The omnipresence of socio-political and cultural conflict in contemporary society poses a challenge to school education and its teachers when they choose to address in classrooms the controversies that divide it, and make its treatment have a protected and formative character. This article offers a conceptualization of the intrinsic tension of this double requirement and the teaching strategies to address it. At the same time, it empirically characterizes how is this tension currently experienced by teachers of the subject of Citizenship Education in Chile. Specifically, it asks about the criteria and teaching practices for the treatment of controversy in the classroom and, in order to give an answer, presents the results of a survey to 103 teachers of schools in three regions of the country, carried out in 2019, as well as qualitative evidence from interviews to 10 teachers of the subject of Citizenship Education carried out during 2022. The study found a high valuation of this pedagogical strategy and a low frequency of its use, due to a series of difficulties, such as fear of accusations of proselytism and lack of control in the classroom, which hinder a more widespread approach. When it does take place, the controversy predominantly arises in the classroom informally and spontaneously at the initiative of the students, in the face of which teachers adopt positions in which neutrality prevails. Based on categories of comparative literature, the article proposes a model for analyzing teaching strategies and argues that these should vary according to the context.