- Group 1: teacher providing explicit examples of ways of calculating on white-
board. I then asked the children to ‘put down on paper’ what they had found out. - Group 2: discussion of possible ways of representing calculation; children offering
their own suggestions, some based on previous teacher-modelling and some chil-
dren’s original ideas. The children’s different suggestions were valued and they
were asked to ‘put something down on paper’ to show what they had found out.
For the purpose of this research, I taught each group in turn in a shared area outside
the classroom, whilst the other group was engaged in choices of their own in the
class writing area. The numbers I used were identical for both groups and I explained
what I was doing using identical language. Whilst the first group watched as I drew
teddies and wrote a standard horizontal calculation, I made sure that none of the
children in the second group heard what we discussed or saw what I put on the
whiteboard. The main part of the lesson focused on adding small quantities.Group 1 – teacher example
Taking three teddies from the bag I put them beneath the whiteboard in a row and
subsequently took two more teddies from the bag. We talked about what I had done
and then I drew three teddies on the flip chart followed by the word ‘and’, then drew
two more teddies. I used the words ‘three bears and two more bears’ and ‘how many
bears are there altogether?’ I asked several children how we might find out and all
chose to count the bears in the two sets continuously, counting five in response to
my question.
Beneath my drawing of the bears I wrote the standard ‘3 + 2 = 5’ calculation and
explained this was another way of putting down ‘three bears and two bears’ and
showing ‘how many altogether’. I then asked two of the children to choose a small
number of toys. Taking the four bears chosen by one child and the two chosen by
the other, I asked them to ‘find out how many bears there are altogether and put
something down on paper’ to show what they’d found out.Outcome of Group 1
The children all drew bears and wrote a standard calculation beneath their drawing.
Of the nine children I’d worked with, two had represented the question in the same
way I had and arrived at the correct answer. James was the only child who had not
copied my example. He had been more independent and had combined drawings of
bears, words and the addition sign: he clearly understood what he had done and had
arrived at a total of six bears.
The remaining six children experienced a range of difficulties – with their inter-
pretation of the symbols, with what they were doing or why they had written certain
numbers. Three children who had written the ‘right’ answer of ‘6’ were confused by
their use of standard symbols.206 Children’s Mathematics8657part 2.qxd 04/07/2006 17:38 Page 206