Classic Blog

How to give all UK teachers a 35% pay rise.

Warning, this blog involves lots of numbers. Don’t worry, I had a historian proof read it and he understood 🙂

For the purposes of these calculations, I’m going to ignore inflation and talk in 2018 pounds. The teachers’ pension automatically takes into account inflation, so that makes this a reasonable thing to do.

The average teacher earns, according to the government, £37,400. Each year under the current ‘career average’ scheme, my average teacher, Sarah will earn a pension of 1/57th of her salary: £656 per year.

How much would this pension cost if Sarah wasn’t a teacher? At the age of 68, a pension pot of £100,000 will buy an annuity, which grows with inflation as the teachers’ pension does, of £3,600 per year (see note 1). Therefore, it would cost £18,200 to pay for Sarah’s pension of £656 p.a.

Where does this £18,200 come from? As a member of the mysterious teachers’ pension, Sarah contributes 9.7% of her income, £3,600. This means that each year the government contributes an additional £14,600 (39% of her salary: see note 2) that she never sees and may not even know exists.

My sister is a lawyer and her employer contributes 3% of her salary to her pension pot. Let’s say the government adopted this approach: it takes the £14,600 it currently contributes to Sarah’s pension, pays her £13,100 extra, sending her salary to a healthy £50,500, a 35% increase. It contributes to remaining £1,500 (3% of her new income: see note 3) to her pension.

I’m using Sarah as an example but it doesn’t matter if you think she’s not representative, because we could equivalently increase all teachers’ salaries by this 35%. I’ll say it again, 35%! Starting salaries for teachers shoot up to £31k (£39k in inner London) and suddenly look a lot more competitive. On the other hand, teachers’ pensions are now terrible, along with the pensions of lawyers, accountants and most other professions. But who goes into a job because of the pension?

Could this change help solve the recruitment problem?

ps. I make no comment as to whether or not I think this is a good idea. My wise father-in-law pointed out that it’s a very Conservative suggestion: let people choose how to spend, or save, their money.

Notes:

(1) I interpolated based on the figures given. This is actually a conservative estimate because I used the figures for a single pension: in fact, the teachers’ pension also pays 37.5% to a partner after the teachers’ death, so would be worth more than what I calculated. This all assumes that a private pension pot grows at the same rate at the teacher’s pension (CPI + 1.6%). I suspect that some pension schemes may do better than this, but they will be much more variable and may also go down significantly, for example in 2009.

(2) Officially, Sarah’s school contributes 16.5% (in the case of state schools, this is just the government shuffling numbers around on a page) but the £14,600 is actually 39% of Sarah’s salary of £37,400. I understand that the government doesn’t actually ‘save’ this money as teachers’ pensions are unfunded, but it does have to pay it eventually. In the short term, this policy would cost the government quite a lot of money, but in the long term, it wouldn’t make a difference.

(3) My wife thinks this paragraph is confusing, because she is eagle-eyed and noted that 3%+35% does not equal 39%. Why doesn’t it add up? These percentages are of different numbers (3% of the new salary, 35% of the old salary), a pretty classic tricky idea with percentages.

Scheming, Part 1: Sequencing Topics and Prerequisites

I have probably spent about 40 hours in the past two weeks working on my scheme of work.

I started with the base scheme of work from my first school in Highgate. It stands out amongst schemes because it spends just 2-3 lessons on each ‘unit’ before moving on. This isn’t because it tries to pack in the whole syllabus into two years, but because each ‘unit’ consists of just one major new idea.

I really enjoyed teaching this way and was surprised when I first found out that other schools spend around a month teaching one narrow around area of maths before moving on to a different area. I wonder how on earth the students are going to remember a topic that they last studied two years ago. If you teach in small blocks, the difficulty is that pupils may not remember the prerequisite material. However, this forces you to constantly recap and provides spaced-practice by default.

So, what have I done to improve (in my opinion) on Highgate’s scheme? I have put a lot of effort into checking that the topics flow well from year to year, with each new ‘unit’ introducing a similar amount of new material. I have referred to some other schemes in the process:

I used these mostly to give me an idea of what year group pupils usually meet a topic. Jemma’s scheme in particular gave me new ideas of the key points within a topic and helped me to break down some of my topics more carefully. Where I needed more help on this, I also asked for help on twitter. This poll was the culmination of loads of great suggestions I received on teaching HCF and LCM, which led to me introducing a section on algebraic forms of these as a prerequisite to factorising, adding algebraic fractions and more.

