## Ray Maher at Athena

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

#RayMaher still does teaching in school – says best teachers should be in Year 3 – it's the engine room of the school
#RayMaher- best resource in schools is human
#RayMaher – if get foundations right, you get the rest right – times tables by rote – make sure 7 year olds know them off by heart.
#RayMaher wonders why some Year 6 don't have methods for + – x and Ã·
#RayMaher says UK is 4th in World in maths (behind, Korea, China, India)
#RayMaher -think of a number, double it, add 5, multiply by 50, +1760, – year you were born. My answer = 738
#RayMaher talks about weighting of maths. 20% U&A, 50% N@C, 20% SSM, 10% DH
#RayMaher questions how secure children are at end of Year 3. (should be level 3)
#RayMaher says if you get the calculation right, you're going to get standards up
#RayMaher – child methodology: in my head? Using drawings / jottings? can I use expanded / compact written method? need calculator?
Teaching one method means less able improve, but more able stay the same… #RayMaher
#RayMaher says models and images in Y1-Y3 are really important
#RayMaher – sort out misconceptions in Year 3
#RayMaher Use number lines to develop mental imagery – then move quickly on to efficient written methods when understanding is secure
#RayMaher advocates using Grid Method – Level 3: 2 dig by 1 dig / Level 4: 2 dig byt 2 dig. Can't do grid method unless timetables secure
#RayMaher gives example of using bus stop for 47 Ã· 8. #fail!!!!
#RayMaher Chunking is repeated subtraction. Egof Y5 non-divider who caught on with chunking 10 lots of 17 on a number line (for 191 Ã· 17)
#RayMaher indicates that children need to OWNtheir one method for +, -, x, Ã·. It's not one method per teacher, but one method per child.
#RayMaher – we need progression of calculations policy from foundation stage to Y6. Gives example of very simple policy.
#RayMaher says use calculations policy as displayed curricular targets
#RayMaher use easy-language display of calculations policy to go home for parents
#RayMaher has marvellous counting stick with velco on and 'Mortimer' a puppet who counts up and down.
#RayMaher shows place value mats for Lower KS2. Place value strips for addition. Number squares – 0-99 better than 1-100.
#RayMaher shows viewfinders for number squares. – Algorithmic Ls – great resource for revitalising our number squares
#RayMaher Know 1, get 3 free sheets. Show that one addition fact gives 3 more (1 +, 2 -); 1 multiplication fact gives 3 more facts (1 x, 2Ã·)
#RayMaher – round tables – look ace. TAs – make up packs of all these FAB resources
#RayMaher – Language pyramids for maths language
#RayMaher – shows kinaesthetic resource for counting
Useful numbers game like countdown http://bit.ly/1HqVtn #RayMaher
Good place for maths games (although the cost…) http://bit.ly/cAghdW #RayMaher
#RayMaher shows Busy Bees good SODA (Start Of the Day Activities) for maths http://bit.ly/dqDGOZ (it costs Â£20)
#RayMaher – can you gain 5 minutes during register? Research shows that if you do the children will get cleverer…
#RayMaher advocates buying Nintendo DS to support mental recall – brain traing / maths training
#RayMaher uses numeracy passport to support progression of key skills. http://bit.ly/8ZEHNl
RT @frogphilp: #RayMaher uses numeracy passport to support progression of key skills. http://bit.ly/8ZEHNl
#RayMaher says Wirral Authority give children a 'travel bag' for pre-passport activities where children get stuff when they achieve learning
#RayMaher demonstrates resources that include left-handed children
#RayMaher shows Fiery Ideas Passport kit. Costs Â£55 but is comprehensive for developing mental maths and instant recall http://bit.ly/b0FX3h
#RayMaher points out that doing bonds to 6, 7, 8, 9 are as important as bonds to 10.
#RayMaher – organisation of passport instant recall means that you can focus on skills for different groups during main activity of lesson
#RayMaher – passport objectives: know all recall by Year 5; more confident at doing sums in heads; key skills for ECM; kids love it!
#RayMaher argues that APP should be standardised – 5 schools on this day – we could meet to standardise our practice
#RayMaher Shows a grid of standardisation
#RayMaher warns that great resources like Pitch and Expectations http://bit.ly/bn0sia may be removed from website as funding is withdrawn
#RayMaher says learning objectives should be broken down – different buzzwords 'steps to success', 'learning ladders'
#RayMaher example of steps to success for Grid method: partitioning, multiply by 10, recall of times tables, spatial awareness, addition…
#RayMaher shows resource linking AFs – Objectives – Steps to Success – Resources
Robin at #RayMaher day points out that steps to success can become a barrier for teachers if they don't use common sense.
Robin at #RayMaher says that a teacher's job is to make planning exciting and relevant; not to pull planning from the ether.
At #RayMaher day, http://bit.ly/OuI2Y (Mathletics) is demonstrated. Looks great – Education City rival – Athena have paid for 2 years
#RayMaher endorses Mathletics
"If there's a problem, there's a solution" says #RayMaher about to introduce section on problem solving…
#RayMaher says put maths into context – 'Deal or No Deal' with special offers from supermarkets
#RayMaher Shows problem solving frames – RUCSAC (Read, Understand, Choose an operation, Solve, Answer, Check)
#RayMaher Problem with RUCSAC – no estimation
#RayMaher 6 schools meet #Athena My tweetdeck is keeping me fully informed with @frogphilp chirps. Sounds great. Chirp…
#RayMaher Other Problem solving Frame – RACECAR (Like RUCSAC but with estimation)
#RayMaher Problem Solving – Use maths in a real context – real money, use roleplay, prices, 5-a-day, special offers, price vs mass, data.
#RayMaher – lesson idea work out how much Cola is replaced by ice at Macdonalds (Tip: answer = about 67%)
#RayMaher shows free game to show supermarket maths http://bit.ly/bTKk8H
#RayMaher shows Number Crunch Bunch http://bit.ly/cHgOzt (Â£25) to encourage dialogue
#RayMaher – Could use Flips to film children speaking about conceptions / misconceptions to promote class discussion
#RayMaher If there are 196 legs and 126 eyes at a dog show, how many people and dogs are present?
#RayMaher shows Maths Talk TV http://bit.ly/bqfsA9 (Â£60) (NB Teacher.tv has stuff on dialogue http://bit.ly/ckYhd9)
#RayMaher shows beginning of Charlie and the Chocolate Factory and asks: What maths can you see?
#RayMaher Logic and Reasoning is possible area of weakness in UK primary schools
#RayMaher shows logic problem: http://bit.ly/bTzAXT – Can you solve it?
#RayMaher shows progression for making decisions – build up complexity from simple decisions
#RayMaher points out you can get free education resources about London Olympics from http://bit.ly/bCLD21
#RayMaher shows Professor Problemo – interactive software and resource sheets (Â£25) http://bit.ly/9atnwC
#RayMaher recommends free resource: Mathematical Challenges for able pupils http://bit.ly/apfZxn #gtchat #mathchat
#RayMaher recommends Gecko Maths http://bit.ly/aIFBqj Korean problem solving that has contributed to SK being number 1 in maths

