## ABSTRACT

OUR AIM in this chapter, and in the remainder of Part I, is not a systematic study of the concept of the equality of two angles. Actually, we already know how the concept is constructed: that it is first acquired at the level of concrete operations.2 But it is precisely the fact that the concept is already so well known by the time the formal level (stage III) is reached that makes the reasoning process involved in the discovery of the equality between the angles of incidence and reflection so instructive. One of the aims of this study, then, is to isolate the operational mechanisms involved in the formal reasoning process itself, when this reasoning rests on notions already constructed at the concrete level.