This title is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, it follows students' inquiry co-operation as well as students' obstructions to inquiry co-operation. Both are considered important for a theory of learning mathematics. Special attention is paid to the notions of "dialogue" and "critique". A central idea is that "dialogue" supports "critical learning of mathematics". The link between dialogue and critique is developed further by including the notions of "intention" and "reflection".