This thesis "The mediation of hand-held geometric instruments and dynamic geometry software in learning the formal concepts of parallel and perpendicular lines in two cultural and educational environments" uses a theoretical framework derived from activity theory to investigate the effect of both geometric instruments (ruler, protractor, right triangle, pencil, paper) and dynamic geometric software (Geogebra4) in learning the formal concepts of parallel and perpendicular lines in fourth and seventh grade children from two different countries, Jordan and Greece.The qualitative data is relevant to an empirical study of a group of approximately 120 children from both countries Jordan and Greece. The participating children were subjected to lessons in geometry using the instruments tools (ruler…) and in using Geogebra4. They were then subjected to seven tasks in which they had to identify with justification, whether the lines on a plane in various figures are parallel, perpendicular or intersecting mediating the two different tools. The data was collected and analyzed according to Van Hiele's levels of geometric thinking.