How do children come to sort objects according to geometrical properties? How do children come to sort geometrically given that they tend to sort, as many studies show, according to properties such as size or color? These questions are especially important given that in the “intuitively given surrounding world . . . we experience not geometrical-ideal bodies but precisely those bodies that we actually experience, with that content that is the actual content of experience” (Husserl, 1997a, p. 23). That is, the question in this chapter will be how children come to classify objects (bodies) according to geometrical properties when they do not experience, at fi rst, geometrical-ideal bodies? And yet, if they do classify in and through classifi cation experiences, what children bring to the classroom are the very methods, grounds, and materials upon which truly geometrical classifi cation is built, however inadequate educators might deem these “preconceptions” to be.