The research presents results of an investigation about the process of continuous training of teachers in service who teach mathematics in the initial years of Elementary School in schools of the municipality of Ponta de Pedras, in Marajó, Pará, Brasil. Researches indicate that in the early years of Elementary Education (aiEF), there is still greater emphasis on teaching other blocks that make up the mathematics curriculum, compared to working with Space and Form, more specifically, when compared to studies related to geometry. However, these same research points out the importance of teaching this content in aiEF. Faced with this problem, the question that emerged and which guided this research was how gemetry has been taught by teachers who teach mathematics in the initial years of Elementary School? In these terms, we present as objective, to investigate how the geometry has been taught by teachers who teach mathematics in the initial years in the municipality of Ponta de Pedras. To collect data were used questionnaire, audio recording, documents and logbook. The research was structured in two stages, applying a questionnaire that allowed to draw the profile of the teachers and to detect their experiences and experiences related to the teaching / learning of geometry and the planning and development of five training meetings, with the purpose of reflecting on teaching / learning geometry. In these terms, the research was carried out from March to November 2016 and had as participants a group of teachers and graduates of the Integrated Degree in Science, Mathematics and Language Education offered by the Institute of Mathematical and Scientific Education. As a final product, differential of this modality of masters, a proposal of continuous formation in service on the block Space and Form, in particular, teaching/learning of geometry for the initial years is presented.
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