Children\'s Mathematics

of children). This left her with ‘R1’. Several other children wrote out a string of mul-

tiples of threes as in Chang’s example (Figure 9.14b).

Finally, several children drew ‘stick people’ in threes as in Harriet’s example (Figure

9.14c). Several children used a way of showing that only two of the figures in the last

group would be counted, as Harriet did by crossing one out.

Figure 9.14a, b and c Nectarines for a picnic

Ann used various methods to self-check (Figure 9.15). To begin with she wrote ‘3 × 26’

but was clearly puzzled by this. She then wrote multiples of three followed by icons of

boxes with three dots in each apart from the final box. Finally, she used an empty

number line on which she counted in jumps of three to 27 and then back one to 26.

See also Miles, Figure 7.12b, p. 129.

Evaluation

These children incorporated methods they had learnt in the classroom and were able

to select from a range those that made sense to them. Counting in multiples of three

and using an empty number line had helped them to work on this problem in ways

that made sense to them.

Case studies from early childhood settings 189

9.14a Grace 9.14b Chang

9.14c Harriet

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