Children\'s Mathematics

On the fourth planet a businessman was engrossed in counting:

‘Three and two make five. Five and seven make twelve. Twelve and three make

fifteen. Good morning. Fifteen and seven make twenty-two. Twenty-two and six

make twenty-eight ... Twenty-six and five make thirty-one. Phew! Then that makes

five-hundred-and-one-million, six-hundred-twenty-two-thousand, seven-hundred-

thirty-one.’

‘Five hundred million what?’ asked the little prince. (Saint-Exupéry, 1958, p. 41)

There is one essential reason for teachers to encourage children to represent their

mathematical understanding on paper that we explored in Chapter 5.

It is through exploring mathematical graphics on their own terms that young

children come to understand the abstract symbolism of mathematics. Using their

own marks and making their own meaning – shared, discussed and negotiated

within a community of learners – enables children to become bi-numerate. This

allows children to translate from their informal, home mathematics to the abstract

mathematics of school; to ‘bridge the gap’. Being bi-numerate means that children

can exploit their own intuitive marks andcome to use and understand standard

symbols in appropriate and meaningful ways: developing their own written methods

for calculations is an integral part of this.

Practical mathematics

There is a view that ‘practical mathematics’ with the use of resources supports early

mathematical understanding, for example Thompson argues that ‘all calculations in

the first few years of schooling should be done mentally, using whatever aids they

need – counters, bricks, fingers etc’ (Thompson, 1997, p. 98).

However, a study in 1989 confirmed that ‘the link between practical work and the

move to formal symbolic representation is often tenuous’ (Johnson, cited in Askew

and Wiliam, 1995, p. 10). Askew and Wiliam advise that results from this and other

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Understanding

Children’s

(^7) Developing Calculations
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