Does DIRT work in maths?

I adore the idea of DIRT. Writing feedback that never gets looked at is absurd, and I love the “ethic of excellence” mentality. I’m struggling a bit with making it work for me right now, though.

This is my standard procedure.

I set and mark an exercise with a selection of problem types from the last 4 lessons.

I hand it back to the students. Their DIRT task is either to retry the question type they got wrong, or try my extension question in green pen.

I now have students doing individualised tasks right at the cusp of their understanding. Great.

Except.. how am I expecting them to successfully answer the questions? There’s been no additional explanation of the work to help them suddenly be able to answer this question that they couldn’t answer yesterday.

I’ve noticed a few students answering in green pen studiously and carefully; the only problem being what they’re writing is mathematically incorrect.

You can argue the comments I write are enough guidance for them, but I’ve found these fall into one of two traps

  • For my top sets, the work is complex and the misconceptions they have are hard to explain without a full paragraph of writing. Even writing a paragraph isn’t ideal. What I really want is to talk to them, read their body language, give them a chance to ask questions before I set them off to have another go.
  • For my lower sets, the average reading age is under 9. Teaching through the medium of writing comments in red pen is the most alienating thing I can do.

Plus the more I have to write, the more time-consuming doing DIRT is for me, and the less likely I am to do it frequently.

No one would argue the best way to teach new content is for kids to sit in silence reading your hastily scribbled comments. This seems even more crucial when you’re giving them work which you know they’re currently getting wrong, or alternately extension work which they’ve never seen before.

So, how to proceed? I’m going to experiment with prefacing DIRT work with a teacher-led explanation of the most common pitfalls, but I’d love to hear any other suggestions.

Critical thinking

This is the front page of a handout I was given at a lecture at the Institute of Education, a world class university for education:


Because of course my “critical thinking” ability in relation to a photograph is easily transferable to the context of being critical of education research and my personal practice.

Or not. (I’m sure I’m preaching to the converted but if you need convincing, see Daisy here or Willingham here or here).

I am later informed that:

You’ll be happy to know that you are already a critical thinker! You engage your critical thinking skills every day. Whenever you make a decision, solve a problem, or prioritize tasks, you are using critical thinking… When you shop for groceries, when you decide which bills you should pay first on a limited budget, when you work out problems and arguments between you and your friends or you and your coworkers, you are being a critical thinker.

The toxic implication of this is that there is no need to teach us any content; we already know how to be critical of any education literature you could care to put in front of us.

How can this stuff still be being doled out unthinkingly by top academics and institutions? Are more chalkface teachers cognisant of cognitive science than academics nowadays?

Someone once told me that at Pimlico Academy, every head of department was given a copy of Why don’t students like school?. Maybe that’s a policy the Director of the IOE should adopt.


This is how to write RJA1 and retain your sanity.

Dearest 2013 cohort,

Well done for still being alive. I’m sure RJA is the last thing you want to think about, so I am going to attempt to give you a bare bones structure which will get you a pretty decent mark and allow you to maximise half term sleep.

I think the title’s changed slightly this year, but this is the rough structure I used last year when it was about behaviour management.


Behaviour’s dead important. A reference or two, like Steer and Charlie Taylor.

I’m going to reflect on my behaviour management because reflection’s dead important. A reference or two, like Hattie.

I’m going to use Kolb. Kolb’s model is the following:

. What’s great about Kolb is X and Y. However, Z is bad. It could be improved in this way. Criticality criticality criticality. And a final sentence saying I’m going to use Kolb anyway (or that I’m going to use it with X amendment because I AM A DEMIGOD who wants top marks).

Looking at my [post-hoc conveniently doctored journal], a consistent theme has been [consistency of sanctions/positive behaviour management/some other theme that comes up in the literature]. This will form the basis of my key reflections in this essay.

Experience 1

A key/recurring/seminal experience has been [my year 9s refusing to be quiet/the low effort put into written work/pupils being rude to one another]. I reflected on this after it happened. Reference to photo of relevant reflection in appendix.

I’m reflecting on this using Kolb. Here’s a picture of Kolb’s cycle I’ve annotated with reference to this experience [they really love the annotated pic of the cycle].

Details about what I thought about this experience, which involve more references to literature and less swearing than my genuine thoughts. Two or three paragraphs about the two/three main insights I gained from this reflection. Each of these paragraphs makes a point about what I’ve learnt; then refers to my own real experience and my journal; then refers to multiple sources of literature; applies literature to my experience; evaluates and critiques with reference to any opposing views or glaring holes in my arguments; and finishes with a sentence that may be more nuanced than the first sentence in my paragraph, but certainly doesn’t contradict.

Rinse and repeat this paragraph for other insights from this experience.

Now a paragraph about how I’ve changed my practice as a result.

Here’s a quick conclusion about how [consistency is important/whatever my theme is]

Experience 2

Here’s another related behaviour issue I’ve been having. I’m going to repeat the above section here.

Experience 3

If you’ve still got some words spare, stick in another one.


In this essay I have cogently argued that the theme I chose was key to the bad behaviour I’ve been experiencing. If only I displayed my sanctions like Charlie Taylor told me to, it would all have been fine.

This is what I’m going to change as a result. Reference to my action plan [definitely do an action plan; easy marks].

Finally I’m going to consider how useful this assignment and model has been for my practice. I’m going to say that whilst it has been SO useful I think it would have been even better if I’d used Brookfield’s model because it considers a wider range of sources of learning such as colleagues [this sets you up nicely for RJA2].


Journal photos, journal photos, journal photos.

An action plan.

What can I learn from trendy maths?

