In the present school context in Ceará, it is still evident the difficulties in which students and teachers face concerning the teaching and learning process in Mathematics. These obstacles become more sensitive when it is directed to the conception and perspective of spaces and tridimensional shapes, Spatial Geometry’s object of study. Therefore, the present research, aiming to develop abilities, techniques and strategies to improve the degree of abstraction of those involved, it is introduced the Fedathi Sequence, a kind of didactics session that places the mediating posture applied by the teacher as a significant factor in the building and stimulus of the autonomy developed by the student, based on the knowledge construction that is proposed. Within this setting, the present work concerns a case study of the problem situation “The fly, the ant and the honey drop”, in which, mediated by the Fedathi Sequence, will analyze the formation of the Spatial Geometry’s concepts under the vision of three approaches: traditional, manipulable materials and the application of the GeoGebra software. The activities were developed with students in the second grade at high school of a public school in Fortaleza, organized into 42 groups and subdivided into 14 of them by approach. At the end of the presentations, discussions and results were shared with considerations about what was appropriate or not that was found in the problem regarding the approaches designated