With this article we intend to give a contribution to a unitary picture of various terms and concepts, spread in the international community of those who deal with mathematics education, giving them back unity and looking for the historical roots of their introduction in that community. Although the different acceptation with which they appear today, many of these terms were introduced from the origin mainly by Guy Brousseau, striving for synthesis and ad hoc redefinition. They evolved in time and some these evolutions regard the most classical topics; we focus our attention on the example relative to the didactic contract.