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Science, Technology, Engineering and Mathematics
Teachers Using NRICH 1
Stage: 3 and 4
Article by Peter Hall and Jennifer Piggott
Published January 2009,February 2011.
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.
[Readers may also be interested in other
about teachers using NRICH]
Do I have to do problem solving all the time?
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.
But I've got a mixed ability group
I'm tempted to say that every class is a mixed ability class... but I think one of the strengths of an open ended task is that different students can work on it in varying degrees of depth. Many problems work well at both a superficial and an in-depth level (something about being a pool in which a child can paddle but also an elephant can drown?). Perhaps you can take advantage of the mixed ability in the way that you structure the groups. Maybe this is an ideal time for AfL to come to life - it has worked quite nicely to have groups present their solutions as a poster and then have the class move around the room and rate the poster.. This also means the students are able to see the varying responses to the question. On several occasions I've found the better mathematicians have not been the ones with the best ideas - and have not had the most creative approach to an unfamiliar problem.
How can I make group-work work to my advantage?
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...
At my school we teach fractions every year. We still find year 12 seem to have "forgotten" how to add up fractions correctly. So perhaps it is worth taking more time to "do fractions" in year 7 so that they understand them better. Perhaps a problem solving approach will yield other ways of approaching a topic that you haven't thought of before. Maybe there are critical subjects that you can identify where it would be worth taking a little more time. If you're redesigning the KS3 curriculum perhaps you can create more time for some topics. Of course some students seem to benefit from constant revision and re-covering topics -maybe it is worth saving the problem solving lesson on fractions for a later point in the year- so that the problem solving lesson becomes a revision lesson as well as a lesson on problem solving.
But this problem doesn't have a right answer?
Be brave! Encourage them to work on these sorts of problems. Be excited when they find an answer you haven't thought of. Give prizes... If you get more than one solution can you involve the students in judging what is a good solution - or which is the better one? From time to time it could be good for the students to work on a problem where you don't know what the answer is -and tell them that. Is that a nicer feel for their thinking than just trying to discover the thing that you know already.
How is this going to engage my students?
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
answer than me" - and a whole new direction evolved.
What about other teachers?
I think this year I've found three groups of people - some are very keen to work in this fashion and have been keen to discover the NRICH website - especially the curriculum map and the topic search, and for this group of staff I've only needed to point the way. Others have wanted more help. This help has included me choosing "good" problems for their classes or collecting together resources for their use. A further group of teachers have found the whole process too scary. Right now they're not used to teaching in this fashion - they are still fairly didactic and uncomfortable trying anything else. But as the new KS3 curriculum unfolds, and as we look for more rich tasks and try to incorporate more functional skills. ... I think more people will be converted to think in a problem solving fashion.
How has your attitude changed?
I think working in a problem solving way has encouraged me to be more flexible in lessons, with some problems I've had a go beforehand and then I've expected the students to tackle them in the same way as me. It has been interesting when they haven't. I've seen more evidence of how they think, and the areas of maths they don't like / aren't comfortable with when I've encouraged them to try their own ideas. With some classes this has needed more support to ensure they're all still doing something when they easily might not be.
How are you going to use these problems next?
For next year some of the problems have been included in our scheme of work, so I want to help other staff get the best from the problems as we get to them. For my classes I want to try harder to foster a changed learning environment and try harder to make problem solving a more natural approach to a new area of the curriculum. I'd also like to try harder problems with my sixth form classes- I'd like to believe they'll make a better job of it...
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!
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