Children\'s Mathematics

curriculum. What we need in education is the co-ordination of the two’ (Athey, 2002,

p. 10).

Skemp explains the functions of schemas by saying that they integrate existing

knowledge, act as a tool for future learning and that they make understanding pos-

sible. Skemp recognises the importance of schematic development in understanding

mathematics. Like most mathematicians, Skemp’s analysis of schemas is from a

mathematical viewpoint: these are the ‘logico-mathematical’ concepts that children

need to learn first before they can understand higher concepts. As he reflects on

teaching young children, Skemp acknowledges that they already know some

number concepts before they start in an educational setting. He asks if it matters that

they do not yet have an understanding of sorting, sets and matching and one-to-one

correspondence, as long as they ‘tag on’ these concepts at some point. Skemp seems

to wrestle with young children’s schemas because his ideas somehow do not totally

fit into his current knowledge of young children’s development. He has followed the

Piagetian theory and the research model of clinical tasks and has not balanced this

by following the young child in real-life situations; at home, at play or in

autonomous situations where they are following their own thinking (Skemp, 1971).

Figure 3.1 Note from Chloë’s mother

Piaget particularly looked at children’s very early schematic behaviour such as a

baby dropping an object on the floor and the parent retrieving it, only to find five

seconds later that the baby has dropped the object again. This Piaget called ‘object

permanence’ (Piaget, 1958): the child may be thinking ‘is the object still there if I

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