In this paper, we focus on the practices of teachers who teach mathematics to non-specialist students. Referring to the anthropological theory of the didactic, we investigate university teachers’ personal didactical praxeologies. Drawing on the literature on the specific issues met by non-specialist students, we identified five didactical types of tasks situated at the level of the discipline belonging to ‘the praxeological problem of the teacher’. We conducted interviews with three experienced teachers teaching mathematics to first year non-specialist students about their practices and collected their resources. The data analyses indicated that the three teachers developed their didactical praxeologies for ‘Teach basic mathematics’ and ‘Link mathematics and other disciplines’. The analysis at the lower levels (domain/sector/theme/question) and the consideration of the mathematical praxeologies they proposed to their students allowed us to question the relevance of the actual implementation of the techniques they use.