Children\'s Mathematics

methods in such instances may have been implied.The children in Hughes’s research

project may have used strategies that were appropriate to them, though it is difficult

to ascertain this when children are unused to representing mathematics in their own

ways. As we show here, when children put down part of a calculation – the numer-

als without the signs or only the answer – what they have omitted may be implicit.

In the story of The Little Prince, the pilot was asked to draw a sheep. Finding this

difficult to do he finally drew a box explaining, ‘this is only the box. The sheep you

asked for is inside’. The little prince understood the drawing and bending over the

drawing observed, ‘Look! He’s gone to sleep’ (Saint-Exupéry, 1958, pp. 10–11). It is

possible to see in children’s mathematical graphics, the meaning children have

impliedbut not shown, like Saint-Exupéry’s sheep in a box.

Standard symbolic calculations with small numbers

This stage arises directly out of the preceding ones. All their previous knowledge

combines to support simple calculations with small numbers. Calculating with larger

numbers is challenging. There can be a problem here since children:

Understanding children’s developing calculations 123

Figure 7.8b John

Figure 7.8a Fred

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