We study concentrated colloidal suspensions, a model system which has a glass transition. Samples in the glassy state show aging, in that the motion of the colloidal particles slows as the sample ages from an initial state. We study the relationship between the static structure and the slowing dynamics, using confocal microscopy to follow the three-dimensional motion of the particles. The structure is quantified by considering tetrahedra formed by quadruplets of neighboring particles. We find that while the sample clearly slows down during aging, the static properties as measured by tetrahedral quantities do not vary. However, a weak correlation between tetrahedron shape and mobility is observed, suggesting that the structure facilitates the motion responsible for the sample aging.