Both classroom discourse and professional discourse about classrooms constitute forms of social performance undertaken within affordances and constraints that are both cultural and linguistic. The nature of those discourses performed in mathematics classrooms provides a key indicator of pedagogical principles underlying classroom practice and the theories of learning on which these principles are founded. The discourses about mathematics classrooms give expression to these pedagogical principles sometimes explicitly and sometimes through embedding privileged forms of practice in the naming conventions by which the mathematics classroom is described. Research will be reported to suggest that each of these discourses is culturally and linguistically specific. As a consequence, conceptions of accomplished practice (or excellence) are contingent on the history of custom and insight embedded in the conventions of practice and the language with which that practice is described. In the same way that the differential promotion of fluency in spoken mathematics in different classrooms around the world enacts a different classroom mathematics, teachers, other educators, and researchers in different countries have at their disposal very different linguistic tools with which to conceptualise, theorise about, and research the mathematics classroom. The performative realization of teaching competence is framed and constituted through such culturally-situated discourses.