Our research focuses on ways teachers envision argumentation in their secondary mathematics classrooms. Semi-structured interviews were conducted with 31 secondary school mathematics teachers in Israel. They were asked to envisage a hypothetical classroom dialogue focusing on mathematical tasks which would engage their students in some argumentative activity. Analysis of the teachers' responses identified categories related to both "structural" and "dialogic" aspects associated with three dimensions of argumentation: (1) task characteristics, (2) teaching strategies, and (3) students' characteristics. From a cross-analysis of the teachers' statements certain categories appeared more frequently than others. We interpret our results from a theoretical and practical perspective and make recommendations for areas of future research.