Resistance and routine use: an analysis of university students’ solving processes related to asymptotic behaviour

Abstract This study explores the relationship between resistance, as conceptualised by Wertsch, and the use of routines within Sfard’s commognitive framework in university students’ solving processes. Focussing on tasks involving asymptotic behaviour, we investigate how routines evolve in response to constraints interpreted as resistance. We analyse the relation between overcoming (or not overcoming) resistance and three characteristics of routines: flexibility, applicability, and objectification. The study draws on task-based interviews with 16 mathematics students working in pairs on unfamiliar problems concerning the asymptotic behaviour of functions. Results indicate that the characteristics of routines are closely related to whether resistance is overcome. Overcoming resistance was associated with broader flexibility and applicability, while its persistence was associated with these characteristics remaining more locally constrained. By theoretically networking resistance with commognition, the study contributes to research on university mathematics education by offering a refined account of how constraints shape the evolution of mathematical routines in unfamiliar contexts.