Outcome of Group 2
Looking at the written methods these eight children chose and talking to them, it is
clear how much they understood about what they were doing and that this early
addition made personal sense. The methods chosen by the children in the second
group contrast sharply with those from the group who copied my example.
These findings point to the value of teacher-modelling in real contexts through-
out the week rather than at the beginning of a mathematics lesson or group session,
and discussion with the children to help elicit their ideas. When we directly model
written mathematics we try to ensure that the mathematics we use is for real pur-
poses and real people – because someone needs to know the outcome. In the models
we provide, we focus on aspects we want to introduce to the children such as use of
a particular symbol or a clear way of setting out some data. The children have access
to a growing bank of possible written methods, ways of representing, layout and
meaning of symbols and can select those that are most appropriate for their current
stage of development. In this way, we are adding to children’s personal mental ‘tool
boxes’ by using additional symbolic(cultural) tools(see pp. 213–14).
In the following section we explore our research into the effects of teacher-mod-
elling in a class of 5- and 6-year-olds that one of us visited on several occasions.Modelling: children develop their mathematical representations
In a second study of the impact of direct teacher modelling, I focused on direct mod-
elling of different aspects of data handling during short fortnightly visits to the school.
I modelled a number of aspects including layout and analysing data, based on what I
had seen in the children’s graphics on my first visit. Following my final visit we com-Alice drew the six bears and then counted them, adding a numeral to each in
turn to arrive at her total (Figure 10.8c).Scarlett also used shapes to represent the bears, but to indicate the two different
sets she drew two circles and four squares (Figure 10.8b). Counting continuously,
she then wrote the total of ‘6’ beneath and finally she added to her circles and
squares, turning them into balls and presents (using icons to stand for the bears).Brendon was clear that he needed to count all the bears in front of him.
Beginning in the centre of the paper and moving to the left, he wrote a number
for each bear as he counted. Although not yet very secure in his knowledge of
standard written numerals, he was able to self-correct and read what he had
done as ‘1, 2, 3, 4, 5, 6 bears’ (Figure 10.8a).210 Children’s Mathematics8657part 2.qxd 04/07/2006 17:39 Page 210