Some of my considerations in designing the scheme were:

I don’t want to recover material that pupils have already learned at primary school, so I haven’t included the lessons on basic number and geometry that many secondary schemes do. Instead, I will check pupils’ prior understanding when introducing new topics as part of my planned mastery approach.

I want my scheme to only list each new idea once. Of course, there will be need for review and if necessary, reteaching, but in general, I really dislike schemes which have exactly the same ideas in two different places. I want to know what the pupils should have already learned (even if they haven’t fully learned it!) and what’s new.

I tried to put at least one bit of each ‘topic area’ in each year group. I feel that this is generally a good idea, as pupils have to see a topic each year and so have an opportunity to recap it. It’s also particularly important in my international context, as we have a higher turnover of pupils, so it will allow me to get new pupils up to date with each topic.

I don’t want to accelerate higher-attaining pupils and I don’t want to finish teaching before Easter in year 11, so the ideas are spread evenly throughout the 5 years.

I used specifications to mark the topics which only feature on the higher tier. With a few exceptions, I made sure these topics are in year 10 and 11 so that if I decide to enter pupils for the foundation tier, they will be able to spend more time on the other topics in these final two years.

So, the final product… You can see / download it here: http://lukepearce.eu/scheme-of-work/

I’d really welcome any criticism to this as it’s definitely still a work in progress.

In particular, I’m working through the geometry tabs to check that I have listed all the relevant prerequisites. I’m also aware that while the topics are very interleaved, there is little genuine interweaving of them.

In Defence of Detailed Written Plans

I didn’t write a lesson plan for the first 5 years of my teaching career. It was a mistake.

For starters, my claim may be hard to believe for many teachers; how did I get away with such a lax approach? I taught in an independent school in Highgate. No lesson plans were required, observation was frequent but informal and observation grades were an alien concept until I joined the GTP in my 6th year.  The fact that this may surprise many teachers is a sign of a disconnect between the maintained and independent sectors, which manifests itself in many areas.

From my external perspective, the above conversation is funny; Sam now teaches at Highgate and Katharine has (as far as I’m aware) always worked in the state sector. Whilst, to Katharine, no observation grades may have been ‘unthinkable’ 10 years ago, this was exactly what Sam’s independent school was doing then (though it was long before he worked there).

Anyway, back to the main point: I love a debate, and this time I’m taking on two big names: @teachertoolkit and @teacherhead, who have both made a similar point in recent blogs.

Whilst these blogs make some excellent suggestions (click the extracts above to see the whole blogs), they both suggest avoiding written lesson plans. On the contrary, I think we should strongly encourage teachers to write down lesson plans.

A detailed written plan is like a path worn into the hillside.

When I come to teach a topic, what do I have at my disposal? I have years of classroom management experience, an understanding of major misconceptions that pupils have in my subject, but do I remember the finer details of when I last taught the topic two years ago? Probably not. Even if I think I do, my memories are not necessarily accurate.

A friend of mine once explained why, as a classicist, he loves paths: they represent years of accumulated knowledge and experience. As a teacher, my written plans are my paths. When I head in a direction that leads to dead-ends or rocky ground, I backtrack and find a different route. In this way, the best path becomes more worn and so easier to follow over time. As a Mountain Leader, I am capable of navigating away from paths, but when doing so I’m less likely to point out the interesting geological features or flora and fauna along the way.

To be fair to @teachertoolkit, their post suggests that there shouldn’t be an obligation to write lesson plans, which I suppose I agree with. And if you read the detail,@teacherhead says that teachers should have a list of objectives and resources, which is what my ‘lesson plans’ mostly contain. To be precise, I’m not specifically advocating individual lesson plans (though they may be useful for some teachers) but rather ‘topic plans’. However, I don’t believe that ‘lesson planning’ should feature on such lists because this suggests to teachers and managers that written plans are not helpful. For me, if you write down a plan, update it after the lesson to emphasise good bits and delete or alter what went badly, this will reduce your workload in the long-term, as you don’t have to plan afresh every year.

