TThhee mmaatthheemmaattiiccss::addition and subtraction; commutativity; negative numbers.
PPaarreenntt//ccaarreerr’’ss ccoommmmeenntt::Joel’s dad said that his son often gives the family calcula-
tions to work out during supper and shows his own mental calculation skills through
doing this. Number bonds are his current favourite. He also spends a lot of his spare
time with a puzzle book he was given for his birthday, which includes many number
puzzles. Joel’s family recognises that he had been anxious in his previous school
where the emphasis had been on correct spelling and right answers rather than his
thinking. They are pleased that he has begun to explore mathematical ideas in his
new class – he appears to feel happier at school now.
AAsssseessssmmeenntt::trying to reverse the subtraction calculation led to the area of negative
numbers and his description of ‘super-zero’ was quite an insight of the move below
zero. Joel has not worked with negative numbers. We discussed what he had done at
the end of the lesson and many of the children were so intrigued by his term for
moving into negative numbers that they burst into applause.
TThhee nneexxtt sstteepp::put up both a vertical and horizontal number line with negative
numbers – this will provide a useful resource for Joel to explore some more subtrac-
tion sums in reverse. I will also borrow a fridge thermometer when we make some
ice in the fridge in science next week and make sure Joel’s group do this.Having a dialogue with a child is not always easy, yet it is crucial in helping children
discuss their mathematics. To find out about children’s representations one needs to
ask them about it. If the atmosphere and culture of both the classroom and the
school are of listening, children will get more articulate about their mathematics.
The importance of thinking and language is well documented (Brissenden, 1988;
Durkin and Shire, 1991).The pedagogy of children’s mathematical graphics
There are clearly some specific aspects of our pedagogy that support the range of
children’s own mathematical graphics, although it is not easy to be entirely objec-
tive about the practice we have developed. We are aware that we acknowledge and
respond to all children’s meaning-making and representations as though they make
sense.We negotiatemeanings to encourage deeper levels of thinking and to make an
ever-widening range of representations available to the peer group for discussion and
for further negotiation, appropriation and adaptation. We give representation a high
profile within children’s play and through our observations of children’s play are
able to identify mathematics that offers potential for representation. In conven-
tional, didactic teaching the pedagogy is a clear-cut transmission model where it is
easy to identify the teaching method. Our approach to teaching is much more of a
two-way communication, where the children can also lead and the teacher uncov-
ers their thinking in order to support and develop their learning. A significant
feature of our teaching is the very specific way in which we interpret and use mod-
elling to support children’s mathematical development.204 Children’s Mathematics8657part 2.qxd 04/07/2006 17:38 Page 204