Philosophical Understandings for An Alternative to Geometric Thinking

Abstract

Our goal here is to openly understand the scenario that comforts a variety of geometries, telling their origins along the Geometric Transformations. Considering the Euclidean geometry to be elementary geometry, other geometries based on this or in the succeeding ones were constituted by study of  movements - among which the displacement and the projection- which underlie new ways of designing geometric meanings and, as effect, new geometries. The movement in these constitutions made itself significant and, based on its epistemological potentialities we articulate, as well, an essay to understand the so-called Dynamic Geometry , so described due to its design for movement-enhancing software. We question: Are there any geometrical treatments more likely than others to conquer terrain in computer screens for open graphics software? We have used the bibliography to understand the institutionalized geometries; these are understood potential generators of other geometries. This search allowed us the joints that support understandings around our survey; the potentially transformative dynamics that underlies geometries can also transform the ways of being with them as well as the way to treat them inside the classroom. This suggests epistemological and methodological variations in school pedagogy, which also allows the projection of multiple geometric pedagogies, such as those concerning software, opening possibilities to school curricula.