Children\'s Mathematics

John is finding out about capacity, area, perimeter, shape, space and volume through

his schemas. When he is inside that cuboid (telephone box) he explores the space,

the shape, the corners, the vertices, the angles. He also explores these concepts in

different ways through smaller containers. He may be asking himself: ‘Is this the

same? Is this different? What else can I do to explore this kind of inside? I am

curious, I want to know.’

Children’s schemas help them grasp ideas intuitively. They notice certain aspects of

their environment that they want to use. Athey (1990) wrote that children will use

whatever they can in the environment to try out their present concern. Children in a

transportingschema will use any object at hand to move the object from one place to

the other. Adults may often not see the logic of this because it is not adult logic.

Many early schemas provide a thought ‘footstool’ for a variety of more

complicated mathematical ideas. Very early schemas can combine together, for

example:

• horizontalschema – carefully lining objects up horizontally


• connecting schema – lining objects up, one touching the other


• numberschema – putting numbers to objects, but not necessarily in the standard
  way. Children use numbers in their everyday talk.

Eventually all these schemas can work together to produce counting (Carruthers,

1997c).

Key points about mathematical schemas

• The majority of schemas identified are mathematical.


• Through observations of children’s schemas we can see the early development of
  mathematical concepts.


• We can support this mathematical development.


• Mathematics can be seen in its broadest sense through children’s schemas.


• It may also help the practitioner understand the mathematics through the chil-
  dren’s schemas.


• Schemas highlight the mathematics in the world.

In later childhood, mathematical schemas develop into mathematical concepts

though, as Bruce argues, ‘we are only at the beginning of understanding this’ (Bruce,

1997, p. 78). It is possible to see the links between the examples of children’s

schemas and specific mathematical concepts when we consider the examples of

Sovay, Naomi, Zoë and Aaron in this chapter.

Schemas and mark-making

We have both found our study of children’s schemas fascinating. It has helped us

understand one way children explore their worlds. This schema interest is a window

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