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In the first part
of this article
, we described how the Enriching Mathematics
Project in Devon came about. Having been introduced to the NRICH
website and 'rich' mathematical tasks, teachers in the county
agreed to trial some of the investigations and games with their
children and complete evaluation forms, reflecting on the lessons
as they did so. Four months after this initial launch, we all met
again and the teachers shared their experiences of how NRICH had
impacted on teaching and learning in their classrooms.
During the afternoon of our second day, the Lead Teachers took the
lead! In the previous part
this article, we heard about examples of problems used by three of
the Lead Teachers: Katie, Barbara and Anna. They highlighted
changes in the ways the children worked and ways that they
themselves as teachers had developed. In this article, we will
share the comments of three more Lead Teachers: Jayne, Amy and
Jayne, a Year 3 teacher at St Leonard's Primary School, told us
about one of her experiences of using NRICH problems. In this
instance, she had wanted to find an activity to use with her whole
class, many of whom have behavioural issues. She wanted to focus on
appropriate use of apparatus and meta-cognition.
She found the Sweets
in a Box
To begin with, Jayne modelled how she would have started a solution
on the board, verbalising her thinking. She deliberately made a
mistake and asked the pupils how they could improve what she had
done. They talked in pairs about what they would do and then
carried out their plans. Jayne encouraged them to use everything
and anything in terms of equipment.
Jayne reported that it was interesting to see their different
methods of representation - some drew images, some used
multilink. Some went on to investigate multi-layered boxes and some
changed the rules slightly so that they could ignore diagonal
lines. One child used symbols to represent the sweets. Pairs went
on to make a poster, which described their thinking as they had
been working on the problem.
Jayne summarised her presentation with the following
- children made their own decisions
- they were challenged, regardless of their starting point
- the class worked for two hours!
- the task naturally promoted use of apparatus
- the pupils refined and reviewed as they worked
- the problem encouraged them to talk.
Amy is a Year 6 teacher at Whipton Barton Junior School. She
began by explaining that the majority of her class didn't like
taking risks in mathematics and some children also exhibited very
Amy told us that one of the group, I'll call him K, often
displayed aggressive behaviour and found working with others very
difficult. She told the group that she would take some still
photos, but then secretly filmed them as they worked. We saw a few
clips of key moments. One showed K and his partner very excited at
being able to predict some of the results of the calculations.
Another clip showed K spotting a mistake in the working of the
other pair of children. He politely and carefully went through the
correct version with them several times until they saw their error,
which Amy reported was a real break-through as previously he would
have been very dismissive of, and rude about, their mistake.
Amy said that K really wanted to share the investigation with
the rest of the class. He suggested that if each pupil started on a
different number, they would then have lots of examples to see
whether the pattern always worked. He 'pestered' Amy over several
days to allow him to try this out, which he did. He'd been thinking
about it at home and suggested that each member of the class began
on their number in the register. Unfortunately, some of the
children couldn't cope with the addition and subtraction of
negative numbers, so not all the arithmetic was correct and Amy had
to intervene, but it was great to see K so determined to lead a
maths session with his peers.
Amy reflected that filming in this way had also enabled her to
think about her own interventions, which had been important for her
own professional development. She found herself wondering what
would have happened if she hadn't said ..., or if she had said...
at particular moments.
Amy commented that, gradually, the children in her class have
got much better at working in groups and communicating with each
other about mathematics, and they now have the confidence to try
things out. This has also transferred into other curriculum areas.
Amy led a staff INSET about NRICH in the autumn term of 2009.
Justine, a Year 5/6 teacher at Newton Ferrers C of E Primary
School, wanted to see how some of her higher-attaining children
applied their knowledge and she was keen to assess their reasoning
and explanations. She worked with a small group and didn't tell
them these intended learning objectives.
They watched the video in the problem Multiplying with
, without any explanation from Justine. (It is impossible
to convey the contents of the video here without losing the impact,
so I urge you to take a look before reading on!) The children asked
to see it again so they watched it one more time. The challenge was
to figure out why this method for multiplication works and Justine
simply let them get on with it. They began asking their own
questions, such as "Does it work with all numbers?", "Does it work
with decimals?" ... Justine asked the group if they could relate
this method to other methods of multiplication with which they were
familiar. One pair videoed themselves comparing this line method
with the grid method, explaining the links. Justine reported that
the children were inspired by the task and it took away barriers as
they had no idea what she as the teacher was looking for!
This afternoon session led by the Lead Teachers was amazingly
inspiring. The teachers' presentations were informed by a rich
range of evidence including children's work, photographs,
dictaphone recordings and video clips. Liz was completely bowled
over by their commitment and drive, their enthusiasm for
mathematics and the overwhelming desire they each had to create
engaging, challenging and meaningful mathematical experiences for
their children. Reflecting on the afternoon sometime later, Liz was
particularly struck by the following:
- Several teachers' willingness to adapt the existing NRICH
resources to suit their learners demonstrates a professionalism and
confidence that truly impressed her.
- The fact that Barbara was inspired to create her own
'NRICH-style' problems- it is interesting that she herself had a
clear idea of what made an 'NRICH-style' challenge and by
identifying those characteristics, she was able to make resources
which offered the same kind of experiences herself.
- On many occasions, the children were motivated to ask 'what if
...?' questions and to create their own versions of the
- It was evident that some learners began to think about
mathematics and particular problems beyond the classroom situation.
Isn't this exactly what we would like children to be doing
- mulling over a problem over a series of days or weeks?
- Modelling a solution, possibly making mistakes, and inviting
children to improve and continue it is a powerful approach.
- All the teachers had high expectations of all their
- Being involved with this project seemed to prompt some teachers
to reflect on their own practice, carefully considering the
questions and prompts used, and deliberately deciding not to share
the learning objectives with the group.
The feedback day was a resounding success and Liz would like to
think that everyone went away feeling very inspired and enthused -
she certainly did. She was so taken aback by the quality of the
teachers' responses, not just the Lead Teachers', but also the
feedback received from everyone who filled in a form, that she
cannot stop talking about it. Since March, Helen and Liz have been
busy collating the information we have received in over 200
feedback forms! Some of the comments Liz is able to act upon
relatively easily where appropriate and others she has been sharing
with NRICH colleagues. It is only through constructive feedback
that the NRICH website will continue to improve and therefore Liz
is indebted to all the Devon primary teachers who took part in this
To celebrate the success of this partnership between Devon and
NRICH, further dissemination is planned through links with NCETM
, SWMA (South West Maths
This article first appeared in
Primary Mathematics, a journal published by The