As concepções de geometrias de um grupo de professores de matemática da educação básica - Lovis, Karla Aparecida (2013)
The ideas on Euclidian and non-Euclidian Geometry of twenty-seven teachers of Mathematics are analyzed. Further, the knowledge, opinions, preferences and notions they have on these types of Geometries are provided. Analysis was foregrounded by studies on Ponte (1992), Thompson (1992; 1997), Cury (1994), Guimarães (1988; 2003), Dewey (1953) and others. Selection of participants was undertaken by questionnaires and data were collected through semi-structured interviews plus 36 charts filled with the Geometry-related concepts, results and terms. Interviewed teachers work in government schools of the state of Paraná, Brazil, each of whom belonged to a different Regional Nucleus of Education. Research investigated the concepts that teachers have on the construction of geometric knowledge, Euclidian geometry, non-Euclidian geometries and their importance. With regard to the first item, the teachers underscored four relevant moments: before, at and after graduation and during the teaching years. The second item showed that most teachers think that Euclidian geometry is made up of the geometrical beings from Plane or Spatial geometry, such as point, straight line, plane, figure and solids. Notions and opinions on non-Euclidian geometries were presented by many teachers. However, the study of non-Euclidian geometries did not provide or restore new concepts since only eight teachers had deeper ideas on the subject. The teacher emphasized the applicability of geometry in people´s daily life. However, as a rule, knowledge, ideas and opinions of teachers with regard to Euclidian and non-Euclidian Geometry are highly limited and shallow.