Children\'s Mathematics

separate instance of dots on the dice Amelie drew, she counted them out loud. Four-

year-olds do not only represent things they physically count, but also can often repre-

sent and count some things that they cannot see, such as Jenna’s raindrops (Figure 6.8).

Figure 6.8 Jenna’s raindrops

Horizontal and vertical arrangements

Next, children appear to represent items or numerals in a line, usually horizontally –

as in his drawing of books that William counted (Figure 7.3). Occasionally the items

they draw are set out vertically, as in Jenna’s raindrops (Figure 6.8).

Several researchers have demonstrated the vital importance of counting in the

initial calculation strategies young children use (Carpenter and Moser, 1984;

Fuson and Hall, 1983; Gelman and Gallistel, 1978). Gelman and Gallistel identified

five basic principles that are guided by young children’s implicit understanding. It

is interesting to note that in their graphic representations, children’s strategies do

indeed appear to be governed by the principle of one-to-one counting: they

invariably arrange items or numerals to be counted in a line, and then begin

counting with the first item they had represented (Gelman and Gallistel, 1978).

Jenna, 3:9, began writing her name in the top right-hand corner. After writing ‘J’,

she was obliged to continue from right to left to complete her name. She also

drew and counted the raindrops from top right, counting each vertical column

before proceeding to the next, in the same direction that she had written her

name. Perhaps the coloured pens she’s used reminded her of a rainbow and this

suggested ‘raindrops’.

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