Published December 2009,February 2009,December 2011,February 2011.
Kirsti Ashworth was one of
four NRICH Teacher Fellows who worked on embedding NRICH materials
into their teaching. Kirsti worked with pupils from Key Stages 3, 4
and 5 during the year 2008 -2009. This article talks about her
I found that NRICH problems can be used with anyone. I tried
using activities with all of my groups from Year 8 to Year 12. I
teach the full range of abilities.
I mainly chose to focus on my Year 8 group. They are a middle
ability group who will be aiming for level 6 to 7 at the end of Key
Stage 3. I decided to use them for several reasons. Firstly, I
wanted to see how a group of their ability would get on with NRICH
resources as I have used problem solving and open tasks with top
sets before but not often with lower ability groups. Secondly, it
was a challenging group to work with.
I went through my Year 8 scheme of work and matched it to the
curriculum mapping document on the NRICH website. For each topic, I
started with the Year 8 activities but also had a look at the Year
7 and Year 9 ones. If there was a problem I really liked, I
followed the links on the bottom of it to other problems that
hadn't made it onto the mapping document. I also did this for
curriculum areas that didn't seem to have many activities
I started off with short tasks and problems that wouldn't
involve too much of a change to my teaching style and might not be
too much of a shock to my pupils. They also have the advantage that
if the pupils really didn't get on with them, I could just bin them
and move on.
Then I started looking for tasks that could be used to
consolidate the topics we had covered. I used these initially to
replace the worksheets I would have used previously, although
obviously at greater depth and with greater scope for going off at
Finally, I used a series of problems that focused on problem
solving skills and techniques rather than specific topics.
Definitely not. I started out using short fairly closed tasks
and problems that I could use as starters or plenaries. Virtually
all of the problems that I introduced to the class initially were
relevant to the topic that we were covering at that time.
I was surprised (although I probably shouldn't have been) at how
long it took the pupils to notice that the activity was related to
the bit of work we had just been doing. I often had to give them a
huge hint to that effect. I also found that the activities took a
lot longer than I expected before I started. I did have lessons
when the starter took 40 minutes!
I found that I had to make some difficult decisions early on in
the project. When the starter began to stretch out I had to decide
if it was worth pursuing or whether we should just cut our losses
and move on to the main part of the lesson without having
I took both approaches. It depended entirely on how it felt at
the time. There were a couple of starters where we were really
motoring and it was bringing out some excellent maths or exposing
huge misconceptions. In those cases I stretched it out as long as
it seemed to need. At other times it just seemed to be taking a
long time because pupils weren't very interested or were finding it
too challenging. So I called a halt and moved on. In those cases,
on a couple of occasions some of the brighter pupils came to find
me at the beginning of the next lesson to tell me that they'd
carried on with it at home and this is what had happened.
That was my real concern before I started this. I suppose that
this was another reason that I focused on my Year 8 group -they
were my only non-exam class so the pressure to get through the
curriculum was not as great as with my other groups.
I certainly felt under pressure initially, especially when
activities took longer than I had planned. As the pupils became
more used to solving problems and working in groups, the whole
thing became slicker and more focused. A lot of the slowness
initially is time wasted with pupils becoming accustomed to a new
way of working and having a panic about doing something
I used the problems to consolidate their learning more than to
discover new topics, although there were times when I used them to
introduce new concepts and then backed it up with a bit of chalk
and talk to make sure they had all taken it on board. I did find
that after about half a term or so, I could use the problems and be
confident that the pupils were not only covering the curriculum but
exploring it at greater depth than before -in the same amount of
time. I had to get to the point where I was happy to use the
problems in place of a nice exercise with 50 questions.
Firstly, you have to think carefully about what you mean by
horribly wrong. I felt very uncomfortable at the beginning of the
project with using problems as consolidation or even to cover
topics as I didn't feel that I could be sure that every pupil would
leave the room having learnt the bit of maths I wanted them to
learn. However, as the project progressed I have gradually become
more adaptable and flexible in my own approach. I am far more
willing to let the task develop in the ways that the pupils want to
take it rather than trying to control the outcome too rigidly. So
if I introduce a problem that I think will cover adding decimals
and it actually drifts off into area and perimeter then I will
develop that and come back to adding decimals another time.
