## Great teaching leads to student progress

Today the Sutton Trust report “What makes great teaching?” by Rob Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major was released. It’s a report I’ve eagerly been awaiting and I very much enjoyed reading it. You can download the report in full here free of charge. It’s only around 50 pages long and I’d say read it, but if your lacking in the time or the inclination I would say you should definitely still download it, and read the executive summary which is only around 3 pages long. This executive summary is a brilliant summary of the report, so I feel no need to summarise it here, but there are a few points I’d like to comment on.

Above is a screenshot of the start of the executive summary which includes the quote:

**Great teaching is defined as that which leads to improved student progress.**

That, to me, seems the most obvious thing in the world. If the pupils are progressing well in your subject, then the teaching is great. If the students aren’t progressing, then you need to look at what’s going on and put things right. Unfortunately, this hasn’t been the case in recent years.

Last year I was discussing the progress of my NQT with the SLT member in charge of the department. He had completed the penultimate NQT observations on those in the department and had graded one as outstanding and the one I mentored as requires improvement. We discussed this and he said that there were things missing from the lesson, the sort of things you would expect from all singing all dancing lessons – one example he gave was “he didn’t use lollipop sticks”!!! I found this particularly bad as the class he’d seen my NQT with was his year 9 class and I knew that the class in question had made significant progress throughout the year. More progress across the year, in fact, than any other class in year 9! Which to me proves that the teaching they were receiving was great. This points to an issue highlighted in the report:

I also had a discussion with a HoD at another school who told me he didn’t understand how his AS results had been so poor when he’d had a “consistently outstanding” teacher teaching them all year. My advice was simple: “you need to redefine your conditions for outstanding. If the students aren’t making progress, then you need to try something else.”

I’m glad that this report, and recent ofsted guidance, is signposting a move away from the idea of preferred teaching styles and single lesson judgements. Different things work for different teachers, and different things work for different classes. Context is key. There’s a wealth of ideas and things research suggests works in this report, and I’d suggest trying it out, I will be, but you need to always bare in mind that things that work elsewhere won’t always work for you.

Another key point I noted was the strength of evidence to say that **Pedagogical Subject Knowledge** was important, especially in maths.

This is something I’ve written about before, and again something that seems obvious. Yet I’ve often heard people say “If you can teach, you can teach anything.” I’ve experienced in my own education teachers that were one page ahead in the text book and it wasn’t effective. We need to ensure our pedagogical subject knowledge is up to scratch, that we know the links between our subject and the misconceptions likely to occur. This is particularly important now, as we are in the middle of massive curricula reform which will see a large amount of teachers teaching topics they havenâ€™t taught before, and we all need to make sure we are prepared.

**Teacher observations**

A strong theme throughout the report is around observations. The report seems to favour heavily the idea that they are most effective when done in a formative developmental way.

They also have some pointers as to how this development can be helped:

These are ideas I like. I think all teachers should be constantly developing, and striving to improve. Hattie’s research suggests that there us a massive positive effect on outcomes when teachers see themselves as learners and this backs that up. I’ve noticed an uptake in the number if teachers I know undertaking further study, and this can only be a good thing.

The model of formative and development observations seems to oppose the recent move to performance related pay, and the report has this to say on it:

The report talks about creating a culture where teachers are comfortable discussing their shortcomings, and working to improve them. But if they are tied to pat progression then teachers may not feel comfortable owning up to them.

I was worried to see in the report that apparently **90% of teachers still buy into learning styles**

Which is terribly worrying given the weight of evidence against then. It’s easy to find a bucketload but here’s one to start you off.

*As you can see, there’s a wealth of fantastic stuff in the report, these are just a few key themes I’ve picked out that interest me. The mainstream media seem to think the main theme is about “lavish praise” but that’s just a tiny part!*

If you have strong views on any of this, or anything else in the report, I’d love to hear then.

*I’ll leave you with an interesting page on effective teaching of numeracy:*

## More maths in the playground

My daughter is now a little over two, and as such I spend quite a lot of time at children’s play parks and the amount of maths you can find there is incredible.

I’ve written along these lines before. From silly things, like the fact our local park was the only place I’ve seen with a simple abacus that’s set up for a base ten, rather than base 11, world. To the more intricate mechanics behind swings and roundabouts.

