Resumen

In this article I present some notes that reflect on some changes in the educational process at school, taking them as support to argue about the possibility of including research as a principle of teaching and learning. To this end, I chose the training of teachers who teach mathematics as the focus of my discussion, because this training in teaching (Mathematics and Pedagogy) must be founded on epistemological bases which suppose the investigating spirit as a learning agent of the mathematics addressed in these academic courses. The article has been divided into six parts. In the first one I present the initial assumptions on the subject of research and knowledge production. The second one refers to the epistemological foundations of research in the production of knowledge as support so that in the third part, I might be able to address the problem solving, imagination, elaboration and representation of knowledge. Then I discuss the didactical aspects related to research as a teaching and learning mathematical principle. Finally I describe some experiences in the training of teachers who teach mathematics and point out possibilities of a teacher training for research in the teaching degrees focused on in this article.