Learning to Count

Even if young children can recite the number sequence (i.e. say one, two, three, etc) we cannot assume that they can count small sets of objects. Learning to count involves learning several important principles (references):

1. Each object to be counted must be given one and only one number name.
2. The number name list must be used in a fixed order every time a group of objects is counted (i.e. you have to say 1, 2, 3, 4 in the same order each time).
3. The order in which the objects are counted doesn't matter. The child can start with any block and count them.
4. The last number name used gives the number of objects in the set.
5. The arrangement of the objects to be counted does not affect how many there are.

Each of these principles can cause difficulty for some students. For example, principle 5 above relates to Piaget's ability to 'conserve number'. Some students in the early years do not realise that moving the objects in a set does not change the number in the set even though the arrangement may look different. Piaget's experiment showed that they may think that there are fewer flowers when the same number are close together in a vase than when they are spread out on a table. Students can know the sequence of number names and even be able to count a small set of objects but lack understanding of conservation.

The difficulty for most students is to coordinate in a one-to-one fashion the recitation of the verbal sequence with checking off the objects (principle 1 above). The coordination of two actions becomes more difficult as the number of objects in the group gets larger, or when the child has to think about what number name comes next.

Students who can count quite well will have difficulty with principle 3 until counting is well established. For example, put 5 objects of different colours in a row, with the yellow one in the middle. Ask children to count all the objects, starting with the yellow object as '1'. For a greater challenge, ask the children to count all the objects, making the yellow one '5'.

 

References

Gelman, R. & Gallistel, C.R., (1978) The Counting Model. In The Child’s Understanding of Number. (pp 73-82) Cambridge Ma: Harvard University Press.
Reys, R., Suydam, M. & Lindquist, M. (1984) Helping children learn mathematics. New Jersey . Prentice-Hall