims of their action, during a mathematics sequence. Our study is anchored in compared didactics and more precisely in the TACD (Théorie de l’action conjointe en didactique = Joint Action Theory in Didactics), initiated by Sensevy (2007, 2011). In this article, we shall focus our reflection on the offside phenomena (Sensevy, 2011). Basing ourselves on two cases, we differentiate two types of offside that are produced by the pupils. So the results of the research shed light on the specific relationships that these offsides have with knowledge, and the impact they have on teaching action, since knowledge can enhance and/or block offsides.