  We begin a study of the intersection theory of the moduli spaces of degree
two stable maps from two-pointed rational curves to arbitrary-dimensional
projective space. First we compute the Betti numbers of these spaces using
Serre polynomial and equivariant Serre polynomial methods developed by E.
Getzler and R. Pandharipande. Then, via the excision sequence, we compute an
additive basis for their Chow rings in terms of Chow rings of nonlinear
Grassmannians, which have been described by Pandharipande. The ring structure
of one of these Chow rings is addressed in a sequel to this paper.
