This paper reports a model of teacher training levels based on the mode of interaction of online education, adapted to the profile of mathematics teacher in service and oriented to the recognition of the mathematics education as a field of knowledge for teaching math. We discussed the report that each teacher performed from a first didactic laboratory, as the product of the discursive strategies developed at various levels and formats of interaction of the proposed model. On each level the teacher discusses and reflects about the redefinition of the school notion of angle and implements these elements to interact with students in an controlled school experience; showing that the recognition of the discipline as his field of knowledge is the product of a continuous exercise come and go between the educational theory and educational practice.
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