Children\'s Mathematics

These narratives appear similar to drawings described by Oers – either

representing imaginary or real situations – or, in a mathematical context, abstract

or concrete ‘they are symbolically representing a narrative’ (Oers, 1997, p. 244). To

make sure that all the features of the narrative are understood children use talk (or

sometimes add writing) to qualify their representations. In his research of the way

in which children use speech as an ‘explanatory function’ to help adults

understand the meanings of their drawings, Oers argues that most of the children’s

explanations ‘refer to the dynamic aspectsof the situation (what really happens),

which they apparently feel is not clearly indicated by the drawing alone’ (Oers,

1997, pp. 242 and 244). These findings are relevant to young children’s written

calculations: in addition to verbally explaining, children often use symbols of their

own devising to indicate their action – usually something they have done in a

concrete situation. These symbols include drawings of hands holding an item or

numeral (implying adding or ‘taking away’), and arrows pointing away from the

calculation to signify removal or subtraction: we term this ‘narrative action’ (see,

for example, Figure 7.3).

Figure 7.3a John Figure 7.3b William

The ‘melting pot’

At this stage we can see a wide variety of different representations of operations

which we refer to as a ‘melting pot’.Carpenter and Moser studied the range of strate-

gies children use to add and subtract and found that a variety of informal counting

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