The Road to 3D Geometry: Why is the astounding 3D Geometry virtually absent in the Teaching of Mathematics?

Mathematics is characterized as rational, abstract and exact. However, the road for learning mathematics starts with concreteness, progress with experimentation and is guided by approximations. Twenty years ago I stumbled over some very straight-forward 3D Geometry problems, which I could not solve. From that moment on, I became increasingly aware about how ludicrous was to live in a 3D world and spend most of the time studying just 2D Geometry. Thus, I started to develop a methodology which effectively could enable me, to learn 3D Geometry and solve those problems. Born in Uruguay, developed in France and tested in USA, emerges iMAT (integrating Multi-type representations, Approximations and Technology) a didactical engineering designed to tackle the inexplicably little explored, yet amazing world of 3D Geometry. The approach, which is deeply rooted in the Epistemology and in the Didactics of Mathematics, has also strong implications for a substantial improvement in the teaching and learning of other mathematical areas. Here, you will find an attempt to open an innovative road for learning mathematics, a road where concreteness and abstraction are wonderfully intertwined.