Today, however, it was this that got me thinking:

“A slide?” I hear you thinking. “Surely there’s nothing too mathematical about that? Gravity means you go down it.” Well in some respects you would be exactly right. However, we don’t live in a model world, and there is the question of friction.

Today the park was rather damp, it had been raining over night, so we took a towel to dry the slide. Once the slide was dry my daughter went down it, but at an incredibly slow speed and stopped about halfway down. I have always noted that the speed of the slide varies incredibly, and had assumed it was due to the coefficient of friction varying between different materials. Her cotton trousers provide a much faster slide than her jeans, for instance. But today she had denim on and it doesn’t normally stop halfway down. I then thought about another recent trip where the slide had seemed slow, and that day it had been particularly warm.

It got me thinking, does the temperature affect the coefficient of friction between two materials? Or perhaps it’s humidity that has an affect? A little bit of research leads me to believe that both can be contributing factors. Definitely more ammo for investigation in a mechanics school trip!

After the slide, she wanted a go on this:

As you can see, the local see saw is fairly basic and works best if two people of a similar mass are on each end (obviously we aren’t). It’s still easy enough to work, but it made me think about another local-ish park that has a much more complex see saw where there are 3 seating positions on each end. That gives more variability to the user’s and would mean two children of different mass could select positions,that give similar, but opposing, moments and hence work the see saw as well as if they had equal mass. What a fantastic idea, and a fantastic use of maths!

*I love the amount of maths that is present at local playparks, and one day I do hope to take a mechanics trip (perhaps a cross curricular one with physics) to investigate all these things. It would be awesome to make a TV show around it. Perhaps I’ll make my own Numberphile – esque video on it one day!*

## 5 reasons to go into teaching

*This post, like many others I’ve read over the last day or so, is inspired by Rob Carter (@robcarter2012) who wrote this post on a similar topic. It’s been a joy to read the posts which have provided much needed respite from the negativity pedal in some areas, such as the dreaded secret teacher.*

**1: You get paid to talk about your favourite subject.**

I love maths, I love talking about it and I love doing it. All things that happen as a natural by product of my job. It keeps me engaged with a subject that had been vanishing from my life in the years between university and teacher training and it certainly keeps my brain sharp.

**2. You meet a lot of amazing people.**

Some jobs can be lonely, you can spend the majority of your time in a solitary relationship with your computer. Teaching is not like this, you spend the majority of your time with people, whether they be learners or colleagues. And I’ve met lots of amazing people who are both.

**3. It’s a constant learning curve**

No one is the finished product, we are all learning, all the time. There’s always a new piece of policy to implement, an impending curricula change or just a new pedagogical approach that might be worth a try. I’m currently studying towards a masters qualification, which I’m finding extremely interesting, but even without that there are tons of opportunities for continual development.

**4. Making a positive impact**

Every day I spend time working with young people to improve their prospects in the “real” world. The world beyond 18. This takes many forms. Teaching maths, obviously, equips some with the basic maths skills they’ll need in life, helps them achieve a qualification that will open doors and secures a good footing for the future. For some it goes further, inspiring take up of the subject at A Level, or higher education. I even had one student go on to do mathematics with QTS which has a knock on effect on a whole host of future pupils. It’s not just that though, helping with UCAS, helping learners decided what course in HE is best for them and writing UCAS references are equally important in making that impact. Then there’s listening, sometimes that’s all that’s required, and sometimes even imparting a little advice, when learners feel they need it.

**5. An end to monotony**.

When I think back to the time of spent in office jobs between university and teacher training I realise just how bored I was. I wasn’t being challenged intellectually and I wasn’t being challenged in any other way either. I had some good people around me, and that made the job enjoyable enough, but I would hate to return to that. I sat opposite a guy called Will who was great. He once said “do you feel your brain melting when doing this job?” we both decided a career change was in order. I followed nt long held dream to teach, and he followed his into the medical industry.

*I’ve tried to keep this post fairly short and concise. I’ve written before in more detail about Teaching, why I would recommend it and what I think about the much reported downsides here.*

If you’ve written a 5 reasons to go into teaching post, do post a link in the comments or send me it via twitter. I’d love to read them.

