So it transpires that year 10 students do actually know how to tidy up a classroom (aka a word in the ear of Teach First subject mentors)

Being on the second year of the Teach First programme has been a revelation to me…about quite how insane last year was. This year is hellish hard work still, but my stress levels are around a tenth of what they were last year.

Something happened this week which caused me to reflect on the contrast between this year and last year. It was Thursday and I’d been rounding off a sequence of lessons on the area and circumference of circles with a task of designing Bilbo Baggins a new house (everything had to be round). It was a messy lesson – coloured card, scissors, compasses, pencils, calculators, glue, felt tips etc. everywhere. I’d lost track of time, and (as will be familiar to you all I’m sure) realised with three minutes of the lesson to go that the classroom needed to be tidied, I needed to get together the resources for my Year 12 class happening immediately afterwards across the school, had homework to give out and had five reports to sign. Eek.

So I got the class quiet, gave out (rather loose) instructions to tidy up, put everything back in the right drawer and pick up a copy of the homework. Then I busied myself signing reports, disconnecting my laptop and prepping for my next class.

2 1/2 minutes later I looked up to see an almost spotless classroom with Adelle (bless her!) just emerging from my cupboard having put away the felt tips for me. Mason had taken it upon himself to hand out homework, and students were just tucking their chairs in. Bliss.

My point here isn’t to put across how wonderful my year 10 class are (although they are pretty awesome). It’s the contrast with last year that is so instructive. I am not doing anything fundamentally different at the end of class from what I did last year. I am no more organised (in fact I’m less ‘on it’ than I was at this time last year). And yet things just work this year, whether that is getting students to tidy the classroom quickly, keeping students ‘on task’ in a lesson, or getting students to attend detentions.

So this post is really a word in the ear of Teach First subject mentors. Don’t judge your mentee too harshly if their classroom is a tip at the end of a lesson, you look through the classroom window and see students off task, or the pace of their lesson drops because they are demanding (and not getting) the attention of every student. Your mentee might be doing everything right, and might be working far harder than anyone else in the department, and yet because of their inexperience and the reaction of the kids, the impact of their efforts will be different to anyone else’s in the department. Part of this is down to the authority they portray in front of the students, but part of it is also down to the kids and their reactions to new teachers. Rest assured your mentee is probably killing themselves trying to get it right, and will reap the rewards (as will the rest of the department) next year. Please help them get that far.

Fun with infinity

I’m lucky enough to teach two top set year 8 classes (year 7 last year) who are at least semi-geeky about their maths. Last summer I did a lesson with them on the nature and craziness of infinity, with the able assistance of the amazing Vi Hart (or at least her Youtube vids), and Jordan Ellenberg’s book: How Not to Be Wrong. They loved it, so I’ve reproduced some of the resources below.

Vi Hart videos:

The infinite series paradox (1):

What is the sum of: 1 + 2 + 4 + 8 + 16 + …?

To answer this, first multiply the sum by 2: 2(1 + 2 + 4 + 8 + 16 + …) = 2 + 4 + 8 + 16 + …

Now: 2(1 + 2 + 4 + 8 + 16 + …) – 1(1 + 2 + 4 + 8 + 16 + …) = 2 + 4 + 8 + 16 + … – 1 – 2 – 4 – 8 – 16 – … = -1

But the LHS simplifies to: 1 + 2 + 4 + 8 + 16 + … = -1

Thus we seem to have proved that the infinite sum of ever-increasing terms is -1. Huh.

The infinite series paradox (2):

What is the value of the infinite sum 1 – 1 + 1 – 1 + 1 – 1 + …?

Answer 1: (1 – 1) + (1 – 1) + (1 – 1) + … = 0 + 0 + 0 + … = 0

So far so good. But hang on…

Answer 2: 1 – (1 – 1) – (1 – 1) – (1 – 1) … = 1 – 0 – 0 – 0 … = 1. Huh.

Answer 3: Suppose T is the value of our mystery sum: T = 1 – 1 + 1 – 1 + 1 – 1 + …

Take the negative of both sides: – T = – 1 + 1 – 1 + 1 …

But this is just what you’d get if you take 1 away from T i.e. T – 1.

So T – 1 = -T, which is only satisfied when T = 1/2. Eek.

I find answer 3 both most counterintuitive and most satisfying. Brilliantly, some of my year 7s came up with this solution themselves.


Relevance to the classroom:

This stuff isn’t going to be on any curriculum, and one observer in my classroom was heard afterwards to mutter ‘he just let them doodle!’ But for some of our most gifted mathematicians, we have to squeeze in real maths around the staid content of the GCSE curriculum – it might just inspire them to carry on with the subject to A-level and beyond. Plus everyone loves to have their brains messed with.

