About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.

10. What do I do with their exercise books?

Use them as a record of their achievement

Your school may have a strict policy about exercise books, or it may have no policy at all.  Either way, here’s one approach you can take towards them, and its associated benefits.

Philosophically, treat the book not as a jotter, or a space for working, but as a record of their progress and achievement over time.  The work they do isn’t for their own benefit, or to improve their learning, it’s a presentation for an audience.  Of course, it *will* have the effect of improving their learning, but we just don’t put the emphasis there.  These books need to be presentable, in part so you can read them, but also for Ofsted, and for parents to look over.

Create an audience – the bigger the audience, the more care they’ll take.  Make it clear that you’ll be reading these books regularly, as will the head of department, other teachers, the head teacher, Ofsted, their parents, school governors, etc.  It may or may not be true… but give them the feeling they’re writing and working hard for some kind of recognition, and then make sure that you, at least, are checking their work every few lessons.

What they write in the books and what you do with them once you take them in varies now from subject to subject, but provided you regularly show them you’re looking at their books, and get them to write as though they’re doing it for an audience, you’re likely to reap the following benefits:

  • Increased effort during lessons, and an ability to track those who are being lazy
  • Improved writing and presentation skills
  • Less graffiti in books, potentially eradicating it completely over time
  • Improved learner understanding

For maths teachers I’ll add the following brief suggestion for what they can write in their books in 80-90% of lessons:

  • Today’s date in full (e.g. Sunday 8th July)
  • A title or learning objective (not because that will help them learn anything, but because it helps to structure the book when you or others look through it)
  • A new mathematical fact or formula you’ve given them (if applicable)
  • 2-3 model examples copied from the board, which they can refer to when they’re not sure how to answer the problems you set.  These should demonstrate *exactly* how you would like them to set out their working
  • The questions you ask them to attempt, with full complete working – they should write the problem as well, if it’s short enough.  If it’s long, don’t waste their time with copying it.

One caveat:

Some kids can get so fussy about their books being ‘perfect’ that they stop doing any work at all for fear of making mistakes.  You need to make it clear to them that the books almost *have * to have mistakes in them, to demonstrate their progress, and that a ‘perfect’ book would be expected to have mistakes, with their corrections nearby, showing how they learnt and progressed.

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5. What’s the secret to assessing pupil progress every lesson?

 

Use exit tickets to get a snapshot of what every student took away from your lesson

This is the single most powerful thing I’ve done all year, from lesson one, maintaining it consistently, and it’s impressed external observers and internal mentors alike.

The exit ticket provides a snapshot of whole class understanding for each and every lesson, in under two minutes.  For effort to impact ratio, they’re a no brainer.  I can’t even imagine planning the next lesson without them.

How do I set it up?

5-10 minutes before the end of a lesson, throw up a single question on the board (sometimes you might want two, but be careful about going over this – really ups the workload!)  They write their name and answer on the ticket.  As they leave, they hand it to you.  This does two things:

  1. They have to leave via you, establishing you as an authority in the room
  2. Gives you a powerful tool for planning/tweaking the next lesson

What do I do with my fistful of tickets?

It’s up to you, experiment.  Here a few possibilities:

Light touch – Flick through quickly and organise them into piles:

  1. 100% correct
  2. Didn’t have a clue
  3. Different piles for the same mistake

It’s an immediate picture of their understanding.  I might modify and redeliver an entire lesson if the results are bad.  Now throw them away.

More time, more impact – After arranging the tickets into piles, mark them; tick everything that’s correct (for motivation), circle errors and comment if you can, maybe even providing a model solution.  Next lesson hand them out and discuss the misconceptions on the board.  This has the (significant) advantage of making sure they know you value their effort, and you’re doing something with all those tickets.  Now they can throw them away themselves.

Maximal effort, good for Ofsted – At the end of the lesson, they write the question in their books. Sort the tickets into piles again, mark them and hand them out in the next lesson, but this time they glue the tickets into their books, maintaining a record of their end of lesson understanding.

They can be used to assess student’s feelings as well – how confident they understood the lesson, how well they feel they met a behaviour objective etc.  This is a good way of showing you value student voice.

4. Entering my classroom, what do students do now?

Set up a crystal clear routine and step-by-step instructions on the board that tell them unmistakably: ‘This is what you do now.’