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*## Mathematics – the app

A while ago I blogged about the Wolfram Alpha app, which I love and which has been the limit of my mathematical apps on my phone since. I haven’t really needed anything else. The other day, however, I was on the play store trying to find a decent app which would allow me to type maths easily. I failed in my search *(if you know of a good one for android do let me know!) *but I did find this app called “Mathematics – for android” by daboApps.

The app was free so I downloaded it (along with many others) to see what they could do. Most of them I deleted fairly quickly, but this one is one I feel could be extremely useful. It does some of the things Wolfram Alpha does, but it isn’t a like for like, there are things WA does that Mathematics doesn’t, and vice versa. Here is a screenshot of the menu screen:

What you can’t see are two sections titled “Calculator” and “Calculations”. Which are excellent high powered calculators.

There are also many other functions that I’m just beginning to explore. There functions section will plot and solve polynomials, differentiate, integrate etc:

It will solve equations, even systems of equations:

The stats section has these tests:

Which seem easy to use. I’ve not managed to fully explore yet but I had a little play:

So far, I’d certainly say it isn’t bad at all for a free app!

## How to assess year 9

Earlier today I saw a tweet from Luke (@bettermaths) which said that the subject of those evenings #mathschat was “how should we assess year 9, in light of the new 1-9 grading system?”

This got me thinking about year 9. It’s a funny year group in general. Traditionally it falls within key stage 3, but in many schools these days it us counted as key stage 4. This year’s are in a stranger place still, as they will be the first year to go through the new KS4 curriculum and sit the 1-9 exams. And they will do this without having done the new KS3 curriculum, never mind the KS1/2 curricula. This means they run the risk of having gaps in the assumed prior knowledge where said assumed knowledge is on the new curriculum but not the old.

It is important schools address this this year. We need to ensure that we are equipping year 9 with the requirements to access the new curriculum. Edexcel have drafted a transition curriculum for year 9 that is freely available on their website. *(I don’t think the other boards have, if you know they have send me the link and I’ll add it!)* As all the boards are using the new curriculum with no additional content, this transition scheme should help if you haven’t yet put anything in place.

**So how should we assess?**

The answer here is pretty obvious to me. We should be assessing against the content they need to know, identifying the gaps in that content and using that to inform our teaching. I believe that that should be the main focus of all our assessment, particularly with this year group who face extra challenges.

I do, however, feel the question is intended to be about tracking, rather than assessment. I think it’s really asking “should we be using levels, a-g grades or 1-9 grades?” This to me is an entirely different question. And I see it as far less important. We are moving into a “life beyond levels” and I see that as an opportunity to take back assessment. To restore it to its former glory as a way to identify gaps, rather than a way to impose a linear model of progress onto learning that doesn’t take a linear form at all. I know at the recent #TLT14 event Tom Sherrington (@headguruteacher) spoke about the removal of levels from reports at his new school and recently wrote this excellent piece in assessment.

**So what are you suggesting?**

Well obviously we need to have some progress tracking, but does it need to have a numerical value every half term? Should we even be collecting data that often? I believe Kev Bartle (@kevbartle) spoke at #TLT14 about how he’s moved his school to 2 data collections per year, believing that this will mean more accurate data, which I think is a good idea.

**So what should we use? **

We know, as teachers, what are students need to know to get where they need to be. We know their start points and we know where they need to be at each step. Should we even be quantifying this with numbers or letters? Could we nit be rating them as “On target”, “Above target” “Below target”? In a post level world where progress is king (fingers crossed progress 8 moves us away from a threshold pass!) should we not be assessing against, and reporting on, progress?

*#mathschat is a twitter chat which happens Wednesdays at 8pm. Follow the hashtag to join in. And feel free to comment here if you have opinions on this, I’d love to hear them.*

## A nice little thought puzzle

Earlier today I listened to episode 19 of my favourite podcast, “Wrong, But Useful“* (if you haven’t listened, and like maths, then go listen quick!). *Every month the hosts Colin Beveridge (@icecolbeveridge) and Dave Gale (@reflectivemaths) set a maths puzzle for listeners to solve.

This month it was Colin’s turn and he set a nice algebra puzzle:

*Show that n^4 + 4 is not prime for any integer greater than or equal to two.*

Have a little go if you haven’t already….

