Teaching in general and teaching of mathematics in particular are matters of great importance for contemporary society. Over the years, societies have established institutions in order to incorporate mathematics and science into the culture of society with the clear intention of encouraging a scientific vision of the world among the population. This intense social process of scientific "enlightenment" has helped us recognize the need to implement educational modifications in the specific field of mathematics based on designs that are better adapted to school practices. Mathematics education deals with the systematic study of the effects of such processes; in this paper, we have decided to describe a certain evolution of its research problems.