There were times when I did abandon an activity before I felt
that it was finished, at these times it was because it had become
obvious that the pupils were no longer engaged and weren't making
progress, but that happens in other lessons too!
No. Although I tended to use group work extensively -mainly
beause the pupils felt less exposed if they were working with
someone else. It also allows them to discuss what they are doing
and what they have learnt and make progress by comparing ideas.
I tended to organise the class so that initially they worked in
pairs and then built up into groups of four for some activities. I
usually put them in boy-girl pairs in the hope that the good
working practices of each would rub off on the other.
Obviously this depends on the group, the problem, the prevailing
wind and all the rest of it. Generally though, it does need more
planning than a textbook lesson the first time you use a problem. I
arrived at the following strategy that I found worked with my Year
8s. I gave them the problem and let them have a minute to read it
through and think about it in silence. At the end of that time they
were allowed to ask me any questions they needed to clarify the
meaning of any words or symbols (but not how to tackle the problem
or about the maths involved). I then put them into their pairs to
talk over the problem and discuss whether there was an obvious
starting point or what bit of maths they thought they might need. I
allowed anything up to five minutes for this depending on the level
of complexity of the question.
Once they were working on the problem, I circulated and
eavesdropped on their discussions. If I heard anything that I
thought would help the rest of the group I called on pupils to
share their thinking. This could be anything from a partial
solution to a method such as "Let's put it in a table". If all the
pupils seemed to be missing a trick like working methodically I
would stop them and suggest a method.
If pupils finished the task quickly then I tried to have an
extension question for them. "What if...?"
I introduced problem solving and open-ended tasks gradually to
my groups. We started with short tasks and built up. There was
never a time when no-one had a suggestion (even if it was wrong)
that could give us a starting point. There were times when it
needed drawing out and adapting but I did this with the class as a
whole so that they could start to see possible strategies. This
meant that as the project progressed pupils began to build up a
range of strategies. That way when their initial approach didn't
work they had another plan to fall back on.
They also began to learn that maths isn't just about getting the
right answer, it's also about playing about with concepts and
exploring what is happening. As they realised this they started to
make more and more suggestions and see links between different
parts of the curriculum.
The first time this happened, the pupils hated it. They felt
that I had tricked them into doing lots of work and then there
wasn't an answer. However in a lot of ways this was a real turning
point as they stopped being inhibited by the need to get it right
and started thinking more about strategies they could use and what
might happen if...
As the year progressed, my Year 8 class became noticeably more
interested and engaged in the problems. This enthusiasm spilled
over into other lessons. The vast majority of the brighter boys are
now keen to be involved in the tasks and persevere on them. The
girls no longer approach lessons assuming that they won't be able
to manage the work. They are all willing to have a go and are
flexible in how they approach problems. They will try more than one
approach if the first one does not work.
The culmination of this was their reaction to a recent topic on
3D shapes. I had intended to use a problem for one lesson. The
pupils became so engaged in it that they asked to move on to the
computers to spend another lesson on the problem. Some of them
spent 45 minutes on a single problem, trying different things. At
the end of that lesson they asked to carry on with it in the next
lesson. That level of engagement, enthusiasm and feeling of
ownership would have been unthinkable at the start of the year to
say nothing of the idea that the boys could have spent that long
actively involved in a lesson.
Having been through the Year 8 scheme of work and selected some
tasks and problems for our various modules, I gave an annotated
scheme of work to the other members of the department who were
teaching middle to upper ability Year 8. I also provided them with
printouts of the activities and any necessary resources that I had
used and felt to be successful. I passed on any tips that I thought
would improve the activity or any hints or tips that the pupils
might need to access the task. After a term or so of this, I found
that these teachers started to find their own activities and share
these with each other and the rest of the department.
I also ran a workshop on an INSET day for teachers from across
our local federation of schools on using NRICH and other rich tasks
in the classroom. I delivered the same session for PGCE students at
the University of Cumbria.