Sophian, C. (2002).  Learning about what fits: Preschool children's reasoning about effects of object size. Journal for Research in Mathematics Education, 33, 290-302.

Preschool childrenís understanding of the mathematical significance of unit size was examined through problems that involved making judgments about the number of larger versus smaller objects that would fit in a container or bounded space.  Childrenís judgments about effects of object size were elicited both before and after the presentation of a series of demonstration trials. The accuracy of childrenís judgments about the effects of object size improved significantly from pre- to posttest, and the degree of improvement was similar for 3- versus 4-year-olds and for Head Start children versus children who attended private preschools.  The Head Start children, however, were much less likely than peers attending private preschools to be able to articulate relevant quantitative features when asked to explain the outcomes they observed during the training trials.