Mathematical graphics or play? Does it matter?

The focus of HEI day 3 at Edge Hill University was on the Early Years. Although the theme of the morning was developing children’s mathematics, much of the talk was about getting ‘play’ right. The implied assumption then is that if you get play right, children naturally develop mathematical graphics correctly… By the end of the day I had worked out that we had been treated to two of the top experts on Early Years education in the UK and possibly beyond. Much of their practice has informed recent government policy. The two in question were Maulfry Worthington and Elizabeth Curruthers. They have an website that explains much of their work called the Children’s Matehematics Network. Here’s my tweeted journey through their lectures, with a spot of explanation.
Tweet 1: ‘Early years experience should build on what children should know and can do’ #masthei3. What you be the connectivist equivalent?

Aside from the fact that this comment reveals I can’t spell when I’m typing fast, it struck me again that all current ‘best practice’ is based on constructivism. For those who aren’t sure, or who have forgotten what it is, it is pretty much summed up in the above statement. Constructivists would say that all education should be based on what children should know and can do. The seminal writers on constructivism were first Piaget and then Vygotsky, I’ve blogged about them recently when challenged to keep a diary of my daily teaching experiences. You can read those blogs here:

• overview
• day 1
• day 2
• day 3

Constructivism has always been rivalled by behaviourism (and a little by cognitivism – but I am really unsure of what that one is about), but there is a new theory on the block – connectivism a concept defined by George Siemens in 2005. It is summed up for me by the statement ‘the pipe is more important than the contents of the pipe’ – it’s all about how we connect with each other as sources of knowledge, skills and attitudes – getting the connections right is more important than actually having the knowledge in your head.

So in my round about way I’m coming back to the question I asked – what would be equivalent statement about early years experience based upon a connectivist view point? ‘Early years experience should build on who the children know and how they relate to each other’? It’s a possibility. The thing is I’m not entirely a connectivist – I believe connectivism is the best theory to be applied for gaining knowledge, but I think constructivism is more appropriate for skills and behaviourism is the best way of describing how people pick up new attitudes. Mainly. I think. But that’s the pub theorist in me again.

Tweet 2: Maulfry at #masthei3 says there is no place for worksheets in foundation stage or KS1. Contentious? Wise? True also for KS2?

Maulfry (which, incidentally is the best name I’ve heard in a long time) Worthington came up with this statement at the end of her talk on mathematical graphics. It resulted from her explanation that chat children need to learn to represent maths in their own way first, developing from making sense of their own play, before being taught over-prescriptive ways of recording maths. She did go on to say that direct teaching of skills was important, but child-initiated play is to be a significant part of the day for early years children with teachers acting as gentle guides.

Tweet 3: Elizabeth Curruthers at #masthei3 says that her children’s centre has a postmodernist perspective. Prof. G. Lynch says there’s no such thing

Bizarrely, as I write this I’m going to stay with the inestimable Professer Lynch at his small family home in London. Something of an expert on culture, he once told me that post-modernism was a myth. I have no up to date knowledge myself on this front, but I’m sure he will educate me in a few hours time.
Tweet 4: Warnings about superficial play at #masthei3. Not just a prescribed roleplay area but plenty of materials and resources for free-choice.

Elizabeth’s lecture was more about the pedagogy of play, not so much about the theory. This was good for us teachers because we like to see how all these high-falutin educational theories are put into practice. She warned us not to limit play to a roleplay area, but not make it broader and messier. Messier because it requires putting the resources out and clearing them away again. In other words play that’s worth it is hard work (for the teachers).

Tweet 5: Support early maths development by timetabling big chunks of time for play with teachers supporting and guiding.

She actually specified an hour and a half in the morning and more again in the afternoon. That’s a lot of play.

Tweet 6: #masthei3 other good tips: real equipment (spirit level) tech for food (mixers), food room, growing number lines, numbers on trikes

This speaks for itself – make the play real (not plastic), use real things that the children would see at home, do stuff with things the children already know a lot about (like food) and develop it – don’t just stop your numberline at 10, give it space to grow over a few weeks. Number the trikes like racing cars and make the numbers get bigger as the year goes on ans the children get more confident with number. It’s the constructivism principle working out in practice.

Tweet 7: Pedagogy is to build on children’s interests at #masthei3. Could be one child, a group or sustained themes I’ve a period of weeks (should have said ‘over’)

Elizabeth gave an example of a non-English speaking family who ran a restaurant in the city they were in. On a home visit, the teacher was amused by the child treating her like a paying customer, waiting on her and writing down a series of marks and shapes that (to the child) indicated the order that she was going to take. Back in the nursery, the teacher gave that child a chance to carry out that roleplay further and involved other children in the play, so that one child’s graphics soon started influencing others.

