mark. He put a tick to show that eight could be shared. On the second paper he drew
two faces depicting two people at a bowling alley. He drew the skittles and linked
arrows and the symbols ‘1, 2, 3’ to the faces. In this example he also put a tick and
said ‘a tick shows us that six is a sharing number’. In a third example Kamrin moved
away from pictorial narrative graphics and used iconic/symbolic forms. This was
much more efficient for him as he understood the symbols he was using. He wrote
nine, a question mark and a cross sign to show us nine is not a sharing number. His
own symbols meant something to him and he understood the sharing concept
through them. In this one session it was significant that Kamrin realised that there
were quicker ways to represent his mathematical thinking and was able to use them.
Elizabeth, 4:9, chose the numerals four and eleven and used cubes. She said
‘four is a sharing number but not eleven’. She put a heart beside the four to show
us it is a sharing number and a sad face beside eleven, to show that this was not a
sharing number.Evaluation
The examples of the children’s representations on paper show a wide range of
responses. All the children’s marks were respected and accepted because the adults
viewed them as intelligent responses. Many of the tasks that teachers set children
are not always fully understood by the child but they make their own sense of
them. In this session, because the children’s choice of marks was accepted and
analysed carefully, the teacher understood more about the children and their
thinking.
In the last part of this session children shared their marks with each other. I wrote
on the board the numerals zero to fifteen. I asked them to tell me what they had dis-
covered about each one. I put a line beside the numerals that the children indicated
shared equally and a cross beside the numbers that did not share. We also discussed
other symbols that could be used instead of ticks and crosses, for example, Eliza-
beth’s hearts and sad faces. They could see a pattern and some children were able to
predict the numbers that shared. I introduced the class to the words ‘odd’ and ‘even’.
Their teacher asked them if their age was odd or even. This prompted a very lively
and interesting discussion.A zoo visit
THE MATHEMATICS data handling
AGE 4-year-olds
CONTEXT adult-led group
FEATURES range of strategies chosenA class of 4- and 5-year-olds had just returned from a visit to a local zoo. Bursting
with excited talk about their favourite animals I used this opportunity for some data
handling. Each child chose their own way to put down three or four of their personalCase studies from early childhood settings 1778657part 2.qxd 04/07/2006 17:29 Page 177