Today, UK Maths expert, Ray Maher visited the Athena schools in Birmingham. This is the record of the tweets I made of the event.5 schools meet for #Athena day at the Beeches for #RayMaher on Raising Standards in Mathematics
In researching for my assignment (about whether social media can enhance maths learning), I've come across lots of interesting stuff about language. I'm bemused with myself that I'm saddened at the fact that the mere 2500 words I've got to write my assignment won't be enough to include many of the interesting things that I've found out. Interesting questions more than anything – because it's a whole world of learning. But it's also another essay to be written at a different time.
Two Year 6 children explain how to deal with remainders after division
Two year 5 children try to explain how to do column addition.
Many people would say: divide 3 by 4? No can't do it.
I love using different number systems to teach understanding of number. I often use binary, base 6, Egyptian and roman, but here’s four more that will definitely find a place in my lessons.
Do you know which is which?
This is my definition of maths.
a spoonful of numbers,
a sprinkling of symbols,
200g of quantity,
100g of measurement,
All mixed together and moulded into the
shape of your choice!
Did you know you can count up to 1023 on your fingers? It takes a while, but this video shows how you start…
Earlier today @tomhenzley tweeted about models for teaching addition and subtraction of decimals. I've often found the 10 square and 1 square to be a useful addition to other strategies. In many classes, children are very used to the 100 square to add and subtract 2-digit numbers. It is a natural progression to use the 10 square and the 1 square to move on to decimals.
Alistair Smith, in his book "Accelerated Learning in Primary Schools" told me that one of the secrets to learning new things is re-categorisation. That's the reason that I'm writing this post. It's also the reason I failed as an Electrical Engineer (I took notes in the lectures, but didn't look at them or do anything with them soon enough to properly learn the ideas). You see I was at this maths training day yesterday and I took all my notes on Twitter. So all of the information is out there in the ether, but it's not going to get any deeper into my brain unless I re-categorise it. This post is the first step in the re-categorisation process. There's another step to come when I refine my thoughts and write some focussed posts. Tweets in bold, extra thoughts in normal writing:
- Am off to #mastHEI4 armed with a metre stick. Getting rather dubious looks already on the train – Yes. 100 primary maths teachers all walking through Birmingham City Centre. Slightly reminiscent of some kind of re-inactment society meet, except with maths teachers. Still it showed the dedication to the task in hand – you've got be into the subject to be willing to face that kind of embarrassment.
- Mathematical talk by Phil Butcher at #mastHEI4 effective classroms include high quality dialogue. Dialogue = AfL – (explanation: AfL stands for Assessment for Learning) that's really important. As a senior manager in a school, I'm really concerned that my teachers have the right skills and opportunities to spend their time as effectively as possible for the benefit of the children, without spending all their time doing it. It's why I'm so disappointed by the recent APP framework. (APP stands for Assessing Pupil Progress). The APP focuses on the correct skills to raise standards, but it is paper-based and cumbersome. It takes too much time. And what's worse some schools have begun using it as a summative assessment tool, when it was designed as a tool for increasing teacher subject knowledge. Teachers with high subject knowledge have the confidence to assess their children with dialogue, to implement interventions on a minute by minute basis and not to waste their time on meaningless paperwork. They assess as children learn. Children learn whilst they assess. We should be concentrating our efforts on developing our dialogue skills and increasing our subject knowledge. The two go hand in hand.
- RT @frogphilp: Mathematical talk by Phil Butcher at #mastHEI4 effective classroms include high quality dialogue. Dialogue = AfL – thanks to @TLTP for re-tweeting this line.
- #mastHEI4 misunderstandings shape dialogue. – Skilled teachers know the progression needed to develop concepts and can pick up what the misunderstandings of the children are through dialogue. It means we need to encourage a culture where misunderstandings are seen as good – a step towards success. The problem about doing this for students is that this culture is not in place in any other part of the society: teachers can't be seen to fail by their senior managers; senior managers can't be seen to fail by their governors or local authority; local authorities can't be seen to fail by government. It takes a very brave teacher or indeed headteacher to break this cycle and create a culture where misunderstandings are valued and where process is more important than product.
- Teachers.tv problem solving in maths – children on their knees with real equipment talking to each other #mastHEI4 – I haven't found the link on teachers.tv yet for the lesson that Phil Butcher showed. I will do before my summary most.
- I'm taking my notes at #mastHEI4 by Twitter. I will collect onto a blog later: http://philpmaths.posterous.com – that's what I'm doing now. Although this is only an intermediary post.
- Teachers.tv video shows children struggling to have confidence put data into tables. Is this a skills problem or attitude? #mastHEI4 – I tweeted this because I have a theory that social connectivism is a better pedagogical approach that constructivism for inculcating positive attitudes to learning in maths.
- Effective dialogue: teacher acting as chair of discussions, encouraging all to contribute + scaffolder of ideas. #mastHEI4 – It's really good to see the different kinds of dialogue that teachers engage with – chairing, encouraging, scaffolding.
