Developmental Differences in Children's Understanding of Number Word Conventions

The four studies reported here document developmental differences in children's understanding that symbols for number are arbitrary conventions. Children between 3 and 12 years were presented with tasks in which they had to make judgments about (a) the adequacy of puppets' counting activities when puppets used standard as opposed to nonstandard number words in counting and (b) the adequacy of puppets' token exchanges when the values of the same tokens varied across numerical systems. In both tasks, the findings revealed developmental shifts in children's ability to distance numerical meanings from conventional symbols. In the number words tasks, children increasingly appreciated that, provided the principle of one-to-one correspondence between symbol and counted item is maintained, any symbol list may be used for counting. In the token-exchange tasks, children increasingly appreciated that the same tokens could represent different values in the different systems.