A constituição de conhecimento colaborado em geometria das transformações com ferramentas dinâmicas

Abstract

This study investigated how the Geometric-Mathematical knowledge is made of an investigative and collaborative methodology. We undertook seeing the Geometry of Transformations (GT) coming up as a non-elementary geometry (that is, the usual geometry in our curricular practice) since it sees relationships and invariances in the transformations of figures instead of in their specific structure. In order to do so, we went to the field to live the phenomenon in the form of undergraduate Mathematics Teaching students practicing actions and thoughts on the designed activities and tried to understand this experience. The bias of our research is the way the subjects experienced the prepared activities in the investigative and collaborative space. We achieved significant results that show that GT is a Geometry related to dynamic geometry softwares. We also evidenced the potential of the contribution of collaborative group which commune with a spirit of pedagogical opening to dialogue in order to make up peculiar and significant knowledges, in spite of the traditional ways of building geometric knowledge. The convergences of meanings in our research, grouped in many modes, are the records of our comprehension that the mathematical knowledge built within a group is tributary to various aspects: of how to experience the scientific dialogue, how to coexist with others and how horizons are open according to a pedagogical intent.