Published December 2011,September 2011.
In January 2010, Sarah Grigg from Creative Partnerships got in touch with NRICH to invite us to join her in a project that sounded right up our street. Sarah explained that she had read an article in the Guardian The Science of Fun; why is Maths still an uncool subject? (http://www.guardian.co.uk/science/2008/may/31/maths.science) which describes the 'Gathering for Gardner' event, a conference held every two years in honour of Martin Gardner, attended by experts in mathematics, puzzles and magic. The article's author, Alex Bellos, comments:
Maths is generally not considered fun. At school, maths is unloved, and the prejudice against it continues throughout adulthood. Whereas to hate literature is to be deemed uncultured, it is cool to hate maths and fine to throw one's hands in the air when asked to do a simple sum.
The article inspired Sarah to want to set up a project to investigate enhancing the mathematical learning experiences of primary-aged children through creativity and she felt that NRICH could help. She explains:
"I felt that whilst there were lots of initiatives promoting creative approaches to teaching Literacy, Maths was being left on the sidelines. Historically, it has not been thought of as a creative, fun subject. I imagined what it would have been like to have a magician or a puzzle enthusiast teach my Maths lessons - how exciting would that have been."
This was the catalyst for an idea to implement creative interventions in Maths lessons, whilst still offering real learning in line with curriculum requirements. The difference being we wanted to change pupils' perceptions of the subject with a view to increasing their engagement.
Sarah continues, "To increase the credibility of the idea I realised we needed some specialist expertise so it was important to have the right people on board. We needed to consider it a research project and it offered a great opportunity for some 'before and after' case studies."
In late March 2010, I met Sarah and the maths subject leaders from three Bristol primary schools: Angela Berger from Air Balloon Hill, Clare Broad from Bridge Learning Campus and Maggie Smithson from Sefton Park. Dr Nick Clough from the University of the West of England (UWE) was also involved which meant we would have support from an educational research perspective, giving us
advice on appropriate questions to ask and helping us to collect and analyse data. And so the Maths and Creativity Learning Group was formed.
We discussed the issues that the teachers faced in the classroom, their aspirations for the pupils and how we might approach the project. From this first session we identified the following enquiry question:
How does a more creative approach impact upon the mathematical skills of higher-attaining children?
We decided that a focus group of around fifteen high-achieving children would be selected in each school comprising Year 5 at Sefton Park, Years 4/5 at Bridge Learning Campus and Year 5 at Air Balloon Hill. The reason for choosing high-attaining children was that there was a feeling they were not being stretched or offered the same support as pupils at the other end of the scale. It was
also felt that if this project was successful it would be easier to disseminate the learning with the whole staff team and eventually the 'harder to reach' children. We planned to try to capture a 'picture' of the pupils as learners of mathematics straight away through individual interviews, then to offer a number of creative interventions, then to interview the children again.
Creative Partnerships could guarantee funding up until summer 2011 so we would be able to work with the same groups of children for just over an academic year in total. The creative interventions for the pupils would be in the form of three one-off sessions with three different creative practitioners. However, we also felt a complementary strand was needed which would offer
professional development for all staff in the three schools. One of the main aims of this CPD would be to encourage more creative approaches to mathematics in everyday classroom practice, and this is where NRICH came in.
