Research in the history and philosophy of physics has shown that the formalism of General Relativity can be interpreted in several different ways and, consequently, its teaching is very problematic. The present contribution is an example of a reconstruction of the debate concerning the foundations of General Relativity on the basis of cultural and educational criteria. In particular, the debate will be presented as guided by the concept of space, and by the different perspectives from which such a concept can be viewed. It will be pointed out that the various ways of looking at space give powerful criteria not only to create an order among the interpretations, but also to exploit the educational and cultural value of the debate.