Children\'s Mathematics

strategies persists through the primary years. Children’s choices of ways to represent

operations do not remain static since discussion, modelling and conferencing alter

individuals’ perspectives and continuously introduce them to further possibilities.

Negotiation and co-construction of meaning are taking place. The ‘melting pot’

period therefore covers a huge range of representations through an extended period

of time. Some children in this period may choose different ways of representing their

calculations as they refine their ways and ideas of representing addition and

subtraction.

Subtracting beans

The following account is included to show something of the range of strategies chil-

dren in one class chose, and their use of narrative action, when representing their

subtraction calculations.

Supporting children’s own mathematical marks

It is important to emphasise that as teachers we constantly assist and guide children

as they move towards increasingly efficient processes and standard use of symbols.

Supporting and extending children’s mathematical understanding through their

graphical marks can sometimes cause misunderstanding amongst teachers. When

teaching in classes where children are not used to representing their ideas in

114 Children’s Mathematics

Working with my class of 5 and 6-year olds, I decided to use some surplus beans and

flowerpots left over from science, for subtraction. Although we had explored

subtraction in practical contexts, this was the first time that the children had

represented what they were doing on paper.

Early in the session the children spent time playing with the beans, adding and

removing small amounts of beans from their pot. I introduced a game to play with a

partner. First one child in each pair counted (out loud) a small number of beans which

she put in a pot.The other child then removed one or more beans and her partner

worked out how many remained in the pot. Finally, they both counted the beans that

remained in the pot, in order to check.

After a while I put some paper and pens near the children and suggested they put

something down on paper to help their thinking. Barney (Figure 7.4) began writing

‘10 take 1 is 9’, then changed his mind after he had written ‘2 take 1 is 1’. Next he

drew the flowerpots and beans, using arrows drawn in an arc above the one bean he

removed.The arrows point to the second pot in which he has shown the total

remaining.This narrative action is a very powerful way of representing what he has

done. Using successive shorthand he next simplified this written method by reducing

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