Tweet 8: Adults who really listen to children and their play, then co-construct learning are Insiders vs edgers vs outsiders

Elizabeth defined three positions an adult can take to play – as an ‘insider’, an ‘outsider’ or someone on the edge of play. It seems obvious by now what position an adult should ideally take to make play worthwile – that of ‘insider’. I can’t remember much about the distinction between being an outsider and someone on the edge, because I was thinking about my own children and how important it is for me to be an insider in their play. So today we played with the Brio together for the first time in ages and I listened to them as they made up stories about the different trains going round the track. Then we proceeded to make high towers, only for the youngest to knock them down, but it was still fun. For me too!

Tweet 9: Adults interactions: scaffolding, sustained shared thinking, co-construction, participant observer. (bruner, blatchford, jordan)

Elizabeth stated some different ways that adults as insiders have been defined. She talked about the co-constructor being the most powerful. She went on to quote from someone else in tweet 10: ‘Acting and thinking with others drives learning and at the heart of the process is dialogue’ (Stephen 2010).
Tweet 11: Conversation thoughts at #masthei3. Talking more important than reading or listening for developing maths. ‘Talk time’ is a strategy to use.

Elizabeth defined what a good conversation looks like and played us a video of her nursery angaging in ‘talk time’ a freeflow activity where everybody starts together with some artifacts and stuff to talk about. Children can wander off or back as they pleas, but the teacher is there to guide and be a part of the conversations. The children know that that particular time and space is for talking. I’ve been wonbdering how I can structure that into my Year 6 class, but I’m not quite sure how to do it.
Tweet 12: Discussion at #masthei3. How do we encourage child-initiated learning beyond the early years?

One of the things that was becoming obvious to me was that adults were vital for child-initiated learning because they have to guide it. However as children get older, generally staffing levels are reduced, so there is often less space for child-initiated learning. I personally believe this is where technology comes into it’s own. If you look at the work of @deputymitchell, @oliverquinlan or even my own work with my CATsEYES film-makers (to name but a few), then it is clear that child-initiated learning can still exist for older children through the use of technology. Not that any of this is maths based per se. Not yet.
Tweet 13: Maulfry says she has never seen any evidence that worksheets help develop mathematical thinking.

OK I seem to be repeating old-ground here – but it is quite a contentious statement. Worksheets are such a time-saving device for teachers that is it really fair to say there is no place for them? Ideally I would like to see my school without them, but practically… It might take a few years.
Retweet 13: @timstirrup: who agrees? RT @frogphilp: Maulfry says she has never seen any evidence that worksheets help develop mathematical thinking.

Tim Stirrup retweeted this onto #mathchat and into his own network on Twitter. I’m yet to see any response from this, but it would be interesting to see it come up on the #mathchat forum sometime.
Tweet 14: Maulfry talks about language for thinking and language for communication at #masthei3. Reminds me of @ewanmcintosh’s talk to CCE back in Feb

Ewan McIntosh at the CCE conference in February had talked about a new language that children had to learn – the language of technology. He explained how it overlapped with the language for thinking and the language for communication. Myself, I’ve not really though too much about these areas, but just recognising that there is more than one seems important.
Tweet 15: Maulfry says that recording maths is not the emphasis at #masthei3. Mental methods and thinking are mor important

This backs up some of the earlier points. Just learning how to record maths without thinking is not successful.
Tweet 16: #masthei3 only 36% attain FSP point 8 in mathematical developing. Do some children ever get it?

This made me think back to the previous days lecture by Nick Dowrick when he said that 6% of children do not achieve a level 3 at KS2 and 40% of children do not get a C grade at GCSE. FSP point 8 reads ‘The child solves or attempts to solve problems and challenges by applying mathematical ideas and methods. The child explores problems such as missing numbers, grouping, sharing and estimation, and responds to questions such as ‘What could we try next?’ or ‘How shall we do it?’’. Do some children ever get this? Do all adults have it? I’m not sure.

Tweet 17: @timstirrup: @frogphilp the day sounds interesting, but where/what is #masthei3? I have tried many google searches with no luck.

I’m really gald that Tim stirrup was getting interested enogh in my tweets to ask where I was coming from. This programme is part of a two years Masters level study course that, if passed, should gain the participants 60 points towards a Masters degree. The programme came out of the Williams Review of maths in Primary Schools, which is a good read, I reckon. There are 10 HEI days with lectures given at Edge Hill University and the day I’m writing about was the third of them.

Tweet 18: I need a subject and a title to do with primary maths for my master level assignment (2500 words). Any ideas? #mathchat

It suddenly struck me that there’s a whole network out there who could give me some good ideas for an assignment – thanks if you’ve already made a suggestion – any more suggestions gratefully received.

Tweet 19: #masthei3 is over. On way back home with 2 Birmingham maths consultants. Next stop #gtauk…

Just a word for my consultants, Muriel and Ian -they have been marvellous. Not only did they gave me a lift back to Birmingham from Ormskirk, but they have also fully engaged with the course, had a go at some of the modules and been really positive about it. I’m sure everyone in the Birmingham group would agree they’ve done a cracking job.