Some general comments about the last couple of days and some links to Vygotsky and Piaget…Friday – Drayton Manor I’m not sure that sitting on a bench with a load of lunch bags whilst the class of children run around a theme park counts. I certainly don’t know how to compare what I’ve done today with what I know of Vygotsky and Piaget. Go on. I suppose there is one thing I was thinking of. The children have gone round the park today in unsupervised groups of 2-6, checking back in with the teachers at hourly intervals. When I first proposed this system, my colleagues were horrified that I was suggesting letting the children go off unsupervised – but it has worked really well for the last four years. The children have not only to demonstrate independence and teamwork, but also the ability to tell the time… There is something Piagetian in this. The children are ready for this level of independence, whereas a couple of years ago they wouldn’t have been. There are some children who struggle, but they’re helped by their peers. There are also some children who, either by familiarity with the park (i.e. they have been there many times before) or by their own internal confidence, seem to demonstrate too much independence – they didn’t check back in when we were expecting them, but were still fine. Monday – SRE (Sex and Relationships Education) Theatre. Every year we have a marvellous theatre company coming in to help us with our SRE for Year 6. They’re called Loudmouth and what’s brilliant about them is that they use actors to teach all the tricky bits of SRE. They develop empathy for the opposite gender, so that boys see what girls have to go through and girls see what boys have to go through, and they encourage children to think about what emotions they are causing in others by their words and their actions. Also it means that in any further discussions in class I can refer to Daniel or Claire (the characters in the play) rather than either talking generically or inappropriately talking from personal experience. In terms of ‘readiness’ the children are in exactly the right place to receive this – they’re all curious about the changes they are about to go through in puberty (or for some ‘are already going through’) and they will have heard much rubbish either from friends or from the media that has confused them. It’s interesting watching the play as they use a lot of humour to teach the tricky bits and also to say some of the tricky words to do with SRE. I reckon humour increases the size of the ZPL. The children (and staff) were put at ease by the humour and learned loads more as a consequence. Ah, constructivism – you’re winning out today…
Here’s my second day of reflection in diary format. Remember ‘ZPL’ stands for Zone of Proximal Learning.Thursday 10:10am. Shouted at a girl for not listening at a crucial point. More behaviourism. She took a while to even get a ZPL back again. I wasted learning time for her. In rest of lesson I had to do lots of mini-one-to-ones to scaffold the activity, even for the more able. Children a bit less engaged today, but then it’s very warm, in the classroom and seems like a good day for being outside. I wonder if it’s been proved that the weather affects the size of the ZPL in a child? Thursday 3:10pm. Managed to achieve some social motivation this afternoon – children worked well in groups on group display for their adopt-a-country topics. Have talked much about good working and promised a reward of freetime outside if they could all pull their wait. More behaviourism. I wonder what a ZPL looks like when it’s about learning social skills? Thursday 7:30pm. Heavy going in meeting after school. Air thick with pollen and humidity making it difficult for me to concentrate. Was challenged a couple of times beyond what I felt I could cope with, although on a normal day I might have managed. Had an hour or so back in my comfort zone now (home) – a place I need to reflect on the times when I’ve moved beyond my ZPL into ‘danger’ territory. This is bringing back memories of what I learnt studying ALPS in terms of engaging children in the kind of cycle that is conducive to learning. I wonder if I don’t return children often enough to the comfort zone so they can reflect on their learning. Need to think on, although I doubt I’ll be doing much reflecting at the theme park tomorrow…
For today and the following four days I’m going to reflect on my teaching according to what I understand of constructivism and behaviourism. I’ve called it Vygotsky Diary because I would like to think that I am heavily influenced by the whole Zone of Proximal Learning thing. I’ve called it ‘ZPL’ for short below. Here’s todays entries, each made within minutes of a lesson either finishing or starting…Wednesday 8:10 am – SEN teacher said she was using laptops for rest of children so that she could do tests 1:1 with the other children with the appropriate support – made me think that Vygotsky’s theory about scaffolding within the ZPL shouldn’t be applied to tests, but actually we do because we don’t give children enough independence to do tests. Wed 12:15 pm– Tried a very tricky lesson teaching decimal grid references (the kind Google Maps uses) to mixed ability Year 6 maths group. 5 key areas of prior learning needed – time, angles, co-ordinates, decimals and negative numbers – children find it very hard to connect multiple areas of prior learning (i.e. to add it to their scheme). Especially when prior to this week their grid reference scheme was pretty much blank. Very long into required, but by end over half children could accurately locate (52.45, -3.45) on a map (it’s a place in Wales called Llanidloes). It made me realise that sometimes I expect children’s ZPL to be very large – then I have to do LOADS of scaffolding for the less able children. More able children usually have a larger ZPL (and indeed find small step learning frustrating) whereas less able children need smaller steps. Wed 3:15pm – Children were doing free choice projects this afternoon. I was working with individuals and groups on their 6 weeks plans to encourage children to think about how they can achieve a substantial piece of work by planning well. It’s been more about encouraging good social behaviour than direct teaching. I worry that the outcomes will require too much teacher support when this is a chance for the children to delve into self-directed study and develop their own intrinsic motivation. Behaviourist theory would suggest that I should offer rewards, but not all the time and with some degree of randomness. This should encourage intrinsic motivation. The problem is that if the intrinsic motivation hasn’t developed enough over the next six weeks, the projects will look awful and I’ll look like a bad teacher. Hence sometimes there is a pressure to over-scaffold children. I’ve also noticed a lot of behaviourism in how I speak to children – I expect them to automatically apologise if they’ve made a mistake and I spend a lot of time emphasising this. Oh, the Pavlov in me is coming out at last…
