This thesis addresses the discussion of mathematical reasoning expressed in the knowledge / craftsmen potters of Municipal District of Icoaraci (Belém/ PA), toward an understanding of cognitive and cultural practice, the contributions to abstract mathematics education - knowledge in the area which includes, especially in mathematics education. This last worked, the thesis aims to analyze the reality of the subject by Conceptual Fields Theory, the mathematical educator Gérard Vergnaud, which develops in line with constructivist studies, education of the psychologist Jean Piaget, enabling approach in everyday practice of the craftsman, its conceptual fields, the possibility of the existence or not of theorems and concepts-in-act, a fact that will verify or not the essence or 'mathematics' of educational studies by mathematicians worked ethnomathematical, educators, mathematical modeling experts, sociologists, mathematicians and archaeologists. The epistemology of mathematics education, philosophical discipline, there is guiding this understanding of mathematical reasoning, mathematics through the sensitive, who finds its origins in ancient Greek ideals through the pythagorean, platonic and aristotelian, extending this view to the mathematics of the present world. Thus, the thesis seeks to explain the manifestation of a mathematical reasoning by the artisan, who in his predominantly do not know and / or does not use academic or formal mathematics, as evidenced in other studies. This presence or absence of mathematical understanding will be found through ethnographic and qualitative approach, under the phenomenological approach, using techniques of observation, field notes, interviews and cultural inventory in order to analyze the existing representations in their work and doing / thinking expressed in this production.
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