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Peter Hall is an Advanced Skills Teacher of Mathematics working at Imberhorne School, a state secondary school in East Grinstead, West Sussex. He was one of four NRICH Teacher Fellows who worked on embedding NRICH materials into their teaching during the year 2008-2009. In this article, he writes about his experiences of working with students at Key Stage Three.

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No! There are many ways of using the NRICH problems. I've
tried to think carefully about the classes I've worked with to see
whether an NRICH problem would make a good starter - as a way into
a new topic or as the main activity for the lesson, or as a plenary
at the end of a topic. Some NRICH problems have resulted in the
class being keen to know how to do something - for example,
subtracting with negative numbers. This has created an interest in
the topic and some motivation for the class to want to learn
more.

Go and talk to your English teacher or your Humanities
teacher, go and watch the way that they get groups to co-operate
and work well. There is much more to think about than we maths
teachers tend to realise. I usually just ask the students to get
into groups of their own choosing, but I'm starting to feel this is
a fairly lazy approach and I need to dictate things a little more.
Perhaps I ought to choose groups based on their last maths test-
and even then do I want a "top group" or do I want to structure
each group with a mix of ability. Do I want to put all the naughty
ones in the same group, or all the quiet ones in the same group?
What about giving each person in the group a role - so they have a
job to do? What about a captain (to keep the group on task) a
facilitator (to ensure that everyone gets heard) a resource manager
(the only one allowed to ask for help, or get paper or scissors)
and a recorder / reporter (to do the recording). More radical ideas
- take one student's work from the group and use this to judge the
whole group, make the whole group take a test- but mark one
question from each student...

Some students may find this approach too daunting - and others
may take some time to be comfortable working in an environment
where there isn't any immediate feedback in terms of the right /
wrong answer. Many NRICH problems have a sense of optimisation
about them - this seemed to create a nicely challenging atmosphere
in the classroom. Other times we have found a question about "make
the largest number with..." went into a new direction by a student
quietly saying "I bet no-one can find a smaller answer than me"
- and a whole new direction evolved.

I'm still wondering whether I should leave things a little
less sewn up - perhaps we should have more questions in our
plenary, more things to dwell on - for them overnight, or over a
weekend - again I'm wondering whether this will improve motivation,
or interest, or re-engage some curiosity.

I need to try harder to be more inventive and creative in the
way I use group work. I need to let some groups be quite
unsuccessful and see their reaction to that, rather than stepping
in and helping them too much. I'd like to think about moving the
chairs and tables around on a more permanent basis... but perhaps
that is a step too far!