My thought process went like this:

For even n then the whole things even, but what about the odds?

Could it be solved by induction?

N=3 gives 85. N=5 gives 629. Nothing jumping out there.

I’ll factorise it, see what happens:

After a brief false start where I wrote the square root of 2 is 1 I came up with the solution, which is quite neat.

*n^4+4=(n^2-2n +2)(n^2+2n+2)*

n^2 – 2n +2 is greater than 1 for all integers greater than 1.

n^2 + 2n +2 is greater than 1 for all positive integers.

*Hence n^4 + 4 is a product of two numbers greater than 1 for all integers n greater than or equal to two.*

A lovely little midweek puzzle.

## Mastery and School Visits

This morning a colleague and I travelled over to Huddersfield to visit a school that was implementing a mastery curriculum in maths. The idea of a mastery curriculum is something that very much appeals to me. The crux of it is that each stage I’m the learning of maths is embedded fully before moving on to the next. It is something we are considering adopting as a school and it was fantastic to be invited to go to this other school and see how they’re implementing it.

The visit involved observing a lesson and meeting with the schools mastery lead to pick her brains about the curriculum. The whole experience was worthwhile. It was great to see a different school the set up and the layout. How the kids their behaved, interacted and were turned out. I think we would all benefit from being able to visit other schools as part of our own professional development. Especially those who have only ever worked in one school, as it would broaden their horizons and ideas.

I’m in the middle of writing a report on the visit, and mastery, so will blog some further thoughts here when I’ve had time to research and digest. But some early thoughts:

*– Mastery is a solid idea based on strong theoretical groundwork (as laid out be Kris Boulton at the recent maths conference)*

*– care must be taken to ensure that the most able on the cohort are stretched and not left stagnant while the others catch up*

*– mastery is a big undertaking, and needs to be embedded from year 7.*

*– measuring progress in the way that has been done previously at year seven will not work, and this would need to be addressed, but this needs to be addressed anyway in a post level world.*

## Half term 1

Today my twitter feed is full of tweets from people in Southampton, at the teaching and learning takeover event (#TLT14). The event seems to be going well, and I hope to catch up on the day later via blogs and/or videos, but currently my house us full of the sounds of nursery rhymes, so I thought now might be a good time to reflect on the first half term.

Way back in August I started a new role at a new school. I’d never moved schools before, and as such was stepping into an uncertain world. That first week we went back a week earlier than everyone else which at the time was a tad annoying but is now paying dividends as we are starting a two week break.

Starting a new school is tough going. There’s a ton of new stuff to learn, new acronyms, new systems, new policies, new names for things, new colleagues and, of course, new pupils. This overload of newness hits you like a train, and it took me a while to get my head round it all.

I’ve enjoyed the first half term. There have been challenges, but I’ve learned from them and I think they have made me better at my job. I like my new classes, I like my new colleagues and I like my new role. On top of that I feel that the school are investing in my development and I am really glad I made the move.

As well as moving schools, I’ve also moved authority, and am now teaching in Bradford. The school is part of “The Bradford Partnership” which is a non-profit organisation which is wholly owned by its members (ie the schools). The mission if the Partnership is to improve education for all young people in the city and I think it’s a great initiative. There are opportunities to meet colleagues from other schools regularly and to share ideas and best practice.

This first half term is always a tiring one, as is the next, so I’m glad I’ve got two weeks off to recharge the batteries. I just hope my bodyclock realises it is the holidays, and allows me to start sleeping in a bit!

## Formula Triangles

Formula Triangles, it would seem, are a much loved shortcut in the world of Mathematics teaching. You know the ones, it’s when you get a three term formula that is one thing = a ratio of two other things. They look like this:

I’ve mentioned my hatred for them in passing on the blog and on twitter a couple of times and come under fire for this, which has made me think about it them a bit deeper. I used the term “ban them” in a tweet, and this may have been the cause of the uproar – as with The Great Calculator Debate. The term is more important extreme than my actual viewpoint, so I figured I’d try to set my thoughts out here.