I learnt a lot of ‘big-picture’ ideas in my first 5 years of teaching, but many of the finer details were lost; which examples and tasks drew out the point well and which turned out to be too simple or complicated. I met so many interesting ideas, but many don’t feature in my teaching because I didn’t write them down.

I started to write detailed plans in earnest 4 years ago: a few of them I now deem good enough to warrant sharing online. However, I still look at them and ponder how much clearer the paths would be if I had been walking them for longer.

Absolute vs Relative

A recent episode of Radio 4’s “More or Less”, addressed the issue of Progress 8, which is obviously interesting to me as a teacher. However, it was the discussion about poverty in the UK which most caught my attention.

The Trades Union Congress (TUC) recently hit the headlines by pointing to statistics which showed that the number of children from working households who are in poverty has significantly increased in the last ten years. They claim that the main drivers of this have been cuts to in-work benefits and restrictions on public-sector pay. The government’s response: It doesn’t recognise the TUC analysis; there are one million fewer people living in absolute poverty.

There a few extra details in the programme, but the gist is that both claims are correct. Relative poverty is increasing, but absolute poverty is decreasing. So the question really about which we value as a society? In the UK, my feeling is that the focus should be on relative poverty (although what I have written next has made me question this slightly!). Indeed, I’m surprised that there are many people at all living in absolute poverty: I know I live in a social bubble, but I suspect that the government figures are not based on the international definition as set by the World Bank.

Returning to education, I feel that a similar debate that has been ‘raging’ on twitter for a few months now (perhaps even longer), boils down to the same issue.

Is Ofsted biased against schools in more deprived areas? Clearly, many people on twitter are convinced by Stephen Tierney’s recent blog post  on the topic and regular references to this graph:

It shows that schools with a high proportion of White British children receiving Free School Meals are judged, on average, much worse than schools who have fewer children in this group. The immediate conclusion is that Ofted is biased against these schools. Surely the proportions should be the same for all types of schools? No.

Why not? Because Ofsted’s standards are absolute, not relative. As Jason Bradbury and Sean Harford explain, the evidence shows that when looking at schools with the same Progress 8 measures, inspectors actually give more generous judgements to these ‘most deprived’ schools.

This thorough treatment of the issue points out that there are many reasons why it’s difficult for schools in ‘deprived’ areas to attain the same absolute standards as schools in more affluent areas. However, this doesn’t mean that we should instead use relative judgements: that would be to accept that it’s ok for children growing up in disadvantaged areas to go to schools with lower standards.

What the analysis does show, however, is that it’s much harder to run a good or outstanding school in underprivileged areas. As a result, perhaps management and staff in these schools should be rewarded / treated with leniency to a greater extent than those in prosperous areas? Similarly, should these schools be funded more generously?

Overall, this has got me thinking about whether we need to get better at teaching the key idea of ‘Absolute vs Relative’ in maths classrooms. Up until now, I haven’t taught it explicitly… another one to add to my scheme of work, perhaps.

(Disclaimer: although I am rather convinced by Ofsted’s blog, I don’t think it proves beyond all doubt that there is no bias: judgements clearly account for progress 8 weaknesses, but to what extent?)

Things that are NOT TRUE

A colleague at a previous school produced this poster (it goes on to 29 points: click the picture to download the full version)

If you’ll allow me a brief aside, credit for this poster goes to Robin Bhattacharyya. Robin was the most knowledgeable person I have ever met and at the time, one of my heroes. Originally a University Challenge champion in 1995, he went back for more in 2011 Christmas special, in which he led his college to victory over a more recent hero of mine, Daisy Christodoulou. (strictly, it was Trinity vs Warwick but from memory, it may as well have been Bhattacharyya vs Christodoulou!)

Anyway, back to the maths… A recent tweet from Stuart Price reminded me of this poster.

Stuart was focussing in on one specific type of misunderstanding which features heavily in Robin’s poster: the over- or under-generalising of the distributive property.  Trying to head off these problems early, I’ve been making a specific effort to teach year 8 about distributivity this week. It has gone better than in the past, so I thought I’d share what (I think) I’ve learned.

In the past, the phrase “multiplication is distributive over subtraction” sounds clunky and just saying it, let alone understanding it, has been trouble enough for my pupils. I’ve replaced it with “multiplication distributes over subtraction“. This small change has had a surprisingly large effect. I think this is partly because it relates more closely to the usual English usage of the verb ‘to distribute’; indeed, this also allows for visualisation: the multiplication is literally being distributed over the subtraction.

