Children\'s Mathematics

In different ways, the children’s examples on these pages all include the use of

implicit symbols.

In his study of 6-year-old children’s addition based on the ‘box task’, commenting

on the findings Hughes noted that the most common response was when children

wrote the total, rather than their written method and answer. Observing that the

findings were ‘quite striking’, he suggested that the pictographic or iconic strategies

children used in the ‘tins game’ would have been far more useful (Hughes, 1986).

Hughes concluded that the most obvious explanation was that the children ‘were

actually asked to make written representations whilst working on a mathematical

problem, and so were presumably set towards adopting the inappropriate strategy of

using numerals’ (Hughes, 1986, p. 130). Yet our evidence, illustrated by some of the

examples in this section, is that when young children represent only the total with

numerals, this is in fact an intelligent response since these children were clearly able

to do the calculation mentally. Furthermore, whilst askingchildren to make ‘written’

representations is something we would avoid, we often find that some children

choose to write (in words). The point we wish to make here is that the children’s

In Figure 7.9a, Jax, 5:2, also implies symbols using dots (an iconic form) and

numerals (symbolic).This can be read as ‘6 and 4 = ten’: Jax wrote the initial ‘t’ of

the word ‘ten’. Mary, 5:4, (Figure 7.9d) has also used a combination of iconic and

symbolic responses, with the minus and equals signs implied.William, 5:7, (Figure

7.9c) moved from working out some calculations with small numbers to trying

(for the first time) two with larger numbers: he also implied the plus and equals

signs. Peter, 5:9, (Figure 7.9b) has used his own shorthand which, provided we

know the context, can be read as ‘4 –3 = 1’: from this it is clear that Peter could

work this calculation out mentally.

John chose to use a written response, writing ‘2 grapes there is two, 4 grapes

there is four’. It is interesting to note that John wrote both the numerals and

words for both amounts. Finally John also wrote the total ‘6’ (to the left).We have

often found that children choose to use a written response (see Chapter 6 and

Pengelly, 1986).

Fred, 5:8 and John, 5:5, were also adding grapes (Figures 7.8a and 7.8b,

respectively). Fred has separated the two sets with a line (drawn above one finger

of the hand).The plus and equals signs are implied since the whole can be read as

‘5 plus 1 equals 6’. Fred wrote the numerals ‘5’ and ‘1’ on the left and, finally,

wrote the total of ‘6’ below.

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