Key points are not available for this paper at this time.
Thomas P. Carpenter, Megan L. Franke, Victoria R. Jacobs, Elizabeth Fennema, Susan B. Empson, A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction, Journal for Research in Mathematics Education, Vol. 29, No. 1 (Jan., 1998), pp. 3-20
Carpenter et al. (1998) studied this question.