Secondly, Having checked whether several operations distribute over each other, I asked my pupils to generalise which operations distribute over others. In this section, Colombe introduced a metaphor which helped her peers to remember the general rule: Multiplication and Division are the government: they distribute (resources) to the citizens, Addition and Subtraction but not to themselves. This also ties in very nicely with Order of Operations.

I also used a three-act-math approach in these lessons, introducing the topic with a classic moment from countdown (if you’re a maths teacher, you must have seen this!)

This was my hook: how on earth did he do this? Did you notice that he didn’t actually know the intermediate numbers? This gained interest, and later on in the lessons I tried to set some questions in which pupils applied the distributive property to simplify some expressions, leading up to (318 x 75 – 50) / 25, but it didn’t go well. If I had used the strategy that John Mason suggested on Craig Barton’s podcast, of imagining what I was going to say and how the lesson would proceed, I feel like I may have anticipated this. It wasn’t clear that the equivalent of 318 x 3 – 2 was the ‘final answer’ in the simplification problems I had created. In my updated lesson plan, I have removed these questions, leaving just the explanation of the countdown genius as a teacher-led section of the lesson.

Another issue that came up as part of these lessons was a good question from my pupils: If it doesn’t distribute, what does happen? My answer at the time was fluffy… something like “it depends on the situation, usually you just apply the operation to one of the numbers”. I feel like I need to work on this, perhaps I need to add another sequence of lessons to my combining operations thread.

Overall though, I feel that this is the first time I’ve been even vaguely successful when teaching the distributive property, mostly because I managed to distill it, with the help of a pupil’s metaphor, to this:

One final reason why I think it went better than in the past: I was more committed. Previously, I would always question the value of teaching such lessons, because I suspected that the pupil’s future teachers wouldn’t make reference to the distributive property. Now I know that I will be teaching these pupils for several years and as HoD, I can better integrate this topic into our scheme of work, it is worth the investment.

How a Mathematician Solves a Problem

One of my colleagues at a previous school emailed round this problem and it caught my attention. Possibly just the bright colours, but it has a simple beauty to it, reminding me of the sort of problems that Ed Southall often shares.

I got stuck into it straight away, first putting together the triangles in a rather naive way that wasn’t any use at all. Realising that I wasn’t getting anywhere, I changed tack and went for the ‘brute force’ approach of applying trigonometry to get the answer.

Key point: if one approach isn’t working, don’t get stuck in a rut. Ask yourself what other mathematical concepts you know that may be related to the problem, and try those instead.

Getting an answer of 180 degrees suggested to me that there would be a neater approach., probably involving putting all three of these triangles into one large triangle. I started trying to do so.

Key point: Get as many ideas on paper as possible, don’t give up if your first couple of attempts don’t work out.

This is a bit of a mess, but in retrospect it’s my favourite page. Trying out a load of options quickly can give you a feel for what might work. I eventually got the idea that two of the angles needed to be on the ‘base’ of the triangle, and it was then a matter of varying the two angles and the distance between them until the third angle appeared at the top.

Key Point: Sometimes drawing a geometry problem more neatly will help you more than you might expect.

Then I decided to start trying to draw this out a bit more neatly; this helped me notice that I could create a key isosceles triangle.

Finally, of course you should write your work up neatly in order to present it to your readers (in my case, a triumphal email to my colleague!)

Key point: Rough working is great, but make sure you write up your solutions neatly at the end. Of course, your teacher will be even happier if they can see your rough thought process too.

I looked at my work at the end of the process.
a) I felt that sense of satisfaction that reminded me why I like maths.
b) I thought it would make a good lesson for my pupils.

In summary, here are generalised versions of my strategies:

  • If one approach isn’t working, don’t get stuck in a rut. Ask yourself what other mathematical concepts you know that may be related to the problem, and try those instead.
  • When you’re confident you’re going in the right direction, get as many ideas on paper as possible, don’t give up quickly.
  • Sometimes drawing a geometry problem more neatly will help you more than you might expect.

