The research to investigate the Inicial Training of Teachers from Mathematics Graduate from the Initial Formation of Teachers in Service promoted by the Education Executive General Office and made by Pará State Federal University. The research reports case analyzes of four students/teachers that act in classroom at the States Public School in different towns in Pará State Northeast. The research focused the practical changeovers that took place in classrooms since the entering in initial training course based on students/teachers and professors-formers. We adopted qualitative research as main methodology for data collecting we used a semistructured interviews accomplished with students-teachers and the official documents. In the six chapters this research in done, we showed some referential aspects: The initial training Formation of Teachers in Service in Brazil, The Initial Formation of Service in Pará State, The Teachers in Service Formation Program from the Education Executive Official Office in Pará State, The Curriculum Model in Mathematics Graduate of Federal University of Pará State, For the Initial Training of Acting Teachers, The Initial Formation of math Teachers, The Initial Formation Program for Acting Teachers According to Students-teachers and teachers-formers and the practical changes observed and lived in classroom practice. The results show there are several factors that interfered on systematic knowledge construction in an actions teachers formation course. Four students-teachers from math graduate, two collaborators, one of each institution that celebrated agreement and four teachers-formers of specific subjects in Math Graduate.
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