Being one of the few people to have the Karelian National Anthem on my computer does not, unfortunately, qualify me to discuss at length the two Russian psychologists in the title.Neither of them probably even went to Karelia. However it is refreshing in my latest piece of work from MAST to be reminded of their work in relation to what is currently going on in my school. Refreshing because it was a long time ago that was introduced to them and their theories. It is good to go back sometimes. It is also disappointing that in many schools we do not talk about the nature of education enough. We get on and do it, quite often without thinking it through. It is also ironic that it was only yesterday that I wrote the word Vygostky for the first time in ten years, on my previous blog entry. Vygotsky is the chap who, at teacher training college, you get introduced to right after Piaget. Without them there could be no education. Between the two of them they have fathered something called constructivism or cognitive learning. Piaget seemed to have developed the idea that you can’t learn some things until you’re ready for them – he had 4 stages going up to about 11 years old which is about when a child has developed the ability to hypothesise and think logically. For him a child was a lone explorer in a world of learning. I think. Vygotsky had this idea of a zone of proximal learning, which is where a child can best learn something when it’s near enough to the current understanding to be challenging, but not so far that the child is scared to take the risk. His approach was much more about appropriate scaffolding and relationships. Pavlov, on the other hand, was the bad behaviorist man who made dogs salivate. Of the three, I like to think that my approach is more of the Vygostky. I came across the zone of proximal learning when I studied the ALPS (accelerated learning in primary schools) approach a few years ago – the one thing that has most affected the way I teach. I like the way it merges with so much other good stuff, like the multiple intelligences from Howard Gardner and the 12 aspects of learning from the Excellence and Enjoyment document. I do however resort to behaviourism to manage behaviour. I guess that’s an obvious connection. I do use a lot of rewards and sanctions in training the children to be motivated learners as doing so provides a framework for everyone within the group to learn safely. Sitting at home right now I can theorise and postulate, but it will be interesting over the next week to see how I think each lesson has been – more constructivist or more behaviourist. My prediction is that it will vary from day to day, but on Friday when we take the kids to a theme park there will be an awful lot of behaviourism going on…
Page 8 wonders what I think or know about each of the following:
- Discovery Learning
- Barriers to Learning
- Spiral Curriculum
Here goes:Discovery learning is that vague stuff that was around in the 70s that meant I never learned to hold a pen properly. I read some stuff in an Ian Thompson edited book about maths that didn’t have anything positive to see about child initiated discovery learning in relationship to maths, saying instead that discovery learning had to be adult initiated and often adult guided in the early years in maths for it to have any impact. Interesting. Investigation in maths is when you give children an maths problem and then guide them into solving it. You often have to give a lot of guidance as children who are used to a ‘skills based curriculum’ have often only learnt maths methods and not problem solving skills. One of my favourites is the one about what is the most common outcome of rolling 2 dice, because you can combine experimentation (actually rolling the dice) with theory (when you use a table to solve the problem precisely). Barriers to learning means stuff that stops you learning. It could be attendance or your mum telling you that she was no good at maths so you won’t be either. It could also be your 11+ tutor teaching you bus stop when you don’t really get the difference between sharing and grouping. Interviewing. I’m not really sure what this is in a maths context. I did some interviewing on my fractions video (see below) but I’m not sure if that is what this means. Spiral curriculum is where you have a curriculum that keeps coming back to the same area on a regular basis so that the children can build on previous knowledge. It’s a nice idea but the timings we use in the UK are all wrong. The spiral should be 1 day, 1 week, 1 month, 1 year. Not every term. Readiness is the idea that you can’t learn some things until your ready for them. It works on the short term (I can’t learn this because my mind is buzzing with the way that girl insulted me at playtime) and on the longer term (I can’t learn that concept about adding on 2, because I don’t really understand what 2 is). Making children ready to learn is about connecting their learning with the real world and with previous learning, providing motivation and engaging them. It’s a mark of creativity. Differentiation is when you making the learning suit the learner. This can be by varying the way they access the learning, changing the level of the learning and providing greater scaffolding. I have a dim memory from college that either Piaget or Vigotsky indicated that a single teacher could only differentiate three ways. (I mean for three different groups of children , not with different methods of differentiation.) But I might be making that up. Differention is also something I did at university on my engineering degree. Second Order Differential Equations. They were very hard. I’m glad I’m a primary school teacher.
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…
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: http://www.youtube.com/get_player 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.
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.