- Teacher uses dialogue to guide children to an elegant solution. Remember maths is elegant. It is graceful and swift. #mastHEI4 – despite declaring earlier that process is more important than product (it is!), product is still important. I think of them in a kind of 60/40 ratio. The product in maths should be an elegant solution – it's important to remember that maths IS the most elegant and efficient way of describing the world. And that is why maths is graceful and swift. The teacher in the video didn't just stop at a tabulated answer with an oral explanation from the students. He guided them to a more elegant solution. I love that.
- Following elegant solution, teacher encourages children to explain. This helps embed their learning. Learning becomes development. #mastHEI4 – One of the things that Vygotsky demonstrated was that learning is different from development. Students can forget stuff they have learned, but they can't undevelop. Good teachers hand the learning over to the children, letting them verbalise and picture it in different ways; letting them re-categorise it in their minds to give the students every chance of making that learning become development.
- Recording dialogue provided evidence for MA1. (note to all APP users!) #mastHEI4 – If you are doing the paper-based APP approach, then MA1, which is maths attainment target 1: using and applying maths, must be a nightmare. So much of how children have really developed in using and applying is evidenced orally. Get your video cameras or audio recorders out – it's the only way to record this sort of stuff.
- Teacher dialogue strategies in maths: eavesdropping, chairing, prompting, rich questions (see Bloom's taxonomy) #mastHEI4
- Why is dialogue an important part of learning?validation, identify misconceptions, time for rehearsal (thinking time). #mastHEI4
- Software to support dialogue in unpicking misconceptions: 'the number crunch bunch' tool for stimulating dialogue – Fiery ideas #mastHEI4
- Vygotsky says that talk can take people beyond the 'edge of their thinking' ZPD #mastHEI4
- RT @frogphilp: Vygotsky says that talk can take people beyond the 'edge of their thinking' ZPD #mastHEI4 – These last five tweets have been referred to earlier.
- IRE (Initiation Response Evaluation) many teachers are locked into this – worried that too much talk = poor classroom management #mastHEI4 – Possibly from the pressure of school culture, it was interesting to hear Phil Butcher (the lecturer) talk about how many teachers don't give the children the opportunity to talk in the classroom. Ask yourself the question: 'what does a good classroom sound like?'
- Phil Butcher's experience – takes at least half a term to develop good talk in the classroom. Helps if kids develop the rules. #mastHEI4 – Some practical experience. If children haven't been practised at doing constructive talk, you won't be able to change their habits in a couple of days. It took Phil a half term. Sobering and yet somehow encouraging at the same time.
- Alexander: 'written work tends to be seen as the only 'real' work and oral activity is the prelude to written work.' #mastHEI4 – I think this comes back to what kind of evidence we collect as senior managers. If we only ever judge students on what we see in books, then we are not encouraging teachers to take the shackles off on talk.
- Longitudinal study (Fiona Walls 2007) shows children drawing their maths lessons over time. Depressing to see boredom as get older #mastHEI4 – Fiona Walls had done a study following students through school and tracking their attitudes to maths. It was characterised by younger children drawing themselves in maths lessons having fun, playing with bricks and then building things. As they got older they draw themselves sitting at desks and wrote how boring maths was. That's just sobering without any of the encouragement.
- Games encourage talk. Snakes and Ladders is not a maths game because it relies completely on chance. #mastHEI4
- Games make maths learning purposeful. Puts pressure on children to work mentally. Can create discussion of all kinds. #mastHEI4 – some comments on games playing in maths lessons.
- Bruner: maths representions Enactive – Iconic – Abstract. Don't throw away equipment in Y6 – kids still need it to affirm learning #mastHEI4 – nice to hear Phil Butcher getting Vygostky and Bruner in the same lecture.
- Techniques to come away from think-pair-share: expert groups, snowballing, envoys. #mastHEI4 – Phil discussed some techniques from coming away from the standard think – pair – share that many teachers use. I'll describe all these more in a later post.
- Ideas for dialogue: 'What maths can you see in the picture?' use snowballing. (Note to self: must share @tombarrett maths maps) #mastHEI4 – after the lecture I asked Phil Butcher if I could demonstrate one of the maths maps that @tombarrett had shared at #GTAUK. I had particularly wanted to show the 55 shape activites in Paris. But shock! There was no internet connection. An educational event in the 21st Century without an internet connection? Is that possible?
- #mastHEI4 ideas for pictures: golden ratio, square numbers, shapes, etc.
- #mastHEI4 try googling '10 ideas for energising classroom discussions' – I did and I got to this: http://web.grcc.edu/CTL/faculty%20resources/ten_techniques_for_energizing.htm It's pretty good actually.
- Cambridge review: many children sit in groups but work individually. Why? #mastHEI4 – I'm really passionate that children should sit in positions appropriate for them. Practically it can be a pain to move desks around, but the benefits can be worth it. When I do extended writing sessions I encourage children to sit, stand or lie as the mood takes them. I don't think desks should be a barrier to learning for children. It's interesting that the Cambridge Review noticed the same thing.
- What about vocabulary: In maths what is the different between technical and specialist vocabulary? #mastHEI4
- #mastHEI4 Answer: technical words are specific to maths (eg triangle); specialist words are general words used in a maths context (eg table)
- #mastHEI4 more ideas for talk: talking tins, start with end – children design problem, use huge variety in language for subtract and divide – later on in the day I used this information to tweet @tucksoon about talking tins.
