Dialogue
In all the examples in our book, the sort of dialogue that allows for meaning to be
explained, negotiated and co-constructed was an important feature. It is language
(discussion) that Oers asserts ‘gradually moves the child into more abstract forms of
semiotic activity ... This might be a very important stage in the process towards
more abstract thinking especially in the domains of literacy and numeracy’ (Oers,
1997, p. 244).
It is interesting to note that researchers found in Japanese classrooms ‘emphasis
placed on communication between pupils ... [which] meant that Japanese children
were having to explain their thinking – and in some cases, other children’s thinking- on a daily basis’ (Hughes, Desforges and Mitchell, 2000, p. 113). As a teacher of six-
year-olds remarked to one of us at the conclusion of a demonstration numeracy
lesson, ‘I had never thought of asking a young child to explain (i.e. to read and inter-
pret) what another child had done’. Doing this allows other children to interpret
another’s written methods and the child to whom they belong is able to see if what
they have done makes sense to someone else. In data collection an additional
strength is that this is an early form of analysis, allowing others to interpret data in
order to draw conclusions from what has been written.
There is another sort of dialogue that accompanies children’s marks as they ‘make
sure the observer sees the meaning of the drawing as it is meant’ (Oers, 1997, p. 242).
Oers comments that their findings indicated ‘that not just things are represented in
children’s drawings, but meanings ... so speech has an explanatory function with
respect to drawings’ (ibid., p. 242). We had come across such explanations many
times but were excited when, a few days before we were due to send in the manu-
script of this book, one of us observed Adrian, 6:2, do just this in our classroom.
Within the space of a few minutes Adrian had explored three possible interpreta-
tions of the symbol ‘+’ that he had written – ‘no’, kisses and ‘plusses’. He was explor-
ing these multiple meanings of one ambiguous symbol in ways that he could
understand and wanted to make sure that I understood his meaning ‘as it is meant’
(Oers, 1997). That this example occurred at this moment was even more surprising,
when we reflected on what we had just written about the ambiguity of such symbols
as ‘+’ and ‘x’ (see Chapter 5, p. 73).
As our examples of young children’s calculations in this chapter show, their under-
standing and their written methods develop over time. Children should not be
hurried into written calculations with standard symbols before their intuitive under-
Understanding children’s developing calculations 129Figure 7.12b Miles8657part 2.qxd 04/07/2006 17:21 Page 129