although many claim that children do maths for 80 per cent of the day the reality is
that children are using numeracy skills for less than 2 per cent (Munn, 1994). The dif-
ficulties lie with the knowledge of the teacher and this is carried into school situations.Scott’s use of symbols
Scott’s family had moved into the area and he had had to change schools.
Approaches in his previous class had clearly differed from that of his new class.
Because he was experiencing difficulty in his new school he had been put in a class
with children a year younger than he was. Scott was apparently bewildered by the
abstract symbolism of both writing English and of mathematics. It seemed possible
that Scott had been introduced to formal calculations before he had had an oppor-
tunity to make sense of his own marks. Perhaps before he reached 6 years old, he had
been expected to write and to represent mathematics as an older child would, even
though he had not understood what he was doing. Like Daniel, Scott was also con-
fused by imperfectly memorised ‘tricks’ which he was then unable to apply in other
contexts. As John-Steiner emphasises, representation is one of the important ‘uses of
language ... [and] may not develop well when children find themselves under severe
pressure to acquire a second language’ (John-Steiner, 1985, p. 351).Scott, 6:6, was new to the school. During this lesson it became clear that Scott
had not developed a personal understanding of abstract symbols; to Scott the
choice of which symbols to use appeared almost arbitrary (see Figure 5.1).
This was a lesson in which children were adding small amounts of grapes that I
had brought in.The children were working out their calculations on paper, using
their own chosen forms and approaches. Children used a range of responses –
writing, numerals, their own marks and pictures.
We can look at what Scott did in a positive way. He can represent small
amounts of things he counted: for example, he drew three circles followed by the
numeral ‘3’, four circles followed by ‘4’ and seven circles followed by ‘7’. His
problem began when he tried to use some abstract mathematical signs, for
example: ‘0 4 = 3’, ‘4 5 = 6’, ‘4 3 4’, ‘0 = 0 4’ and ‘5 = 5’. Scott has understood that
written calculations require numerals and signs. However he was clearly confused
when representing these calculations.When I sat with Scott and gently asked him
to show me what he had done, he read his final ‘calculation’ aloud, ‘1 = 0’ (he
knew what the ‘=’ sign was called): he was unable to say what he meant by this.
Scott then took a grape from the plate and reached out for two more grapes: I
asked if he could think of another way he might show how many he had
altogether. His response was to draw round the first grape, followed by the ‘+’
symbol and then draw round the additional two grapes. Beneath this he wrote ‘3’.
He was beginning to make some connections with his marks and the use of an
abstract symbol.Bridging the gap between home and school mathematics 718657part 1b.qxd 04/07/2006 18:10 Page 71