The eager arrive before lunch has finished; the cool saunter in with ridiculous swagger; the obnoxious drag their feet all the way to your door; the complacent roll in late.

Your classroom will fill in dribs and drabs; you need to get them settled and ready to learn as quickly as possible.

At its heart, the Do Now is simply what they should do, now they are in the room.  Think of the Do Now as a settler, and then have another starter designed as a hook to your lesson.

I’ve experimented with many variants over the year.  Here are a few of them:

Simple Questions

  • Simple maths questions based on the last lesson’s learning
  • Simple maths questions that will lead into today’s learning

Bigger Questions

  • ‘If this is the answer, what is the question’ – can be as simple as a big 42 on the board
  • ‘Where have you seen maths in real life’ – e.g. percentages
  • Draw a triangle on the board – what questions might I ask about this triangle?
  • What would the world be like without numbers?

They’ll all have different effects, and you’ll have to experiment with your own groups to see how they respond.  I can’t tell you what will settle your classes best, but I can tell you this: having had to repeatedly circulate a room frantically, persuading all but the hardest working to open their books and start answering questions, the first time I saw a whole group (of Year 10s) walk in and just get on with it was when I wrote three, crystal clear instructions on the board, started an 8 minute countdown timer, welcomed most at the door, then calmly kicked back in my chair, taking care of some admin:

  1. Rule off after yesterday’s work
  2. Write today’s date
  3. Attempt these questions in your book

3. What are the best teaching resources for maths?

Make heavy use of the pre-prepared questions and solutions from the Mathematics Enhancement Programme, to quickly prep lessons

“Don’t try to reinvent the wheel!”

“Look on TES!”

Two oft spoken quotes that aren’t very helpful.  There are limitless maths resources out there, some terrible, some will change your life.

As a maths teacher much of your lessons must necessarily revolve around setting the students questions to practice, and then telling them the answers.  Okay, there are many variants on this model, but practice certainly sits at the core of strong learning.

Creating all your own problems, and solving them, and differentiating them, enough to keep 30 students engaged for 30-40 minutes of practice per lesson, is mentally exhausting.  Don’t try to reinvent the wheel; many people have already produced exactly what you need.  But… where is this wheel, what does it look like?  TES is huge, and mostly filled with what you don’t need.

I want to show you the wheel.

Voila, the Wheel:

One resource, which will potentially change your life.

The Mathematics Enhancement Programme (MEP), produced by the Centre for Innovation in Mathematics (CIMT) back in 1995.

You’ll probably hear a lot of talk about the Standards Units during the SI.  They really are great resources, and they’ll get you thinking about maths in new ways, but they have two major caveats that may not be mentioned:

  1. They are far from exhaustive – They are about deepening understanding of core mathematical ideas, not covering curriculum content (which is your first and foremost responsibility)
  2. They are utterly inaccessible to pupils who haven’t first been taught the basics in a more traditional manner

So how do you teach those basic concepts?  Enter, the MEP!

The MEP is an exhaustive repository of the best traditional teaching resources I have seen.  There is far more content than can be delivered, so I recommend focussing on the ‘Pupil Practice Book’ for each module.

Exceptionally well structured sequences of work, that will help *you* as a new teacher understand how students can set out their working.  Each sub-topic in the practice book includes the facts and processes they need to understand, followed by 2-4 worked examples, followed by well-structured rote practice questions, followed by more interesting worded questions, followed ultimately by more complex relational questions.

If that weren’t enough, look at the other resources for each module to find mental tests you can use as starters, what they call ‘Activities’, which are often investigative resources for deepening understanding, extra practice questions if needed, and diagnostic tests to assess their progress.  There’s even a ‘Teacher Notes’ resource for each module, that usually gives some information on the history of the mathematics, and a little real world context, or some well written maths-lovin’ paragraphs that you can throw up on the board to help inspire your students.

Find them at one of these two links (use whichever you find easier to navigate):

http://www.tes.co.uk/article.aspx?storyCode=6075946

http://www.cimt.plymouth.ac.uk/projects/mep/default.htm

2. How do I plan maths lessons and not look like this?

Quickly get to grips with all the problem types in the maths curriculum

You can teach:

  1. A fact
  2. A process
  3. A specific problem solution

You can guide them towards deep understanding, but that’s another ball game.