Below is a timeline, which summarises the main phases of the project:
Meeting 1: planning, identifying main aims
Interviews with focus children
Meeting 2: each school self-assessing against main aims, discussing possible practitioners
Twilight CPD 1 run by NRICH attended by three maths subject leaders and Nick Clough (UWE)
Intervention 1: Bordeaux Quay Cookery School
Reflection with children
Twilight CPD 2 run by NRICH attended by three maths subject leaders and Nick Clough (UWE)
Meeting 3: identifying next steps in school
Meeting 4: planning peer learning sessions
Intervention 2: Representatives from the British Origami Society
December 2010/January 2011
Peer learning sessions
Twilight CPD session run by NRICH at each school attended by all members of staff
Meeting 5: planning next intervention
Intervention 3: Mike Clarke, children's magician
Children plan and lead magic sessions for others in school, then reflect on their experiences
Meeting 6: reflecting on interventions and peer learning, each school self-assessing against main aims again
Meeting 7: evaluating the process to date, discussing dissemination, planning new research question and future CPD
Meeting 8: finalising next steps in terms of new research question, new group of children and follow-up CPD
Having formed a research question, we identified six aims against which we hoped to assess progress over the course of the project. These were to:
We imagined a scale from 1 to 10 for each aim, where 1 meant that the aim was a long way from being achieved and 10 meant it had been achieved completely. Each subject leader judged where they felt their group of children was on the scale at the start of the project and we recorded this snapshot on a wheel:
The inner blue circle represents a score of 10 so it can be seen from the above image that none of the schools felt they had achieved 10 with respect to any of the aims (in fact the highest score recorded above is 8). Of course the three schools were coming from different starting points, but it is interesting to note that all of them assessed themselves as lacking extensive
opportunities for children to explore ideas in mathematics.
Initial Interviews with the Children
Following on from our first meeting, each maths subject leader individually interviewed the focus group children. We had three set questions that were asked. Here are representative extracts from the responses at the outset of this piece of work:
1. How well are you doing in maths?
Quite well - I was selected for St Werburghs. I get good comments in my book.
Pretty well ... teacher told mum my levels.
... quite well ... don't know how well I am doing
Well: I think I'm in the highest group and I can do it ... I get higher challenges
2. When and where do you use your maths skills?
Mathletics at home. Homework. School, obviously
... obviously school, at home practice times tables very day
In maths obviously ... doing homework ... cooking ... on the computer (to play and to work)
Comes in useful when you don't expect it ... swimming events 400m is 16 lengths because of 4 x 4.
In school maths lessons, on the computer.
At home: mathletics, mum has to count money to pay bills.
3. How do you feel about maths?
Confident ... don't feel like I can't do something
Quite fun ... does depend on what you are doing, some things are not that interesting ...
Its not my top subject ... one of my favourites. If I get stuck I get annoyed
When its exciting I enjoy it, like the school trip to do with maths that was really fun. Designing the classroom, that was fun. Not really exciting carrying on doing the same thing, don't really like doing text book work.
What surprised us was that the majority of pupils gave examples of using mathematical skills in maths lessons but few mentioned any wider application apart from the odd comment about shopping and computer-based mathematical programmes. This led us to the realisation that the children had little real-world context for using their mathematical skills, so this helped us identify our goal in terms
of the 'Meaningful' aim: "All maths has a reason". This became an integral part of the brief when we commissioned the creative practitioners.
We also asked these same questions at the end of the project to gauge any noticeable differences. For the results of this and examples of what the children said, see below.
Continuing Professional Development (CPD)
As stated above, we recognised that while we hoped the intervention sessions would help the children experience mathematics in a way that they may not have done before, these were one-off events. Therefore, we were keen to show that our aims could also be addressed in the context of everyday teaching. To this end, I ran a series of twilight CPD sessions, the first two of which were
attended by the three maths subject leaders and Dr Nick Clough from UWE. In the first, we had a go at the activity Magic Vs and used this experience as a context in which to discuss rich mathematical tasks. We talked about ways in which we as teachers can question and prompt children to encourage them to think mathematically, and how we can create a
supportive climate in our maths lessons.
In the second session, the three subject leaders reported back on their experiences of trying out at least one rich task with a group of children. For example, at Bridge Learning Campus, they had tried the Magic Vs activity. Learners were engaged and enthusiastic, and had persevered with the task. Some commented that it was tricky but they still enjoyed it. Clare
suggested that the open-endedness of the task had motivated the pupils to have a go as they knew it wasn't just about one right answer. We then had a go at two more activities altogether - Nice and Nasty, and Light the Lights Again. These provoked discussions about the benefit of mathematical games and the
immediate feedback offered by interactivities on the website. We also touched on the idea of using these tasks as assessment opportunities.
