Archive | March, 2010

Mathematical Feelings

30 Mar

As part of the MAST programme, I am asked to record my initial thoughts and feelings on mathematics. I see this as a sort of mathematical autobiography, with which I will continue shortly, however in the meantime, a little tangent into the quantity and variety of data storage options available to a person…

The MAST programme, of which I am a part, has a rather confusing array of places to store information. There are discussion areas, chat rooms and an online journal, which all exist on Blackboard, Edge Hill University’s virtual learning environment. In addition there is a personal learning log which exists as a downloadable Word file, but is also handed out in hardcopy at local area meetings. And there is a rather large ring binder file to go with it. My own principle is that I need just one place to put things and it is right here ( a principle that I set out in my first post: ‘Starting in One Place’).

Mysterious Maths

Having a mathematician for a father meant that maths always held a slight air of mystery to me as a child. It was his job and his passion. A bit like Gandalf in ‘The Hobbit’ – an appropriate metaphor as my dad has an affinity for (and a beard like), Tolkien’s famous wizard. So, just as you always get the idea that Gandalf knows more than anyone else does about what’s going on, while Bilbo (the hobbit) and the thirteen dwarves all trundle from one problematic frying pan into yet another life-threatening fire, it was the same with my father and maths. I always had the idea that it was marvellous, mysterious and magical – yet he would always know a little bit more than me. And he still does.

Triumphs and Failures

I’ve had various mathematical landmarks. The Year 4 teacher who managed to teach me long division was an inspiration – my maths really took off under her wing. Then at secondary school an over-reliance on rote and the calculator (I distinctly remember typing 2+2= while trying to solve one problem when I was about 13) meant that I often failed to see the big picture of what I was trying to work out, seeing only the taught method instead. This is something I strive against as a primary teacher – I want children to have a concept of what they are doing to number when they use a method, but as the methods got more and more advanced at ‘A’ levels, the maths got more and more disconnected from real life for me and I struggled to ‘get it’. While I achieved a ‘B’ in maths ‘A’ level, I only scraped an ‘E’ in further maths and I continued to struggle with maths through university (electrical engineering) – being able to just about manage the methods of second order differentiation, but not really understand why I was doing it – I certainly can’t remember much of that level of maths now.

Pedagogical Prescription

It was primary teaching and particularly the national numeracy strategy with it’s emphasis on mental methods above written ones that brought enthusiasm back for maths. Some people complain about the prescriptive nature of the primary curriculum, referring to the written methods that are taught, but I never really got stuck on that, choosing to bring myself and children back to the mental methods whenever I could. Over the last five years as a maths leader, I have tried to instill this ‘mental methods first’ ethos in my colleagues and it is here that my interest in school leadership really began (although that really is another story) because I discovered it is far easier to change children as a class teacher than when you’re not a class teacher…

My current big question in maths is: ‘Is there one successful pedagogy for all groups of children?” By this I mean, can you teach all children using just one approach (as the national numeracy strategy back in1996 hoped)? I suspect that the answer is ‘no’:

  • less able groups of children need a sccaled down approach with an emphasis on basic number skills;
  • middle ability groups need the kind of approach advocated in the national numeracy strategy with a progression of methods that build on previous ones, leading to formal written methods;
  • more able children need a variety of methods and should be given opportunities to use and apply them independently to different situations.

I suspect this only. I have no proof. I need to do more reading, more research and talk to more people to find out…


Fractions: learning something new

23 Mar

Yesterday was a complete surprise to me. I learnt something new about maths. And I enjoyed it.

Without trying to show off, I do know a lot of maths. I won’t bore you with too many of the details, but I am both interested in maths and quite good at it. I recognise that there are a lot of people who are much better than me – without some of those people I would never have got through my ‘A’ level maths (thanks Greg, thanks Yao) nor my Engineering degree (thanks, Jim, thanks Dan). However, in primary teaching I haven’t met too many of those people. Most of my colleagues are good at teaching maths, but would say that it is not their main interest. Some would demonstrate an enthusiasm for a particular branch of maths, whilst a few would express some negativity about areas of maths, particularly at the higher levels of the primary age range.

Yesterday’s topic at the local area meeting of the MAST programme was ‘fractions’ – an area of maths which usually generates the word ‘Hmph’ from children, parents and teachers alike. I was so excited by some of the fractions problems we attempted I took them straight back to school the next day and filmed my Year 6 children trying to solve them. Here’s the video:

Hopefully you can see how the children progressed in the lesson. Many of the children, despite being the most able in the school, had quite a negative attitude to solving problems involving fractions. Through using models and images the children now have a better conceptual understanding of fractions – they have linked the visual to the concrete – and are now ready to move on to using the abstract: numerical fractions themselves.

It struck me that as teachers we often move too quickly from the concrete to the abstract. If the highest ability children needed this level of input to begin to ‘get it’, then younger children and less able will need far more input at the concrete and visual stage before they move on to the abstract. This makes complete common sense, but in our overly prescriptive curriculum, how often do we rush children on to using and failing with the numbers when they don’t get the concept?

So if two and half men take two and half days to dig two and half trenches, how many trenches can one man dig in one day?

My answer was one trench and I was completely wrong. The feeling was exquisite – some maths that I didn’t get. My table group had to work hard to try and solve the problem and we still didn’t get it. Finally when someone provided a solution and the concept started to sink in it was marvellous to realise that I had been challenged with something and learnt something new as a consequence.


Numeracy stifles creativity: creativity develops maths.