I know that the idea of general problem-solving skills (even within the domain of maths) is controversial. Of course, I wouldn’t have been able to solve this problem if I didn’t have a secure understanding of properties of triangles (obviously), proportional reasoning (to scale up and down the triangles) and trigonometry (to give me faith that it was worth continuing!)

However, I do feel that some of the general strategies suggested in  Thinking Mathematically have improved my ability to solve this kind of problem. It was interesting to listen to Dylan William’s thoughts on this topic: Craig Barton suggested that he was moving away from the idea that general problem-solving skills are useful and Dylan was less convinced that he learned general skills from George Polya’s classic book. He did admit, however, that ‘trying a simpler case’ (in the terms of Thinking Mathematically: ‘specialising’) is a pretty useful general principle. This, alongside writing down what you know and want and drawing a bigger, clearer diagram, are the main general strategies which I’ve seen maths students use effectively.

Personally, I’m fairly confident that I wouldn’t have been so effective at solving this problem 10 years ago, when I’d just graduated with a first class maths degree. If nothing else, teaching makes you a better mathematician.

Want to teach your pupils general problem-solving skills? Take a look at my resources here: http://lukepearce.eu/problem-solving/

#mathsresourcechat

I love collaboration, which is why I am very happy to have discovered the educational twitter community. I enjoy the general ideas and big-picture teaching discussions that take place, but I particularly love the nitty gritty: discussions of the practical side of teaching.

I find that I get the most ideas that I can apply straight into my lessons when people share resources and others makes suggestions for improvement.

I’ve done it a few times myself recently, and had really useful feedback from other twitter users. A few other people are doing it, but I’d love it if it was even more common. I find some such posts on #mathschat and #mathscpdchat, but there is also a lot of more general patter.

So to focus in on the detail, I’m going to start using #mathsresourcechat and encouraging others to do the same.

As the examples show, posting a picture of the resources makes it particularly easy for others to see and comment.

Go forth and start resource discussions!

Leaving Highgate

I spent my first seven years in teaching as part of an amazing department at Highgate School. For most of that time, my HoD was Dan Abramson and Robert Wilne (past Head of Secondary at NCTM) was Assistant Head. Robert had revolutionised the department a few years earlier with some radical changes: he introduced a scheme of work with great ideas, loads of links between topics and very specific approaches to teaching. Dan continued this tradition, bringing in many ideas from AfL and relentless energy. In the words of one of my colleagues Peter Davison, Dan could be prime minister if he wanted to.

When you teach maths at Highgate, you feel like part of something special. The whole team, now over 20 teachers, is strongly encouraged to use the same approach to teaching. I remember that Craig Barton sounded pretty shocked when Greg Ashman described a very similar style of department; I suspect that it’s pretty rare and perhaps not for everyone.

The advantages: It makes for an incredibly coherent experience for the students. When you take on a new class, you know what models and vocabulary they’ve seen before and how they’ve been taught to think about every topic. You can be sure that the highest attaining will not have been pushed through more material than the scheme dictates and you can reliably call upon the standard models to help lower-attainers.

Outside of the classroom, the number of conversations about approaches to teaching was probably 20 times what I got at the (academically very similar) school in which I subsequently taught. I think that this is a great advantage of shared teaching methodology: if you wanted to change how you taught, you had to convince the rest of the department that your ideas should go in the scheme. Many teachers stayed in the office to work until 6 or 7pm; it helped that many were young and family-free but I like to think that it was partly because the sharing of ideas made it an inspirational place to work.

If I loved it so much then why did I leave? Mostly because my wife and I wanted to buy a house, which is not easy to achieve for a teacher in London.

What followed was two fairly depressing years. My new colleagues were passionate, highly knowledgeable, experienced, and interested in the success of their students. But there was no scheme of work beyond the chapter list from the textbooks and discussions about how to teach maths were few and far between.

Then I discovered Twitter.

I remember very distinctively one mid-winter run, I was listening to Jo Morgan on Craig Barton’s podcast, talking about how she found twitter and all the great ideas out there. I’d just been through a similar process and it made me feel quite emotional to be part of a community again: I think I almost cried.

Despite my improved mood, I still childishly felt a bit sorry for the people on twitter because I suspected that the reason they were online was because they lacked departments like Highgate. Over time, I’ve come round the view that twitter actually has some advantages over Highgate: I can draw from a much wider range of experiences and ideas, and it has exposed me to many more ideas from the world of educational research. There are negatives too: there are still times on Twitter when I ask for ideas or opinions and don’t get any. In the Highgate maths office it was harder for people to ignore me!