The third CPD session took place separately in each school by which time, two of the three interventions had taken place. The maths subject leaders were concerned that the majority of teachers in their schools were not really aware of the project and even if they did know about it, perceived it as not necessarily applicable to their own classes. So this third session took on a similar
form to the first session, though this time it included all teaching staff. In each case, we played Strike It Out and, when time allowed, Sort the Street, and we used these as a vehicle to discuss rich tasks, questioning and classroom atmosphere. We wanted all colleagues to feel empowered to take risks
themselves and to understand ways in which activities like these allow children to be creative mathematically.
Each creative intervention had a clear brief with target numeracy skills identified by the teachers so that the creative practitioner could build these in to their lesson plan. In addition we asked that each session addressed the following objectives;
The first intervention took place in July 2010 led by Bordeaux Quay Cookery School, working with the project group of children at their respective schools. Each group of children had a half-day session, which involved having a party for friends therefore adapting a recipe for a different number of people and calculating time frames. Where possible, the sessions were attended by a
researcher from UWE who filmed each one, providing us with a valuable record to which we could refer later. It was noted that the quality of mathematical discussion was very high (how do you halve an egg?) and the children readily engaged in the challenge. The need to produce the correct answers in order to create and consume their final, edible product led to some very high quality
mathematical collaboration. Here are the links to the edited film clips:
(Unfortunately the researcher was unable to attend Bridge Learning Campus' session to film it.)
The second intervention, led by a member of the British Origami Society, took place during the autumn term of 2010. Learners were challenged to create trapeziums, equilateral triangles, stars, cubes ... all using just sheets of paper, giving them the chance to explore mathematics in a very practical way. Again, the conversations amongst the children revealed just how much
mathematics they were using - for example knowledge of angles, properties of shapes - and a whole range of skills were required, such as co-operation and perseverance. The edited films from the sessions can be viewed on YouTube:
Bridge Learning Campus:
The third and final intervention took place in spring 2011 and was led by Mike Clarke, a children's magician. Prior to Mike's session, I spoke to him on the phone as we were keen that the tricks should involve mathematics that the children would be able to unpick - we did not want the maths to be mysterious. The idea was that the children would be able to re-create at
least one of the tricks for an audience back at school. This time, learners were applying knowledge of probability, logic, pattern and ratio as well as finding themselves working together and developing explanations. It was interesting to note the way, in one school, a group of girls worked extremely carefully to find the exact measurements needed for the rope trick, with a group of boys
much more likely to dive in and approximate, in order to get onto the practical aspect of carrying out the trick. Here are links to the films taken at each school:
Immediately after each intervention, the children were given time to reflect on the session and to comment on how they felt it had gone. This was followed up with a further session a week or so later that used the film from that school to aid the children in their reflection on the learning that took place.
In addition to the three creative interventions, we had discussed how to develop the aims of the project with the children in their own settings and we identified some clear goals under each aim. At the third meeting, we considered these in turn and the teachers identified 'small step' activities, which could be followed up at school:
Goal: To ensure that all Maths has a reason. Step: Find a room and find a time and brainstorm with children.
Goal: To have enthusiastic independent learners investigating every possibility confidently. Step: Suggest activity for class teacher to use and step back.
Goal: To achieve 4+ average point score (APS) progress over one year. Step: Obtain current data and discuss with class teacher.
Goal: To enable high-quality thinking around past/present/future use of knowledge and skills. Step: Provide post-it notes for children to feed back on.
Goal: To encourage listening, discussing, explaining - building on it and sharing it. Step: Plan a ten-minute session, specifically to give opportunity for children to talk.
Goal: To have confident mathematicians actively experimenting within a supportive environment. Step: Explore alternatives to 'Why?'.
We also thought it would be valuable for the focus children to plan and lead activities for other children in their school. This took two forms but in each case the subject leader worked with the group to plan and prepare, see our jotted thoughts below:
In the first peer-led session, the group decided on a topic they wanted to teach and each focus child was paired up with a learner from another class. Initially, the children had a planning session with the maths subject leader, where they discussed:
They then had a 'practice' session where one partner was the teacher and one the learner before teaching 'for real'. A reflection session followed. At Sefton Park the Year 6s partnered up to work with a small group of year 2s. They chose to facilitate a session developing pentominoes, exploring all the possible shapes that could be made from five squares, then providing a context linked to the
topic work being done at the time. The older children were initially very nervous about being in the teaching role, especially concerned about discipline issues and whether they would be listened to, but afterwards commented on how impressed they had been by the level of engagement, and particularly the ability shown by the younger children.
