Sharing and the understanding of number equivalence by young children

Little is known about children’s sharing skills and the relation of these skills to the understanding of number equivalence. In a series of three experiments, we found that J-year-old children were able to share discontinuous quantities using tem-poral, one-to-one correspondence but usually did not make any connection be-tween sharing and cardinal equivalence. Nor could they cope well with a task in which the recipients had to be given the same total number but different units had to be dealt to different recipients (single blocks to one person and doubles or triples to another). Most 5-year-olds performed correctly in this task. In a final experiment, we showed that children were much better at sharing in different units with the help of relevant color cues and also that experience with such a task improved their performance in a later one in which the color cues were removed. The one-to-one correspondence principle is an essential component of the devel-opment of mathematical skills. No child can be said to have a real understanding of the cardinal properties of number unless he or she has understood that two sets of objects are equivalent in number when there is a reciprocal correspondenc