Children\'s Mathematics

Mathematical graphics are more diverse, not only because children are not

moving towards common forms of a written language such as English or Greek, but

because the different mathematical genres often suggest quite different graphical

approaches. In early written addition, for example, children usually begin with con-

tinuous counting before separating sets (see Chapter 7). In representing data, young

children may use pictures and ticks and gradually move towards increasingly stan-

dard layouts (see Chapter 8).

However, before we analysed children’s own written methods of calculations we

needed to focus on the range of different, graphical marks children choose, and the

evolution of these early marks: (for an overview of the development of children’s

mathematical graphics, see Figure 7.13 in Chapter 7).

Common forms of graphical marks

In analysing our examples of children’s marks and written methods we have identi-

fied five common forms of graphics, including three of Hughes’s categories:

• Conclusion

• pictographic


• iconic


• written


• symbolic.

Dynamic

We use this term to describe marks that are lively and suggestive of action. Such graphics

are ‘characterised by change or activity (and) full of energy and new ideas’ (Pearsall, 1999).

We categorised Charlotte’s ‘hundred and pounds’ (Figure 6.7) and Amelie’s dice game

(Figure 10.3 in Chapter 10) in this way. Both pieces have a freshness and spontaneity.

Pictographic

We have used Hughes’s definition, ‘that the children should be trying to represent

something of the appearance of what was in front of them’ (Hughes, 1986, p. 57).

For example, in Figure 6.9 Karl was representing the tables that he had just counted

in the classroom. In another example, Britney drew the strawberries that were on a

plate in front of her, and which she subsequently ate (see Figure 7.6).

Iconic

These marks are based on one mark for one item when counting. Children whose

marks are iconic use ‘discrete marks of their own devising’ (Hughes, 1986, p. 58). This

can often be reflected in the popular use of vertical strokes as tallies that is taught in

many schools, although to tally is to keep a score of something and need not dictate

only one way. However, when children choose ‘marks of their own devising’ we find

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