The second peer-led session focused on magic and the focus children performed one or more magic tricks which Mike had shared with them. At one school, this happened very spontaneously, with children sharing the card tricks within the next few days, which demonstrates the high levels of enthusiasm generated.
Final Interviews with the Children
In July 2011, the children were interviewed again, using the same questions as at the start of the project. Here are some representative extracts from the children's comments:
Very well, I think in the parents meeting they said I was doing well. I'm doing better than before, I wouldn't have been doing as well if I hadn't done the project - I enjoy doing it and I sort of needed it.
I think I'm doing quite well: today when we did the mental maths test I got my highest score yet, I got 19! I'm aiming for 20. I can't wait to get the results of the non-calculator paper, I like to know the scores.
I think I'm doing quite well. Every time we do a test my scores keep improving, I got 91 then 95 then 97.
Sometimes its easy, too easy and sometimes its hard and its frustrating but I like to have a challenge and make your mind and in the end finally getting it and finally understanding it. The only problem with a challenge is you have to stop and you don't have a chance to finish it. You want to get the answer and you play around with it all night.
I use them at home, when I go shopping. I do it with my granddad, he gets the Daily Mail - there's questions, beginner, intermediate, advanced and we go through them. I enjoy that. Shopping - when there's offers. I was going to buy a necklace and it was 25% off and I worked it out - I could afford it.
When I went to Greece lots of places tend to overcharge or bring you things you don't want - always check the change and the receipt to make sure everything on the receipt adds up!
Homework and I guess using money: it doesn't seem like maths just because its not too much of a bother, you can just do it quickly. Different types of maths, I guess because we do them in school. Cookery: when you're doing cooking you get to know how much you need, you don't need to use the weighing scales, you can estimate.
You could use it for what time a programme's on TV. To check a sell-by date: sometimes I do that, especially if it's meat my mum makes me! For paying for stuff: sometimes my mum makes me go to the corner shop and get her bread and milk and stuff. She always checks the change in case I buy sweets - I've done it once or twice!
Well this is a difficult one: everyone said I was good but I didn't really feel it until I did the project. Because it was different kinds of maths: teaching the year 2s, cooking, the man who came on Fridays: I like that sort of maths because it was different. When we did the work with the professor normally in class the maths was times some, divide some but this was
the history of maths, the changes it had made, why people wanted it, not just a pen and paper activity.
It's my favourite subject because I think, not being big headed but it's like one of the high subjects I can achieve-- its where I do most well. I find it quite fun too, yes I think it's linked.
I feel challenged yes: you can choose your level. I usually start in the middle and go through to the highest: you feel the urge to get it!
I think it's quite fun and I enjoy mixing it with other subjects too. I liked it when we did maths and cooking, I liked all of them, like the magic and maths and the music and maths.
I really like it because I'm pretty good at it and I enjoy doing it. I liked all the bits in maths but I especially liked origami. I'm really looking forward to the SATs paper.
I quite enjoy it because there's lots of different maths and lots of different activities. Some activities can be really good. In year 5 we did an investigation: the classroom was completely empty and we had £1000 and we had to choose what to get for the classroom. We worked in groups. Sometimes I like group activities, sometimes I like to work on my own.
OK It's fun sometimes. Fun: I like it when it's a challenge and it's a bit harder and you have to think about it. I prefer maths when you're doing it and not listening as much. I prefer to make stuff but writing's still better than listening. Discussing it with friends it good.
We noticed how much more expansive the replies were and how the children were now able to give many examples of where they used their maths skills outside the classroom. We have good recorded examples of dialogue during the interventions and reflections with the pupils. This allows us to observe how the learning is happening.
