There are two main directions in the research on teaching practices in mathematics: the ‘cognitive approach’, whose empirical objecto fo study includes teachers’ conceptions, goals, beliefs, and ‘pedagogical content knowledge’ ; and the ‘epistemological approach’ that focuses on the study of institutional didactic situations or didactic organisations. This lecture shows how the Anthropological Theory of the Didactic (Chevallard 1999) connects the description of didactic organisations with the mathematical organisations that are supposed to be built in the teaching process.