ABSTRACT
Two people start counting at the same time and the same speed. One starts at 1 and counts in 8s, the other starts at 25 and then counts in 5s. Will they ever reach the same number at the same time?
Counting From the earliest times counting has been a universal activity among people – probably developed as a way of checking possessions. It involves matching a series of objects (such as sheep) to a standard sequence of names or marks. Most children learn to count reliably by the time they are seven years old, but it is actually a complicated activity with several subskills. Children need to know the standard name sequence. They must then match each number name to one and only one of the objects being counted. This is often supported by pointing or touching. Finally they should realise that the last number name used also refers to the size of the set being counted. This is the cardinal aspect of number. Sometimes children interpret the instruction ‘count’ as telling them to point to the objects and recite the number sequence. They do not think of it as an activity to answer the question ‘How many?’ They may even write 1, 2, 3 to represent the size of a set of three blocks. The ordinal aspect of number depends on the fact that numbers are always in the same order. This means that they can also be used to order objects or events, so we can talk about the fi rst or second day of the holidays or the fi rst child to fi nish a race. By the time they complete Key Stage 1 most children should also be conserving numbers reasonably well. This means that they understand that the number of objects in a set remains the same even when the objects are moved around or counted in a different order. Although researchers such as Piaget did a great deal of work on this, it seems that children’s understanding of this develops slowly and depends both on context and the size of the numbers involved.