Abraham Wald and the bullet holes

So I’m constantly on the hunt for ways to relate maths to real-life, and to find hooks for topics. Over the summer I read Jordan Ellenberg’s book ‘How Not to Be Wrong’ and the following story is lifted straight from that book. It’s a great intro to a probability topic.

The premise
You’re in the air force during World War 2. Your job is to stop your planes getting shot down by enemy fighters, by armouring them. But armour makes a plane heavier, less manoeuvrable and uses more fuel. So you have to compromise between weight and protection from bullets.

The data
You are presented with the table below, which gives average bullet holes on planes returning from missions:

Section of plane Bullet holes per square metre
Engine 1.11
Fuselage 1.73
Fuel system 1.55
Rest of the plane 1.8

The question:

Where is the best place to put extra armour?

Continue reading

To all new Teach Firsters

Welcome to the hardest (but quite possibly the best) year of your life.

There is no getting around it – from the start of your Summer Institute until about now next year is going to be hard. Harder than you can imagine. People will tell you this but it won’t hit home until you’re in the middle of it.

A few thoughts from someone who is just coming to the end of their first year on the programme (in no particular order):

1. Keep going. Unless you are very, very unusual, there WILL come a time where you want to quit. I don’t just mean ‘I can’t really be bothered with the workload any more’, I mean ‘I cannot physically, mentally, emotionally continue’. If this point comes (it did for me in January), draw on all the support available to you, cut back on everything, and take a few weeks respite by dropping everything except planning and teaching. But whatever you do, don’t quit. Because it does get better. Everyone will tell you this too, and you won’t be able to believe them. But it does. I now absolutely love my job – only four months ago I was in pieces.

2. Don’t try to do everything at once. Remember that you are about the least experienced teacher that will ever be responsible for delivering curriculum content. You need to remember that, even if those around you, those giving you feedback, those asking you to improve, forget how inexperienced you are. Focus on doing a few things well: get behaviour right, plan well, get to know the kids. Everything else (differentiation, AfL, marking, teaching creatively) can come later. Get the basics right first.

3. Get used to failing. By dint of getting onto the Teach First programme, you’re a high achiever, probably an over-achiever. You won’t be used to failing. In teaching you fail every single day. Get used to it – don’t let it get to you. Because you will also succeed every single day. It’s a bit overwhelming to deal with all this failure, and all this success. Keep both in proportion if you can.

4. Be a beginning teacher, not a Teach Firster. Over the Summer Institute, Teach First will attempt (repeatedly) to tell you that you are an ‘outstanding graduate’ destined to change the world. Perhaps you are. But from the first day you walk into school, you’re: a drag on the rest of your department; a huge risk to the school; and probably serving your kids poorly, at least at first. Don’t believe the Teach First hype – instead be as humble as you can be with other staff, build relationships, and persuade your department and school that you are an asset not a liability.

5. Be positive. Every day there will be magic moments, although you might not always see or remember them. Whenever you do, celebrate them, talk about them, write them down, remind yourself of them. Positivity is contagious (as is negativity) – the more positive you can be in front of the students and fellow staff, the more you will get into a virtuous circle.

6. Even if you’re doing everything right, it takes time. You will want to be good quickly. Unless you’re a spectacular human being, you will not be good quickly. One reason is that the kids will take a while to accept you as their teacher. You can address every feedback point, practice every outstanding teaching technique, mark every book every lesson. It won’t work. At least, it won’t work in the way it works for more established teachers. This is because of the way the kids will react to you. Don’t mistake a poor reaction from the kids with you failing. If you’re doing the right things they are working. It might take time for this to become evident, but every day you do the right things with the kids brings you closer to the day when they treat you as an established, competent teacher. Then everything gets easier!


Lastly, there will come a time during the year when everything starts to come good. The harder you’ve worked up to this point, the more challenging it has been, the closer you’ve come to quitting, the better it will feel when it comes good. Enjoy it when it comes, because by heck you’ll deserve it!

New teaching idea: exit tickets

Twitter is awesome isn’t it. As a new teacher, I’m learning a massive amount from exchanges of tweets. For example:


This exchange convinced me to use exit tickets every class, which is my new teaching idea for this fortnight. I’ve chosen it partly based on another twitter conversation, this time with @matt___Thompson who suggested that the new teaching ideas should come from Doug Lemov’s Teach Like a Champion. Sounds good to me!

So, get involved! Try an exit ticket or three. Or, if you’re like Joe or Kris, try them for every class. I’m planning that for the next two weeks. Tweet their impact to @weeklymaths using the hashtag #nti. Then come back here and let us know what impact it has made on student progression by commenting on this post.

And, if you want to read comments on the impact of breaking everything down for students, which was new teaching idea no. 1, take a look at the post here. Please do add your comments too!