## Does ‘mean’ mean ‘mean’, ‘mean’ or are you being mean?

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.

Suffice to say, at this point: maths teachers – you are amazing.

Why are we amazing?

Because we can explain to our children when leaves means equals.

And when vulgar isn't rude.

We know that multiply can make things smaller; that even isn't always smooth; divide can mean share and group; differentiation is more than just good practice for including all children in learning.

And we can explain that mean means mean (as in average), as opposed to nasty (although it might feel like it), or intend.

Maths. It's all about the words, don't you know.

## What is Maths?

This is my definition of maths.

Maths is elegant. It is graceful and swift.

However my favourite is by my MaST colleague Matthew Cham who worked with his children on the definition. Together they came up with:

Mathematics –
a spoonful of numbers,
a sprinkling of symbols,
200g of quantity,
100g of measurement,
All mixed together and moulded into the

MaST stands for Mathematics Specialist Teacher. It's a Master's level study designed to help us primary school teachers be a bit more clued up on the big picture of maths. We all had to come up with our definitions of maths, but they're all hidden away on the universities Blackboard system.

So did the exercise with my children on this wallwisher.

Please respond to this post with your own definition of maths or post on the Wallwisher (although as I write, wallwisher does seem to be misbehaving a little at the moment – bizarrely I find it works best on IE8)

## 10 squares and 1 squares

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.

In many ways the 1 square is easer to pick up because it represents numbers in the way that children are used to see them with money. You could even call it the £ square (or the \$ dollar square, or lots of other denominations of currency for that matter). The 10 square is a little bit more difficult to link to real life, although if you produced one with two decimal places you could put it into the context of timing a 100m race.

It is important to remember that number squares are limited as a image for children – number lines are so much more flexible because they are extendable and easier to produce freehand – which is important for jottings – that all-important stage between mental methods and standard algorithms.

If you want to try it for yourself, have a look at my Google Spreadsheet of the 10 square and 1 square.