Examples

  1. Facts:
    1. Angles in a triangle sum to 180
    2. Angles in a quadrilateral sum to 360
    3. Angles on a straight line sum to 180
  2. Processes:
    1. Find missing angles in polygons by summing the angles you know, and subtracting the total from the angle sum of the shape
    2. Find the angle sum of any polygon by subtracting 2 from its number of sides, and then multiplying by 180
  3. Problems: Take a look at the example problems below:
1)  2) 
3)
4)
5) 

The facts and processes involved in finding the missing angles are pretty much the same each time, but the problems and their solutions become increasingly complex.  Pupils understand ‘maths’ in terms of what questions they’re being asked to solve.  Focus on one problem and show them how to solve it.  Try a few examples together, then let them practice.

Introducing a slightly more complex problem can be a good way of challenging brighter students, but don’t be shocked (…you will be) when you find often even the most able can’t go from problem 2 to problem 3 without support; the fact that it looks different is enough to shut down most minds.

Building those kinds of thinking skills in pupils is a long term goal.  In your first term, it’s important they experience success, so they believe they can learn something from you (they *do* want to, even if they say they don’t care).

Before you start, you need to very quickly get your head around the curriculum in terms of facts, processes and problem types that pupils need to know.

For most facts and processes, levelled/graded, see these maps and curriculum overview  (there are still a few omissions and minor errors in the layout; they’re a work in progress):

For problem types… that’s a tougher one.  Look at as many GCSE past papers as you can get your hands on, ask colleagues, see what the MEP (Mathematics Enhancement Programme – post with more detail here) has, Peter Bland has an exceptional catalogue of (higher) past papers and focus booklets here.

In summary

To plan a simple, bread and butter lesson in 20-30 minutes:

  1. Decide what problems you want to teach and copy paste some from the MEP resources
  2. Create some example problems where you can model exactly how you want them to set working out in their books
  3. A better lesson will have something upfront that asks the question ‘why’ this maths might be needed, and helps explain

1. How do I manage behaviour?

What are you afraid of?

Get a system for easily recording warnings, visible to all students.

Imagine it’s your second week, day one, period 4.  You’ve just had a horrendous Period 2 lesson with Year 10, and now it’s time for Year 11.  One lad refuses to enter the classroom, before later barrelling in with another boy draped over his shoulders.  They run around, completely ignoring you… before heading off out the classroom again!  You chase after them to recover the pupil supposed to be in your room, only to find yourself confronting a tall student who looks like he’s getting ready to hit you, prevented only by another teacher intervening.  By the time you get back to your room, another male pupil who, up til now has spent your lessons sleeping, has suddenly awoken, taken your chair and proceeded to wheel himself around the classroom!  You ignore it for a time… because you’ve no idea what to do.  Eventually you pluck up the courage and tell him to get off the chair.  Ah yes, he’s ignoring you.  Then he’s telling you he won’t get off the chair.  You put your foot on the base to prevent him wheeling any further, and his response is to sulkily get off and inform you that you’re gay.  With that, you send him out the room, and lo, he actually goes (maybe you can get them to do what you say after all…).  You take him a textbook to work from, and by the time you get back the whole class are giggling because one of the girls (you suspect… but can’t prove) has written ‘faget’ [sic] up on the board.  You rub it off, and try to continue with the lesson.

Day two, what do you do?

1)      Get people to help out.

They think they can do what they like, because they can.  They think they can bully you because you’re soft, and you’re alone, and there’s 30 of them.  The second they start to realise you’re talking to their tutors, their heads of year, their pastoral assistants, their head of maths, and the moment they see some of those people standing with you in the classroom, suddenly they realise you’re not soft, and you’re not alone.  You still do most the talking, you don’t hide behind them; they’re just there to remind the kids that you’ve got your gang too.

2)      Get a system to lean on.

I adapted Joe’s behaviour system – all names pre-printed on paper, blue tacked each lesson to the board.  Strikes by the left of their name, ticks by the right; the rewards and sanctions don’t matter, make them up (and then you’ll change them when it doesn’t work).  What matters is when faced a belligerent child kicking their feet up at the back, munching Pringles, with a “What are you gonna do about it?” attitude, is your response going to be a meek nothing, or a shouting match you’ve already lost, or are you going to calmly walk to the board and add a strike by their name, and continue to do so until the Pringles are away, or the student finds themself either placed in detention or removed from your room (or both).  It’s about having some kind of action you can take, any action, without having to go straight to sanctions or losing your cool.