pared the children’s first pieces of data handling with their final efforts to assess any
gains. Of the 12 children who were present for both lessons, ten showed that they had
used aspects that I had modelled with them. During the final lesson I had not referred
to any of the features I had modelled in the previous two months. When comparing
the two samples, 25 per cent of the children had included all three significant aspects
I had modelled in their own data handling; a further 25 per cent had improved on two
aspects and the remaining children had included one aspect. The two samples below
from Ashley illustrate this development (Figure 10.9a and b).
In the first, Ashley collected responses from his friends and used tallies to mark
their choices: the writing in this example is an account of three things he likes to do.
In the second example Ashley’s work shows that he incorporated some features that
I had directly modelled during the term.
Lee (2000, p. 29) suggests that ‘one feature of the modelling process is that it is
intended to give an idea of the quality of a way of working, rather than a royal road
to follow’ (emphasis added). Modelling can be summarised using the following key
points (based on Lee, 2000):- When an adult models a way of representing some mathematics on paper, she can
also model her thinking processes. - The quality or way of representing the mathematics needs to be one that the chil-
dren themselvescan use if they choose. - A model need not necessarily be finished or ‘perfect’. This will allow children to
reflect on difficult aspects. - It must be able to be changed by learners to suit their own purposes.
Using models in the way we suggest therefore allows children to take ownership of their
mathematics whilst still offering them support. It is a way of introducing specific use of
symbols within contexts that are real to children that they may use if they understand
them. It permits children to choose ways of representing that match their current ways
of thinking and development, and their visual imagery. As Wray, Bloom and Hall
suggest, children need to see others using literacies to ‘demonstrate when it is used, how
it is used, where it is used and what it is’ (Wray, Bloom and Hall, 1989, p. 66).Modelling in literacy – and mathematics
Modelling allows children to move from what they can achieve alone to what they
can achieve with a more ‘knowledgeable other’ as Vygotsky identified in his ‘zone of
proximal development’ (Vygotsky, 1978).
Barratt-Pugh and Rohl also emphasise the way in which modelling allows adults a
means of introducing a variety of genres (Barratt-Pugh and Rohl, 2000). Different
genres of mathematics in the Early Years can include lists, representing data, recipes
(quantities and measures) or a means of totalling money spent for a picnic (addi-
tion). Modelling these can extend children’s repertoire and support their under-
standing since what they choose to do is something they understand. DiscussingDeveloping children’s written methods 2118657part 2.qxd 04/07/2006 17:39 Page 211