- #mastHEI4 final thought from Phil Butcher: be precise. If we can't define prone numbers accuratly how can we expect children to? – Ah! At last a mis-tweet! I meant prime numbers. Now it makes more sense doesn't it. Prone numbers indeed.
- RT @frogphilp: Cambridge review: many children sit in groups but work individually. Why? #mastHEI4 – thanks to @dan_bowen for re-tweeting this.
- Problem-Cube lowered into water half submerged with one vertex at lowest point. What shape does cross-section make at water level? #mastHEI4
- #mastHEI4 what did I FEEL about answer? Theoretical but nervous that I couldn't see it and do it. Other responses…?
- Possible responses to problems include: I don't care, what did you get, not enough information, j just knew it #mastHEI4
- Insurance salesman question is a cracker. I will share on my blog later. #mastHEI4
- Challenge: with difficult problems how do we stop being smug and give the answer away? How do w stop children being unstuck? #mastHEI4
- At #mastHEI4, Brian Robinson talks about 'Big questions… Small steps' – NRICh masterclass – what can you see? – The problems that Brian Robinson had been sharing in the second lecture of the day were so exciting that I didn't actually share the title of his talk until now (the first tweet was number 35). Brian was advocating a problem solving based approach to all maths. Start with an interesting problem. Decide the skills needed to solve it. Teach the skills, then solve the problem. The small steps are the guidance the teacher gives to the students to take them through the problem – to scaffold their thinking. It's very much a 'Brunerian' approach, although it seems to me that much of Bruner's model has been dismissed practically because of the failure of 'discovery' teaching in the 1970s, my personal feeling is that was down to poor execution of the model, rather than the model itself being wrong.
- Ideas for Say What you see: target words, talk ping pong, use shapes. Also: http://nrich.maths.org #mastHEI4
- RT @KnikiDavies @frogphilp have you noticed… have you tried… why not try… #mastHEI4 (to add to other tweets!) – thanks to @KnikiDavies for your interest in my tweets. I hope this blog is a useful first step in explaining what I was up to on Saturday. I will blog about this particular lecture in more detail at a later date.
- Idea: use SATs questions to ask more interesting questions. E.g table – data handling – ask who gets most pocket money #mastHEI4
- Brian says we need to encourage children to feel good about being stuck. #mastHEI4 – again this theme about being stuck, not fearing failure, encouraging children to demonstrate their misunderstandings so we can work on them. It's all part of a good maths education. It's all part of good education.
- When children are stuck – don't just sit there: mime it; talk it; model it; draw it; act it… Do something! #mastHEI4 – Brian finished by talking about some practical things to do when you are stuck. This was really useful. It's really important to recognise the full range of feelings that are evoked by being stuck so that when it happens some children aren't excluded from the next steps.
- Mary McAteer speaks about approaches to Masters level assignment at #mastHEI4 – May not tweet about this one too much
- Assigment tips from #mastHEI4 – grid evidence against learning outcomes, think audience, understand 'critically', write analytic narrative.
- Assignment tips at #mastHEI4 – fluent English, keep focus tight, evidence claims, be questioning, conclusions be properly supported
- Assignment tips from #mastHEI4 – look at grid that examiner uses to assess you, don't 'go large', articulate the intuitive
- What is 'critical'? Evidence of self-awareness, discussion, descriptivity + #mastHEI4
- Assignments: is mine like chips and custard or like Blackpool? #mastHEI4 – OK – this section was really just about writing assignments. I probably won't blog about it.
- Graham Smart talks at #mastHEI4 about ratio and proportion – Graham Smart finished the day with a highly practical session on ratio and proportion. I will probably blog about it after I've taught it as a lesson and won't say anything further now.
- Ratio and proportion are hard concepts. Hard to separate, then link to division, fractions, decimals and percentages. #mastHEI4
- Proportion = in every; Ratio = for every. Ratio breaks with pattern of fraction – decimal – percentage – proportion. #mastHEI4
- Ratio question: "3 times round my head = my height: is this true?" #mastHEI4
- @tucksoon that's the one. It's been recommended to me for developing math talk in 3-11 year olds. #mastHEI4
- Graham Smart teaches about unitary ratios. Height to head ratio = 1:0.33 #mastHEI4
- RT @frogphilp Graham Smart teaches about unitary ratios. Height to head ratio = 1:0.33 #mastHEI4 or 3:1
- The Giant of Biblical Proportions talked about by Graham Smart (a way of engaging children with ratio) #mastHEI4
- Graham sums up by giving ideas for FDPRP: filling up petrol, mixing paint, number lines, recipes, stories. #mastHEI4
- FDPRP are really the same thing. Model on number lines. Line of people #mastHEI4
- people pie chart at #mastHEI4
- Smart quotes Mike Askew who said the best teachers of ratio and proportion are those who are good at making links. #mastHEI4
- Mary McAteer concludes #mastHEI4 by quoting from 'Dead Poet's Society': "why are we standing here? To see things differently."