more readily through informal and idiosyncratic working’ (Anghileri, 2001b, p. 18).
Newman argues that ‘activities that involve fragments of language, that discour-
age children taking chances, that don’t permit the exchanging of ideas, can only
serve to make reading and writing more difficult’ (Newman, 1984, p. 72). This is true
for all young children learning mathematics but, we argue, it is even more so for
children who may have learning difficulties.
The need to work from where the child is can help us know where to start supporting
children’s own methods. Their own ways make sense to them. In discussing children’s
own mathematics with them we can quite often be excitedly surprised by what they do
know. Children’s own mathematics provides adults with a ‘discussion paper’: for many
children with special needs worksheets are a recipe for failure. They perpetuate a
right/wrong culture. Cockburn believes that when children enter school they often learn
to ‘play the (mathematics) game’ where the emphasis is on finding the right answer –
which is always the teacher’s answer (Cockburn, 1999, p. 9).. Additionally, when children
represent in their own way, because they have to think carefully about what they do and
consider a range of possibilities, they will learn more about the mathematics. It is
because of this struggle that occurs within their minds that ‘they will do better than
their perceived best’ (Brighouse and Woods, 1999, cited in Robbins, 2002, p. 5).Children’s questions
Listening to children, not only to what they have to say about their marks but what
they have to say in general, can instigate a change in your teaching. I remember when
I asked the children in my class what questions they had when we were discussing
Holland. One child asked, ‘How many cows are there in Holland?’ I was not expecting
that kind of question although it is an interesting one and I believe only a child would
ask it. The questions below are from children in our own classes and from other classes
in which we have taught. We have included questions and comments from children
in classes where teachers had just started to support the children’s own mathematical
graphics.Lia, 7:0 AArree yyoouu aalllloowweedd ttoo sshhooww yyoouurr wwoorrkkiinngg??
Response: If writing down your mathematics helps your thinking, then of
course. Sometimes just putting something down helps your
memory when you have a lot of calculations to do – otherwise you
may forget. However, if you can do the mathematics in your head,
well, just write the answer down.
Jason, 8:2 CCaann II uussee aa rruubbbbeerr??
Response: It is better not to use rubbers, because you may want to look back at
the strategies you have used. I like to see what you have written as
it shows all your thinking. All good mathematicians keep all of their
written work, even if it did not work out: they can go over it again
and see where they might have worked in a different way. They
don’t use rubbers – every mark is important.230 Children’s Mathematics8657part 2.qxd 04/07/2006 17:40 Page 230