Young children's understanding of counting and cardinality

4-year-old's knowledge of counting and cardinality--the last count word reached represents the numerosity of the set--was tested in 2 experiments. Experiment 1 investigated the nature of early cardinality responses by presenting different forms of the cardinality question before, after, and before and after the child counted. Both type and time of question has large effects. Experiment 2 examined whether children of this age could recognize errors in 4 counting procedures and whether they would reject a cardinality response arrived at through a mistaken counting procedure. The children were very good at recognizing a standard counting procedure as correct. They had only limited success at treating procedures that violated the stable order of count words or violated the one-one correspondence between count word and object as incorrect. They lacked an understanding of the order irrelevance in that they judged valid, nonstandard counting orders as incorrect. The children did not seem to link their evaluation of a cardinality response with their evaluation of the counting procedure used to reach that response. The results do not indicate that counting principles initially govern the child's acquisition of counting knowledge. They are consistent with the suggestion that early cardinality responses are last-word responses.