This research is from research participant perspective and is longitudinal in nature involving undergraduates and teachers who teach mathematics in basic education. They have some knowledge about the teaching of mathematics that are being explained in surveys of teachers that are produced in areas of the Master (Professional and Academic) and Education Observatory. The completed surveys mostly are based on the theme of Guiding Activity of Teaching. The teacher is considered systematic and intentional, as Cochran-Smith e Lytle indicate, since they consider the dynamics of fluent math classes, as well as the particularities and peculiarities of the classrooms. Teachers are intentional, study, plan actions and prepare educational products that aim to positively intervene in the processes of teaching and learning in their classes. They are systematic and so academic interventions that occur in mathematics lessons are systematized.
Mathematics teaching; Higher education; Post graduation; Research activity; Teacher formation; Professional development