Abstract
This article is focused on the study of the geometric work involved in the initial teacher training in a learning environment based on the use of GeoGebra dynamic software. The intention is to identify how three figural, instrumental and discursive reasoning genesis are articulated in the Geometric Work Space and to study the role which GeoGebra plays in the construction of this geometric space. In addition, we explore the influence of software in the step from Geometry I to Geometry II in the performance of the student as viewed by the teacher.