In this article I present some notes and reflections on possible ways to be adopted in teaching practice in Mathematics for the incorporation of meanings in teaching and learning of school mathematics in face of the cultural diversity in which the school is situated and constituted in the 21st century through the perspective of globalization. It is a matter of betting on the potential of classroom interactions, subsidized by practices based on methodological approaches that prioritize the direct action of students in the learning process. This is a reflection on the results obtained in experiments carried out in the training of mathematics teachers which were analyzed from authors who base proposals for teaching mathematics through investigative actions to reach learning. These experiences were part of the studies that I have developed since the 1990s and have shown how this approach to teaching mathematics in Basic Education and teacher training contributes decisively to the autonomous learning of those involved.