The present work has as objective to investigate knowledge that needs to be mobilized in a continuous formation in geometry for teachers of the initial years of elementary school. The interest in investigating this teaching is justified, among other factors, by the importance of geometric concepts in the construction of knowledge in several areas of knowledge. The thematic approach was based on the methodology of the bibliographic research, because it allows to know in which level the scientific productions, such as articles, dissertations, books, besides official documents, on the object in question. For this, it was outlined as a guiding question of the research: What knowledge need to be mobilized in a continuing formation in geometry by teachers of the initial years of elementary school? The theoretical reference was established in Pavanello's investigations on the historical abandonment of the teaching of geometry by Imbernón on the conceptions of the continued formation of teachers and with Shulman on teacher knowledge. From this study it was possible to verify that the geometry teaching in the continuous formation of teachers of the initial years, presents / displays lapsed. Considering the insignificant number of researches developed in these aspects, thus contributing, with a high degree of teachers with deficient geometric knowledge, rooted in a fragility practice and full of gaps, from the incomprehension of these concepts to the applicability of their contents in the literacy cycle . Faced with such perception, a set of activities on geometric solids was constructed in order to contribute to the resolution of the lag of this teaching.
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