Sophian, C., & Madrid, S. (2003).  Young children's reasoning about many-to-one correspondences.  Child Development, 74, 1418-1432.

Young children's understanding of many-to-one correspondence problems was studied to illuminate the developmental transition from additive to multiplicative numerical knowledge.  A many-to-one correspondence exists when a fixed number of target objects (greater than 1) is associated with each of a set of referents, as in putting 3 flowers in each of several vases.  Two experiments examined effects of a brief training procedure that highlighted the iterative nature of many-to-one mappings.  In Experiment 1, 5- and 6-year-old children did not benefit from the training, but a subset of 7-year-olds did.  In Experiment 2, 7-year-olds showed training effects that extended to generalization problems.  Patterns of performance across experimental and generalizaqtion problems suggested that some children had difficulty applying what they learned from training to the experimental problems.