Relationship between children's counting ability and their ability to reason about number

The work presented here compares two group of three- and four-year-old children who differ in their school entrance age and consequently in the social expectations of what they should know at these particular ages. The comparison was made in order to assess the effect of children's counting ability on their ability to reason about number. An experiment was designed to make sure that children who succeeded were basing their answers only on the operation performed. The experiment included a set size with more items in it than any of the children would supposedly be able to count. Also, some of the tasks combined addition and subtraction with lengthening and shortening and homogeneous sets were used to avoid the possibility of an answer being based on the presence or absence of a specific item. Three possible outcomes were predicted and the results obtained were analysed in the light of these. The results support the conclusion that young children may reason about number even without having represented it and that children's counting ability does not necessarily underlie their capacity to identify number-relevant operations but rather that the ability, to make number-based judgements develops independently from the knowledge of counting.