Mathematics classrooms in which students engage in argumentation constitute a favourable context to analyse how teachers recognize and incorporate student contingencies. Through exploratory case studies, we examined three mathematics lessons in which teachers support argumentation in contingent situations triggered by student errors. Teachers' argumentation support was defined as comprising three elements: mathematical tasks open to discussion, communicative strategies, and strategies to recognize students' thinking. This three-strategy set is termed "argumentative orchestration in contingent situations." Results show that all three strategies encourage argumentation in the mathematics classroom during contingent situations; more specifically, taking measures to recognize students' thinking significantly fosters the incorporation of contingent situations in the mathematics classroom.