Children\'s Mathematics

we uncovered children’s meanings on paper and began to link theory and practice.

In this book we look closely at the development of children’s graphics and the

teaching to support the connections between informal and formal maths. We have

placed our research in real classrooms, in authentic teaching situations, over a period

of more than 12 years. In support of our premise that the translation between chil-

dren’s formal and informal maths is important, we now explore the way in which

second language learners make this transition.

Mathematics as a foreign language

Through our teaching during this period, our research interest as teachers moved from

a broad focus of different features which supported young children’s understanding in

mathematics to a focus on one aspect. During our discussion one day, the two of us

talked about the fact that there had been almost nothing written that linked theory and

practice about ways of ‘bridging the gap’ (Hughes, 1986). In our teaching we had expe-

rienced some wonderful insights from young children and had been thrilled by their

highly original responses through their mathematical graphics. But in what way did

their own marks support understanding of the abstract symbolism of mathematics? We

discussed this at length and the following is part of one discussion:

‘maybe it’s a bit like learning a second language – you build on what you know in

your first language to help understand a second language. It becomes possible to

move between two different languages – with increasing fluency in the second.’

‘And maths is a language – written as well as spoken – then the social aspect needs

greater emphasis too.’

‘Young children feel comfortable with their first mathematical language – the

informal spoken and written marks of home. If they can gradually make sense of

abstract symbols and written methods in their ownways, surely they would be devel-

oping fluency in both? They’d be able to move between the two languages with

understanding – like being bi-lingual.’

‘Bi-mathematical!’

‘What about bi-numeracy?’

Mathematics has often been referred to as a language (for example, Burton, 1994;

Cockcroft, 1982; Ginsburg, 1977). Pimm goes so far as entitling a chapter he wrote

on this subject: ‘Mathematics? I speak it fluently’ (Pimm, 1981).

The issue of language and mathematics is a complex one. We use everyday lan-

guage to talk about the mathematics we are doing, for example, ‘I’m counting how

many cups we need.’ We use everyday words and phrases in one way at home, such

as the term ‘take away’ (of fast food such as an ‘Indian take-away’) and in another

way in school mathematics when working out subtraction. There are also very spe-

cific mathematical terms that are rarely used in everyday contexts, such as vertex

and angle. Children and teachers also may use language to discuss aspects of math-

ematics such as infinity.

From a different perspective, Oers argues that young children use language to help

make the meanings of their marks clear to others (Oers, 1997). In his book Children

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