In this chapter, I am concerned with the relationship between what the teacher intends to teach to a mathematics class and what the students are capable of learning effectively. The words, teach, learn and know can carry different meanings. I shall clarify the meaning I shall give them here. The working out of a problem is a step in didactic engineering. In this context, the term didactic engineering designates a set of class sessions conceived, organised and articulated, in a coherent way, in a time frame, by a master-engineer with the purpose of achieving the learning of a certain mathematical content for a certain student population. Thus, didactic engineering is, at the same time, a product: the result of an a priori analysis, and a process: the result of adapting the product of the dynamic conditions of the class to carrying out the work. In what follows, I am principally concerned with the relations between the construction of meaning and the acquisition of knowledge in mathematics. In directing the didactic experiences of the class, and with the inevitable institutional constraints and various pressures he is under, is it possible for a teacher to take these relations into account? And what margin of manoeuvre does he have? However, beyond these concerns, there exists a crucial question, of a sociological nature, but which conditions the choice and the conduct of the envisaged didactic actions: In the school setting, what ist the place of knowledge for the teacher, and for the students? Is it something that is at stake in the didactic relation. (ZDM/Mathdi)