An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class of possible answers to ones that "make sense." It is well known, however, that many children do not give reasonable answers when asked to compute or estimate the sum of two fractions. This problem has generated much discussion in the mathematics education community and, in general, such discussions suggest that poor understanding of fraction size is at the heart of children's difficulties. The purpose of this study was to determine what children who compute fraction sums incorrectly and, as it turns out, estimate the same sums poorly do and do not understand about fraction addition. (PK)