Returning to the Aims
Each maths subject leader assessed where they thought their group of children was in relation to the 1-10 scale for each aim. The charts below show the assessment in April 2010 (red) compared with April 2011 (blue):
These are subjective judgments based on the teachers' perceptions of where the children were at each respective snapshot in time. The graphs show improvement across each of the key areas identified as the aims. Each of the goals was considered in turn, e.g. Reflectiveness Goal: To enable high quality thinking around past/present/future use of knowledge and skills. Then we asked
the question "On a scale of 1 - 10, (10 being they have fulfilled the goal) where do you feel this group of children score at this moment in time?". We encouraged an environment where it was acceptable for scores to go down, stay the same, or go up. As mentioned above, the snapshots were recorded in April 2010 (red) and again in April 2011 (blue).
Our enquiry question for this work was:
The children's comments above which were recorded at the end of the project offer some evidence for the progress made. The learning group felt that the children had a greater understanding of situations in which they used their mathematical skills, particularly outside of the school environment. One outcome is therefore a broadening of context and understanding for these skills. Another
outcome is the response to how they feel about maths. Less written work and more practical activities in the lessons proved popular with many pupils.
Below is a table of anonymised data from one of the schools that took part showing the APS progress of the children involved. Whilst the teachers believed that this level of attainment was expected from the outset, it was also felt that the work of this project had much to offer future pupils, as members of staff have begun to consider new ways of approaching maths lessons, namely creating
more interactive lessons with fewer written work sheets.
One of the interesting outcomes for the particular group recorded below arose almost by accident. Additional pupils were included who were not originally identified as high achievers in order to create a more representative and diverse research sample. These individuals surprised their teacher by exceeding their expected targets. This leads us to believe that there is some importance in
demonstrating high aspirations; i.e. if the pupil believes that the teacher believes s/he can do well, then in turn s/he begins to believe in their own ability to do well. This in turn leads to higher than expected attainment. See the table below:
Attainment data on focus Maths group (March 2010-March 2011)
Boy (who left before magic input)
Average progress = 4.1 APS
It was also agreed that following the CPD sessions the wider staff team felt more confident to teach mathematics and make use of the resources provided by NRICH via the website. This was particularly the case for the staff that previously expressed a lack of confidence with teaching numeracy.
Another outcome is the perceived increased enjoyment of the subject both from pupils and staff. This may link with increased confidence and understanding, allowing both teachers and children to relax more with the subject and be more creative in their approach. It was key for pupils to feel that there were many ways to reach a solution and it was important that they felt safe to explore
different ways of problem solving. We wanted to provide an environment that removed "the fear of getting it wrong". The NRICH CPD helped with this.
Implications and Next Steps
We are now in the fortunate position of being able to build on what we have done thus far. The group is very keen to continue the CPD element of the project and Angela, Maggie and Clare (in conjunction with their colleagues back at school) requested that the next phase offers opportunities to:
We have also identified a new research question:
How do we draw on real-life experiences to develop activities that engage children in thinking mathematically whilst achieving identified targets?
We feel that this question addresses a real concern for some teachers, namely that approaching mathematics more creatively can only come at the expense of 'covering the curriculum'. The focus group of children in each school will this time comprise those who appear to be 'stuck', in that although they achieved Level 2 at the end of KS1, they are not on course for a Level 4 at the end of
KS2. The same questions will be used in pre- and post-intervention interviews. We deliberately moved away from higher-attaining pupils for this second phase as we believe that any positive findings might carry greater weight with teachers if the children are not already achieving highly.
So far, this has been an exciting and, I believe, innovative project, which has the potential to go from strength to strength. Enormous thanks must go to Maggie Smithson, Clare Broad and Angela Berger who have amazed me with their commitment to, and ceaseless enthusiasm for, mathematics education, and wanting the best for the children they teach. In addition, it is not an
exaggeration to say that without Sarah Grigg's dedication to the project and her drive to move it forward, none of the above would have taken place.
We hope to report on the second phase of the project in due course.
If you would like further information about the Maths and Creativity Learning Group, please contact the NRICH Primary Coordinator.