The general objective of this research will be to observe and to analyze as the geometry has been developed with the students of a 5th year class (old 4th. series) of the Fundamental Teaching. More specifically, to analyze the established relationships between the teacher's geometric knowledge and the practices developed at classroom with her students, trying to understand that know ledges are mobilized in the process of teaching geometry. Studies emphasize that during all their life, the people will interact with concrete objects in a physical space. The physical space is not the only mathematician source, but its importance should be stood out. In spite of yours recognized importance of the geometry in the formation and the individuals' development, its teaching has been relegated to a second plan and, a lot of times, despised. I intend with this research to identify that geometry has been taught to the students and that way that content is related with their teachers' geometric knowledge. The subject orientating is like this defined: What relationships do exist among the geometric knowledge revealed by the teacher and the practices developed in their classes? The research has characteristics of qualitative research, could be considered as a Study of Case. In this approach type it feels special attention to the characterization of an object in which it has of only and specific, in its relationship with the context and in its history. In the collection of data different instruments will be used, such as: the teacher's depositions, annotations of the observations in the field diary, analysis of class documents and of class plan, analysis of geometric activities used by the teacher in classroom, filmings, interviews, reports produced by the teacher, reflexive texts on the educational practice written by the teacher. For better understanding of the object of my research, the relationship between the geometric knowledge and the teacher's educational practice, we will look for theoretical contributions in the studies of Galvéz (1996), Del Grande (1994), Fischbein (1993) and also the studies of the van Hiele on the development of the geometric thought. The collected data will be analyzed and interpreted have been supported by the theoretical studies that approach teaching processes and learning of the geometry.
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