‘Modelling’ mathematics
One of the problems is that the language used in official documents is not explicit about
the difference between the terms ‘modelling’ and ‘examples’. In discussion with teach-
ers we have found that modelling is usually interpreted as ‘giving direct examples’.
Teachers certainly need to introduce a variety of symbols and ways of recording as chil-
dren grow and develop their understanding, but our evidence is that young children
treat examples as something that we expect them to use. Lee proposes that examples
‘show learners a way ... that frequently would be referred to as theway’ (Lee, 2000. p. 28).The children had all represented the number of eggs in exactly the same way in
which the teacher had done. Clearly the teacher intended to support the children by
providing an example of recording. However, as Lee (2000) has argued, examples are
also ‘restrictive’. The message that the children took from the teacher’s example was
that this was theway they should represent the number of eggs on their cake. Alter-
native ways they might have chosen (dots, other marks, numerals or their own
approximations of numerals) were not used.
This had been our experience in our own classrooms and was a difficulty we recog-
nised. We knew that we needed gradually to introduce children to standard symbols
and various layouts but when we provided an example at the beginning of a lesson –
intending to offer one possible way – the children copied exactly what we had done
with limited understanding. It could be argued that this is a positive outcome since the
children incorporated standard symbols and ways of working into what they did.
However, rather than helping them, we were repeatedly confronted with children who
were confused and could not apply what they had been introduced to in other contexts.Examples or modelling?
To illustrate the ways in which children use teachers’ examplesand learn from
teacher-modelling, one of us explored this question in a class we were visiting. The
children were 5-years-old and in their second term at school.
I divided the class into two, splitting each of the four ability groups so that the two
halves of the class were balanced:An example of ‘an example’
In the nursery, a teacher provided paper for the children to represent the
number of (sweet) eggs they had each put on the cakes they’d made.The children
were hesitant and the teacher drew her own example of a bird’s nest (cake) on a
sheet of paper. She then counted four eggs on one of the cakes on the plate and
drew four ovals in her drawing of a nest.
Following her example, every child in the group drew a nest, counted the eggs
on their cake and drew some eggs on their drawing of a nest.Developing children’s written methods 2058657part 2.qxd 04/07/2006 17:38 Page 205