From Euclidean Geometry To Non-Euclidean Geometry, In Particular Hyperbolic Geometry, In Secondary Education Through Dynamic Geometry.

The current school requires teaching and learning about Euclidean and non-Euclidean geometry from the first educational levels. The research is carried out with the purpose of making a transition from Euclidean to non-Euclidean geometry, through constructions with ruler and compass, with their subsequent comparison in the computer by means of GeoGebra software, contributing to the characterization of the geometric thinking involved, in seventh grade students of Rodrigo Lara Bonilla school. In the research, 10 activities are designed based on the development of constructions with ruler-compass and their subsequent comparison with traditional instruments or dynamic geometry, as well as problem solving based on mathematical visualization and motivation towards the study of mathematics. Through the development of the activities, students begin to build their own concepts about these new geometries, using their geometric thinking on notions of plane geometry. The implementation of these activities and the results obtained, allows improving their learning process, as well as favoring their interest in learning geometry. From personal interviews with the working groups, it is possible to verify the elements that characterize the geometric thinking used and involved by the students.