7 Mar

I was struck by a thought a few days ago. It was a thought that linked a 20-year old memory to the tone of voice of a speaker at a conference. The speaker was urgent yet determined, edgy even. The memory was calm and confident. It was the sharp contrast between the two, both of which hung on the same theme – creativity, which made me want to investigate further.

The memory said, ‘the British education is the best in the world for developing creativity’. I don’t remember exactly who’d said that to me, but it was something that rang true at the time. Now it might be that the memory is skewed. It might have been closer to ‘the British education system is the best in the world for creating graduates who are creative’ – I recognize that this is a long way from saying that the British education system is the best in the world for developing creativity in all students. However it is one of those memories that have entered my psyche – I’m part of an education system that is good at creativity.

The speaker was edgy because the future for schools which have been recognized as creative is uncertain. Funding for the main government body (creative partnerships) which funds such schools and programmes (like the Change School Programme and the Enquiry programme) is uncertain. This is partly due to the impending election in the UK and also the effect of a massive national debt on future public spending.

The thought that linked the memory to the speaker made me suddenly realize that we’re struggling to develop creativity in our schools, when in the past (over 20 years ago) we were proud of the creative students we produced. I’d like to point out that these are massive assumptions on my part, but nevertheless it made me want to investigate a little further.

What has changed over the last twenty years? Well the National Curriculum for one. And with it all those strategies, revisions of strategies, the inception of Ofsted and its subsequent changes, SATs and league tables. And all manner of other stuff.

It’s well beyond me to write about what’s gone wrong with the whole of creativity in the whole of the curriculum, but I can make some pointers about maths.

For a start the word numeracy didn’t use to exist. Maths has become about making students numerate – this is a commendable goal, but I wonder if in trying to achieve the targets of making more children achieve a certain level of numeracy we’ve actually taken the fun out of maths. It could certainly be argued that maths teaching in ‘the old days’ was failing many people, but the prescriptive nature of the numeracy strategy has not necessarily achieved the desired results. To find out more I had to read some articles from a book: ‘Teaching and learning early number’ 2nd edition edited by Ian Thompson – I found chapters 1, 3 and 16 the most enlightening.

The NNS (National Numeracy Strategy) in 1999 moved the focus from mathematical application to arithmetic skills. Strategy advice stated that there should be a high proportion of work with the whole class. A significant influence (according to Aubrey and Dormaz 2008) was Chris Woodhead, then chief inspector who wanted to reduce the wide range of attainment by structuring learning tasks on the basis of what children have in common. This actually had the contrary effect – the middle 50% enjoyed an attainment gain of just over 3% (3% being equivalent to about 3 months), the higher achievers made a small improvement, whereas the lowest 10% actually suffered a decline.

Those early years of the NNS were marked by both:

  • considerable disparity in teaching practice across teachers and schools; and
  • concerns of teacher overload, pressure for acquiescence and undue stress that results in a culture of compliance.

It is small wonder that not all schools were able to equally embrace the Excellence and Enjoyment document – a document with a large emphasis on cultivating creativity within children. It’s like someone realised that we were losing our UK creativity edge and their most creative solution was to write it down on lots of pieces of paper (that’s a bit unfair – I do remember there were videos in the Excellence and Enjoyment pack)

It was against this backdrop of ‘pedagogical prescription’ (Alexander 2004 – I love that phrase!) that the government published the Excellence and Enjoyment document. While this document stated that ‘the NLS and NNS, though they are strongly supported, are not statutory… OFSTED will recognise and welcome good practice… Our aim is to encourage all schools to… take control of their curriculum and be innovative.’

This is an interesting quote – it takes a lot of good thinking, hard work and determination to take control of your curriculum and be innovative with it when you’ve spent 10 years not innovating – this applies on the level of the child, the teacher or indeed the whole school

Meanwhile in the very bedrock of creativity, the foundation stage, there has been some disappointing guidance for the development of maths. DFES 2007 emphasised the need for children to learn mathematics through child-initiated activities in their own play. Not only do I consider this to be a bad plan for teaching early maths skills, but also it’s a bad plan for developing creativity – young children need adult support to develop their play – to make it meaningful, evaluate it and sometimes even to initiate it.

And it flies in the face of Anthony and Walshaw (2007) who say: ‘Spontaneous free play (or child initiated play), while potentially rich in mathematics, is not sufficient to provide mathematical experiences for young children.’ In addition, Siraj-Blatchford et al 2002 find that effective early maths gains happen when adults actively teach maths focused small group activities. Thankfully, the Williams review of the maths curriculum recommends direct teaching of mathematical skills and knowledge in meaningful contexts and opportunities for open-ended discussions of solutions, explorations of reasoning and mathematical logic. This sounds to me the kind of approach that will also develop creativity within children.

In fact, Fawcett (2002) argues that children are likely to be creative when they:

  • show curiosity;
  • use ideas and experiences;
  • make new connections through play;
  • evaluate the process.

I would imagine that the reception teacher who takes this approach will have great success in not only developing the creativity of the children, but also in teaching early skills in all areas, including mathematics.

In conclusion, I’m convinced that the imposition of a national numeracy strategy, for all its (sometimes debatable) gains in maths has stifled creativity , even if for the very reason that it has stopped teachers and schools innovating and reduced them to ‘deliverers’ – the post men of the National Curriculum.

My hope is that, with the Williams Review and the new curriculum starting in 2011, both of which have a clear focus on developing creativity, the processes needed to cultivate creativity in children will be the same processes that develop maths.