Formula Triangles were first shown to me by my GCSE IT/Electronics teacher Mr Walker. The formula he was teaching them for was V =IR (Voltage = Currently X Resistance if my memory serves me correctly). Mr Walker didn’t explain how they worked, or what was really going on. He said “I always have trouble getting them the right way round, so I use this triangle, and cover the one I need.” I’m fairly sure his algebra skills were a little lacking. I was good at algebra and quickly spotted why this worked. I had to explain these reasons to a number of classmates who weren’t happy with the “just do it like this” model and craved a deeper understanding.

I quite liked them as a short cut, and quickly realised they could be applied to any number of similar formula, including speed distance time formula and the trigonometric ratios for right angled triangles, or RAT Trig for short. I’m fairly sure I used these in my exam.

**So what’s the problem with them then?**

Well, since you asked…. It’s the way I’ve seen them taught. I’ve seen them taught in maths lessons the way Mr Walker taught them in IT. This misses the opportunity to cement the algebraic skills required to rearrange formulae, to see the links between different areas of maths and enables pupils with little to no algebraic knowledge to gain a good GCSE pass. This highlights the ineffective nature of the maths GCSE as a measure of mathematical ability, which surely it should be.

These formula triangles are taught as a replacement to algebra, the purpose of them is that you can cover the one you want and get the formula arranged the way you need it without having to rearrange. Becks (@becksta9) asked: “when finding an angle using the triangle you get sin x = o/h how do you make x the subject?” and this is a good question, unfortunately in my experience the use of formula triangles for Trig is normally coupled with the instruction “don’t forget that you press shift when finding an angle”, rather than “the opposite divided by the hypotenuse gives the sine ratio, so you need to use the inverse function to find the angle.”

**Is it ever ok to use them?**

I would say yes. I am fine with people who understand algebra using them as a shortcut to save time (although how long does it take to rearrange them properly? You must save milliseconds!) , I’m fine with teaching them to weaker students who have tried to learn algebra but are prone to mistakes after they’ve been shown how to rearrange them algebraically.

What I’m not fine with is the “do it like this and don’t worry about how it works” use of them. Especially when the learners in question want to go on to study Maths at A Level and beyond, it could damage their chances.

*Becks, Jo (@mathsjem), Martin (@letsgetmathing), Hannah (@missradders) and Colin (@icecolbeveridge) all came to the defence of formula triangles on twitter. There was some sense that I was personally attacking their methods, and that I was making generalisations about the use of formula triangles. Neither of these were my intention and I apologise if it seemed it was. I hope this post explains what I meant better that I could in 140 characters. I was surprised at the massive response the tweet got, and the massive, seemingly emotional, relationship some had to it. I would love to here how Formula Triangles are used to aid rearranging, instead of as a way to avoid it, as is the point. I’d love to hear more views on this in general, do you use Formula Triangles? If so how, and why?*

## Trouble with numbers

I’ve just finished watching ITV Tonight’s episode from this evening entitled “Trouble with numbers”. The show was highlighting the problem we have in this country with maths ability in Adults. I found it pretty interesting, and if you missed it I would certainly suggest catching up on it.

There were a number of things highlighted in the program that we maths teachers already know, but are major issues. Firstly, the fact that the culture in this country finds it perfectly allowable for adults to say “I can’t do maths.” This is a real issue, and last year a number of my year 11s were told this by the head of English, which led them to question the necessity of maths as you could be a head of English while being rubbish at it.

The second point was the fact that learning happens with mistakes. This seems obvious to me, and I have long worked to build a culture in my classroom that it’s fine to be wrong, as that’s how you learn. But the show suggests that this is not the case in the majority of UK classrooms, which is a shame.

There were some excellent examples of initiatives being run by various institutions to help improve adult numeracy, and I was pleased to see that they are effective. I was made up to see that the driver for one bloke was that he wanted to be able to help his daughter with her homework.

I was also pleased at the take up shown in the school that offered classes to parents. While writing my last masters assignment I looked into the effectiveness of this and it’s something I would like to run in the future.

All in all, it was an enjoyable show, although I would have liked it to be longer. And I was slightly annoyed that when they were revealing the scores of the kids vs parents exam they referred to the “average” score, rather than the “mean” score.

I’ll leave you with the worrying fact imparted by Jo Boaler on the program: Girls maths performance drops instantly if their mum tells them she was never any good at maths.

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