Calling all new teachers – let’s join forces on twitter

Two weeks in…teaching is both more thrilling and more challenging than I could possibly have imagined. I’ve never tried to hold so many (competing) ideas in my head at once whilst reacting to curve balls, from all directions, at all times. What a job, in the best and worst sense!

There are so many areas I want to make progress in the classroom, and so many ideas that I want to try, but have no real idea whether they’ll work or not. And, with a previous career as a researcher, the idea of having a sample size of 1 (i.e. me) when testing whether a particular idea helps my students to progress is, well, bonkers.

So…a proposition for any new teachers (as well as existing ones who want to get involved):

Let’s try one new teaching idea each fortnight, and tweet about its impact on student progression.

I’ll collect together any tweets sent to @weeklymaths with the hashtag #nti (it stands for newbie’s teaching ideas) and publish them on this blog every fortnight, along with another new idea to try. New ideas to try can come from anywhere – feel free to tweet these too and I’ll try to incorporate them.

To kick us off, the idea I want to work on over the next fortnight is to:

Break down and scaffold EVERYTHING for students.

More experienced colleagues tell me that one of the biggest challenges as a new teacher is not to assume that learners are familiar with some of the conceptual leaps that you will make in your subject without thinking about them. For example, I was teaching about rounding in maths, and made the silly assumption that learners would somehow instinctively know which number was the most significant.

Over the next fortnight I’m going to focus on this idea by:

– Forcing myself to break down new areas of maths into scaffolded, step-by-step models. Deliver these interactively in class, give students time to practice and then try to gradually take the scaffolding away by encouraging students to generalise their learning and apply it in new settings through practice.

– Get feedback from my students as to whether this scaffolded approach has worked, and whether they have noticed any difference in my teaching and their learning as a result.

There are loads of other ways in which we as teachers could break things down for our students. What works for you? Try it and let us know by tweeting before the end of Saturday 28th September.


So in summary:

1. Alongside the maelstrom of information, let’s work together to try out, and assess the effectiveness of, one new teaching idea every fortnight.

2. Look out for a blog post and tweet like this one on alternate Sundays, to introduce the new idea.

3. Try the new idea out for a fortnight, reflect on its impact on student progression.

4. Tweet your thoughts to @weeklymaths with the hashtag #nti

5. Come back to this blog on alternate Sundays to read what other people have found, and to see what the next teaching idea is

6. If you have an idea we should try (or a way to make this collaborative process more effective), tweet it to @weeklymaths with the hashtag #nti and I’ll incorporate it.


Why do this?

You’re busy. Why add this to your list of things to do?

Because its through collaborating on new ideas that we can progress towards becoming excellent teachers ourselves. We’re in the same boat, more or less. We are facing the same issues, more or less. I see this process as a little bit like being able to observe all of your classes across the country, and have you all observe mine. Learning from each other in this way is hugely powerful.

And, lastly, because at the end of the day when you’re struggling to see a way forward with a particular challenge, its lovely to know that there are others out there trying to do the same, getting knocked down in the same way, picking ourselves back up and dusting ourselves off in the same way and having another go. And celebrating together when something starts to work.

So good luck for the next two weeks, and please get involved!

The day where I thought I’d gone to hell

By and large the Teach First Summer Institute was excellent, especially the bit in Bristol. It was the first year it had been run there, but was up there with the best training I’ve had across a range of jobs and settings.

All the same, there was the odd off-day.  This post is about one of those rare days and, specifically, about remembering that day when I’m in school teaching.

I’m not going to say which day it was, although any single member of the Teach First South West cohort could tell you. But the day involved us spending 7 hours sitting in one darkened classroom, listening first to a poorly researched, heavily biased two-hour diatribe and then to a half-baked pedagogical approach with no relevance for us as beginning teachers, on a blisteringly hot day, hardly moving from our seats except for a paltry 25 minute lunch break and a poorly conceived venture into the local park to deepen our knowledge of the half-baked pedagogical approach that was the pet project of one of our lecturers.

Unsurprisingly, the day brought out the worst in us as learners. We were disengaged, childish and finding any excuse to cause trouble. The highlight of the day was when several of our colleagues got stuck in a lift for an hour.

The point for me to remember is that days at school will probably feel like this for students, especially those who have been in a lunchtime detention. Whilst not excusing disengagement and poor behaviour, if 38 very committed trainee teachers had (temporarily) given up on life, what can we expect of teenagers whose reason for being at school isn’t necessarily clear to them at the best of times?

Action points for me then are:

  • Always try to consider a lesson from a students’ point of view. How engaging is it? Are they actually doing anything? What about the student in the corner who hasn’t spoken all lesson. Have they spoken all day?
  • When I get students at the end of a long, hot day, consider things from their perspective. Don’t excuse disengagement, but try to surprise them with a lesson they’ll enjoy, rather than being the latest in a long line of tormentors.