10 square.pdf

1 square.pdf

## Notes on maths training

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:

1. 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.
2. 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.
3. 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.
4. #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.
5. 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.
6. I'm taking my notes at #mastHEI4 by Twitter. I will collect onto a blog later: http://philpmaths.posterous.comthat's what I'm doing now. Although this is only an intermediary post.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. Teacher dialogue strategies in maths: eavesdropping, chairing, prompting, rich questions (see Bloom's taxonomy) #mastHEI4
13. Why is dialogue an important part of learning?validation, identify misconceptions, time for rehearsal (thinking time). #mastHEI4
14. Software to support dialogue in unpicking misconceptions: 'the number crunch bunch' tool for stimulating dialogue – Fiery ideas #mastHEI4
15. Vygotsky says that talk can take people beyond the 'edge of their thinking' ZPD #mastHEI4
16. 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.
17. 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?'
18. 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.
19. 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.
20. 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.
21. Games encourage talk. Snakes and Ladders is not a maths game because it relies completely on chance. #mastHEI4
22. 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.
23. 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.
24. 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.
25. 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?
26. #mastHEI4 ideas for pictures: golden ratio, square numbers, shapes, etc.
27. #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.
28. 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.
29. What about vocabulary: In maths what is the different between technical and specialist vocabulary? #mastHEI4
30. #mastHEI4 Answer: technical words are specific to maths (eg triangle); specialist words are general words used in a maths context (eg table)
31. #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.
32. #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.
33. RT @frogphilp: Cambridge review: many children sit in groups but work individually. Why? #mastHEI4 – thanks to @dan_bowen for re-tweeting this.
34. Problem-Cube lowered into water half submerged with one vertex at lowest point. What shape does cross-section make at water level? #mastHEI4
35. #mastHEI4 what did I FEEL about answer? Theoretical but nervous that I couldn't see it and do it. Other responses…?
36. Possible responses to problems include: I don't care, what did you get, not enough information, j just knew it #mastHEI4
37. Insurance salesman question is a cracker. I will share on my blog later. #mastHEI4
38. Challenge: with difficult problems how do we stop being smug and give the answer away? How do w stop children being unstuck? #mastHEI4
39. 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.
40. Ideas for Say What you see: target words, talk ping pong, use shapes. Also: http://nrich.maths.org #mastHEI4
41. 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.
42. Idea: use SATs questions to ask more interesting questions. E.g table – data handling – ask who gets most pocket money #mastHEI4
43. 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.
44. 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.
46. Assigment tips from #mastHEI4 – grid evidence against learning outcomes, think audience, understand 'critically', write analytic narrative.
47. Assignment tips at #mastHEI4 – fluent English, keep focus tight, evidence claims, be questioning, conclusions be properly supported
48. Assignment tips from #mastHEI4 – look at grid that examiner uses to assess you, don't 'go large', articulate the intuitive
49. What is 'critical'? Evidence of self-awareness, discussion, descriptivity + #mastHEI4
50. 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.
51. 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.
52. Ratio and proportion are hard concepts. Hard to separate, then link to division, fractions, decimals and percentages. #mastHEI4
53. Proportion = in every; Ratio = for every. Ratio breaks with pattern of fraction – decimal – percentage – proportion. #mastHEI4
54. Ratio question: "3 times round my head = my height: is this true?" #mastHEI4
55. @tucksoon that's the one. It's been recommended to me for developing math talk in 3-11 year olds. #mastHEI4
56. Graham Smart teaches about unitary ratios. Height to head ratio = 1:0.33 #mastHEI4
57. RT @frogphilp Graham Smart teaches about unitary ratios. Height to head ratio = 1:0.33 #mastHEI4 or 3:1
58. The Giant of Biblical Proportions talked about by Graham Smart (a way of engaging children with ratio) #mastHEI4
59. Graham sums up by giving ideas for FDPRP: filling up petrol, mixing paint, number lines, recipes, stories. #mastHEI4
60. FDPRP are really the same thing. Model on number lines. Line of people #mastHEI4
61. people pie chart at #mastHEI4
62. Smart quotes Mike Askew who said the best teachers of ratio and proportion are those who are good at making links. #mastHEI4
63. Mary McAteer concludes #mastHEI4 by quoting from 'Dead Poet's Society': "why are we standing here? To see things differently."
And that was the end of my tweeting. I then walked to Birmingham New Street carrying my metre stick. Today I used Twapperkeeper to collect my tweets, sent them to an Excel spreadsheet (note to Tapperkeeper – it would be great if you could output straight to Google Spreadsheets) and put them into this e-mail to posterous. Do you think Tweeting lecture notes is an effective way of learning something? In my next maths post I will go into more depth on the whole dialogue in maths topic.
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