Semiotics provides a way of conceptualising the teaching and learning of mathematics driven by a primary focus on signs and sign use. It considers patterns of sign use and production, and the con-texts and social rules underlying sign use. It attends to agency in the learner's personal appropriation of signs and the meaning structures embodying the relationships between signs. Learner agency is manifested in communicative activity involving sign "reception" (listening, reading) and sign production (speaking, writing, sketching). It is most marked in individual creativity in sign use, which is manifested at all levels in schooling and in the activities of the working mathematician.