[In
response to the questions: Where would you start? Do
you look at student performance for a start, or is it a
matter of talking to teachers about what's going on?]
It's
probably a combination. We need to look at student performance
and find out what and how the children are thinking about
mathematics, then relate that to the way the teachers are
teaching. If teachers taught differently, then the students
might perform differently. The outcomes that the children
achieve and the behaviours they show will be very dependent
on how the teacher is teaching. So if the teacher is teaching
maths in a way that the answer is the all-important thing,
then the teacher will probably never have the opportunity
to get into the children's heads to find out what and how
they are thinking. The way we teach maths has to shift from
emphasising getting answers using set procedures on paper
to talking about how we can find answers and how we're thinking
about problems.
The
belief in themselves that they can succeed in solving problems
is the core issue. I've taught children in Year 7 who are
surprised when I suggest to them that they can see pictures
in their heads to help them work out problems. They hadn't
latched onto the idea that thinking is something that they
can have control over. They have got caught up in the idea
that maths is only about the answers, not about the process
of getting the answer.
I
suspect that if students like the ones we were working with
are going to really improve their mathematics, it will be
through conversations with their teacher about these ideas.
Through conversation with the student, you can make sure
on the one hand that what you think the students are saying
is what they're really thinking and, just as importantly,
that what they think you're saying is what you think you're
saying. You can only do this through conversations with
individuals or small groups and the classroom will need
to be set up to accommodate these conversations.
Emphasising
talking and thinking in mathematics can be a starting point
to helping students make sense of mathematics. For example,
in the traditional classroom after talking about a new idea
the teacher gave the problems, most often in written form,
and the students gave the answers. Using a strategy as simple
as letting the students make up the problems and then share
them orally will let the students consolidate their understanding
and at the same time give the teacher the opportunity to
find out whether the students understood the new concept.
Any
teacher, anywhere, can now start looking at his teaching
of maths from the point of view of what the students know
— talking to the students about how and what they are
thinking. We need to value the process of thinking, not
just set procedures and answers, if we are going to help
students to become and see themselves as successful mathematicians.
Our
brief was to take a group of students and see if we
could move them on in their mathematics, and then
to analyse what we had done to try and show other
people some strategies that might work.