I can’t actually remember if I discovered edu-twitter or Craig’s podcast first, but if I hadn’t found either of these, then I think it’s quite possible that I would have left teaching. Two years later and I’ve just started a job in which I’m the only maths teacher in the school. That doesn’t phase me because I’m safe in the knowledge that I have my online community of teachers.

Three Weeks In

I started teaching at a new school 3 weeks ago. Overall, I’m absolutely loving it. My job is more varied than anything I’ve done before and for the first time in my life, I actually look forward to going into work on a Monday.

I’ve been writing the timetable. It has been really interesting to learn how our part time staff prefer to work and try to balance this with providing a balanced week of lessons, alongside management discussions about what proportions staff should work. I’m also excited to lead outdoor education: my climbers seem to be really enjoying our weekly indoor club and I can’t wait to get them out into the mountains proper. It has been great to be involved in discussions about the curriculum: how many periods per week should we give to each subject is not a question I’ve ever considered before.

More mixed has been my work as assessment lead. Inspired by Tom Sherrington, I’ve started with the theme of feedback as actions, sharing some of my own attempts to put this into practice, but I have yet to garner much response from my colleagues. Similarly, initiating the process of collecting pupil data is taking some time.

Despite the fact that I have very few lessons and much more experience in this area, probably the hardest part of my job has been teaching maths! Small class sizes mean that it’s been possible to personalise my teaching more than ever before, and I’m enjoying the opportunity to implement some of the ideas I’ve read about during my nine month break. However, a few issues are challenging me.

1. I’ve never taught mixed-attainment classes before and I’m struggling to find a lot of concrete advice on how to best deal with it.. Do I split the class by task or try to keep them all together? Let the children choose their own tasks or assign them myself? Do I provide extra explicit instruction to some? Should this be within, or in addition to lessons?

This flow chart from @mathsmrgordon has provided some inspiration.

2 . How much to use technology? All my pupils now have a Macbook and iPad. This gives great opportunities, I’ve got them using Desmos, Geogebra and Quizlet, but am I going too far? It’s hard to tell when it’s genuinely educational and when it’s just more fun than pen-on-paper maths. And on that note…

3. I’m following in the footsteps of a teacher who sounds like he was much more fun than me! I’ve heard that he was a great teacher, very inspirational and played lots of games. My insistence on copying down worked examples and setting of written practice and extension tasks sounds pretty boring in comparison. To their credit, the pupils have generally been working very well, but I get a sense that we haven’t fully bonded yet.

Any advice? I’d love to hear it.

Bansho

I read earlier this year that Japanese teachers spend years perfecting their “Bansho.”  This refers to a specific practice of recording the thought process of the whole class solving problems together.  I just like the idea of a special word for “boardwork” as mine has historically been pretty awful so I’ve decided to improve it.

My one major change: Make notes during lessons on Microsoft Word rather than a traditional whiteboard or equivalent software. I took this idea from a Spanish course I took at Oxford University, where my teacher always made notes on word. I think it has revolutionised my bansho!

Here is a case study on the topic of solving problems by forming quadratic equations, both lessons taught to year 10 classes aiming for A*-A grades.

This is what my boardwork looked like previously:

I’m actually pretty embarrassed about sharing this in public! In fact, this is probably the neatest my handwriting gets. At least I’ve kept my equals in line, and the algebra is fairly legible, but as notes to look back on, I’m dubious about its use to my students.

This is what my boardwork looks like now:

Thanks to equation editor shortcuts, I have learned to type maths pretty much as quickly as I can write it on a board.  You’ll also notice that I can still add hand written steps in, which I usually do by copying and pasting from word to my board software, then back again: slightly clunky, but I can do it fast enough that the students don’t complain!

Of course, part of the difference between the two sets of boardwork is the detail I’ve included has increased in the second example. Typing my notes has encouraged me to write more explanations as well as just the algebra or geometry involved (although some people may think I’ve included too much commentary?). This is probably because I don’t enjoy hand-writing on the board and so I try to avoid it.

What do my students say? They almost universally prefer the new approach. Do you have terrible handwriting? Why not give mathtype a try.