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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
of 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 Justine.
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
Jayne summarised her presentation with the following comments:
- 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 challenging behaviour.
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.
Problems with Multiplication
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 Lines
, 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 activities.
- 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 learners.
- 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 project.
To celebrate the success of this partnership between Devon and NRICH, further dissemination is planned through links with NCETM
, SWMA (South West Maths Association), SWGATE and the Devon primary maths website
This article first appeared in Primary Mathematics, a journal published by The Mathematical Association