Mathematics—educators, Ball, Goffney & Bass (2005) pointed out—“is not an arena in which differences are resolved by voting.” What is more, democratic, pluralistic societies cannot possibly hope to reconcile all disagreement by vote. The mathematics classroom therefore is a societal opportunity to experience how common consensus is achieved—Is it? How might instruction be designed to serve both mathematical and democratic ends? In this paper we offer a synopsis of approaches from the mathematics education literature addressing mathematics learning in relation to democratic practices. We offer analyses of classroom learning and of political discussion (e.g. the conflict over Stuttgart’s train station), in which conflict, disagreement and argument are mediated by mathematical practices. Our theoretical framework for understanding how these practices can speak to both ends is based on overarching ideas that support each other and are fundamental to human cognition and culture. Among these ideas are “doing and undoing”, “perspective taking and multiple representation”, and “modelling”.