Geometrias na segunda fase do ensino fundamental : um estudo apoiado na epistemologia genética

Abstract

Piaget's theory is notable for the research effort in the construction of space for the child, including how it perceives and represents. According to Piaget and Inhelder (1993), in the field of geometry, the first child establishes topological relationships to later build the projective and Euclidean relations, which occur simultaneously. However, according to the Basic Education Curriculum Guidelines for Mathematics in the State of Paraná (2008), Content Structuring geometry unfolds in the following topics: plane geometry, spatial geometry, analytic geometry and basic non-Euclidean geometries, being presented students of Basic Education, in the order described. Thus, this project aims to identify how children between eight and twelve years, who attend elementary school mobilize some of the basic ideas for the construction of geometrical concepts during the resolution of problem situations. We believe that this research, besides the aforementioned objective, is to give subsidies to confirm the inclusion of non-Euclidean geometries Curriculum Guidelines. Our theoretical results from the Theory of Construction of the Jean Piaget and Barbel Inhelder and Conceptual Fields Theory. The research methodology adopted Piaget's Clinical Method as an instrument with different problem situations.