Some professors who had had some deficiency in its formation, when a child if becomes curious and if she interests in questioning and to place doubts to what this learning, it becomes a child ' ' perigosa' ' , on account of this the professor if places in the defensive, restraining the curiosity of the child. Of this form to teach mathematics of a form criticizes and democratic it implies to look at the mathematics in its way of being, to think, of its formation historical, as to teach and as to learn, searching its creativity and its understanding. The Trajectory of the Lesson Expositiva In accordance with Saviani (1983), until the decade of 30, approximately, predominated in the Brazilian schools the traditional pedagogical conception. In this conception, the professor, seen as center of the education process, would have to dominate the contents basic to be transmitted the pupils. In this context, the expositiva lesson was considered as the technique more adjusted the transmission of knowledge in the classroom.

In the Brazilian schools in the decade of 30 still he was considered the traditional education, in which the professor was the center of the education process, where only it only transmitted the content for the pupils and ready, that is, the pupils did not have the right to make questions, to suggest techniques to have one better exploitation of the transmitted content, thus making it difficult the learning of the pupil. Still according to Saviani (1983), with the advent of the new pedagogia, in middle of the decade of 30, new pedagogical ideas they had started to be assimilated in the schools. The new pedagogical trend gained body from critical severe the traditional pedagogia, fixing itself in the reversion of the education process, in which the pupil, and not more the professor, started to be the center of this process.