Today's method of teaching the concept of falling bodies in French physics classes is ineffective, not only because it ignores the physical aspect of the phenomenon by addressing only its mathematical aspect, but also because it does not take into account students' initial conceptions, which are often incompatible with scientific knowledge. The goal of the present study was to assess the effectiveness of a new educational perspective for teaching gravity, based on an analogical presentation of Einstein's theory of the deformation of space-time. The conceptions of French 15-year-old ninth graders and how they evolve are analyzed and compared for two different teaching methods, the new perspective (n = 102) and an approach based on Newton's theory of bodies interacting at a distance. The data obtained are used to describe students' initial conceptions of falling bodies, and confirm the lesser effectiveness of the teaching approach based on Newton's theory. The results provide evidence of two phases of conceptual change: "positive substitution" (when a correct explanatory system replaces an erroneous one) and "generalization" (when the domain of validity of a correct explanatory system is extended). They also show that Einstein's theory can be understood by ninth graders and promotes more conceptual change than a method based on Newton's theory of bodies interacting at a distance. The new perspective appears to help students not only to extend the domain of validity of the correct conception--that bodies fall because they are attracted--but also to change their conception of attraction, now understood as the effect of a property of space rather than a property of bodies. (Contains 4 figures and 3 tables.)