A quick heads up: Throughout this blog I’m going to refer to “trendy maths” and “traditional maths”, for lack of better terms. I’m going to polarise and make some assumptions about both groups’ teaching style along the way. It isn’t meant to be offensive. It’s just me trying to sort out the mess of thoughts in my head.

I’ve been told “cheer up! It might never happen!” more on my commute this past week than I have been in the past 23 years. Clearly I’ve been frowning a lot. This is because I’ve been spending my journeys to and from school thinking long and hard about Dan Meyer and co. I’ve spent an inordinate amount of time reading many of the blogs on Meyer’s blogroll and trying to see what I can learn.

So. Where to begin? I believe there is a problem with many secondary school pupils’ grasp of mathematics. Well, there are multiple problems. But one of the problems does relate to this notion of conceptual understanding, though I don’t like that term because I think it comes with a lot of baggage.


I think what I mean is best illustrated with an example.

Most students know how to find the area of a rectangle in two ways:

1. Count the squares if the rectangle is drawn on a grid for you.

2. If there’s no grid, multiply the two lengths they’ve written on the sides.


This serves them very well for nearly all the questions they will ever encounter on the topic. Bosh. Job done. They know how to find the area of a rectangle.

Do they, though?

Give them an unlabelled rectangle, and what do they do? They sit, staring blankly, asking where the numbers are. 

Give them a question on grid paper that isn’t a centimetre by a centimetre sized, and what do they do? They still count the squares and write the answer with “cm²” after for good measure.

This is not good.

This is the entirely predictable response of teaching to two specific question types that come up on the exam.

I believe students in, say, Fawn’s class are far more likely to get their rulers out when confronted with an unlabelled square. 

This is the entirely predictable response of giving lots of problems that involve students having to ask for or figure out extra information, or rejecting extraneous information.

Another thing I think Fawn’s students would be better at is recognising when an answer to an area calculation is absurd. That’s because students do a lot more work on estimating and thinking about the real life implications of their answers in her class than students in my class do.


I think both those things are great. I definitely want my children to have the ability to select the information required before implementing an algorithm and the ability to check their answers.


Where trendy maths gets it wrong

So far, so good. But what always seems to accompany this exposure to a greater range of problem types, sense-checking and other good stuff, as sure as PJ accompanies Duncan, is a bucket load of rhetoric around discovery learning. Statements like “the less I speak, the better the lesson is” or “I’ve had to make peace with the fact some students will leave my lesson still not really understanding what’s going on”.

I see no reason why explicit instruction cannot be used to develop the skills Meyer espouses.

I think explicit instruction would do it better. 

Where trad maths gets it wrong

I have a few tentative ideas as to why the traditional maths classroom might not be getting it right at the moment:

1. We are not good enough at naming the steps

I think experienced teachers probably don’t make this mistake, but I’m only just starting to realise how many steps I take when I solve a problem. I start with a ball park answer in my head as I’m answering; before I take a certain step I remind myself not to make that common error; I stop partway through problems at strategic points and apply certain tests to see if my answer is plausible; I visualise my final answer and compare to my estimate at the end. I do all this fluently because I’m an expert, which makes it easy to forget to include when I’m naming the steps. But when I leave out those steps, I am failing to teach the procedure fully. It’s not enough to say “check your answer” at the end. We need to be explicit as to how and when. We need to bang on about it.

2. We spend too little time on the basic knowledge

I use the term knowledge carefully. I mean facts and definitions. Too few children have a precise definition of area in their arsenal. Too few know what we mean by a dimension. They deserve a crystal clear idea of this. Otherwise they don’t have a fighting chance of building up the algorithms they know into a body of relational knowledge. To make this a reality, we need to spend time on it! It’s not level 7. It’s not high level Bloom’s. That does not, however, make it lesser – as Daisy Christodoulou explains in Seven Myths.

3. Our curriculum is far too jumpy

In our current year 7 scheme of work, I have one lesson on measures; one lesson on area; one on perimeter; one on surface area; and one of volume. Then, kids, it’s onto fractions! It’s not enough time to practise much of anything to mastery. And in the age of colour coded trackers and performance-related pay it would take a brave teacher to veer away from the few predictable problem types that will be on the half-termly assessment. We can’t spend time thinking carefully about sequencing when it’s just rush, rush, rush.


So after my week of trendy maths soul searching, what am I planning on changing in my practice?

I’ll be explicitly teaching estimation and sense checking. Lots and lots.

I’ll be teaching problem types as normal. Once those are mastered, I’ll introduce problems with too much or too little information for students to tackle so they develop the ability to select information and articulate what information they need for a problem. Hopefully only doing this after they’ve mastered the algorithm itself should avoid cognitive overload.

I’ll be teaching definitions. Talking about them. Making them chant ’em. Quizzing them on them.

What I’ll not be doing is breaking out the sugar paper.

Electric fences

If you’re a new teacher reading this, you fall into one of two camps:

1. You have had a lovely honeymoon period with all your classes and are feeling dead happy about your behaviour management skills.

2. You are sitting there biting your nails because anything between one and all of your classes seems to be descending rapidly into anarchy. Kids argue back. They talk over you. They sneer. They cause drama over the tiniest things. Every bit of work you give them is too easy or too hard and they won’t do it. They’ve got visibly worse since your first lesson with them and you’re terrified the downward spiral will continue.

I suspect the second group is much larger than the first.

If you are in the second group there is one thing I want to say to you.

Every time a student walks out of your door after a lesson without a sanction, you are telling them how they just behaved for the last hour was A-OK.

It seems obvious, but is it genuinely the case that every child who misbehaves is sanctioned in your class right now? It wasn’t for me. There are a myriad of reasons for this. Maybe you let Jack earn his detention off. Maybe you felt unfair giving Jessica a detention when she wasn’t anywhere near as bad as Dane. Maybe you felt like your lesson was so awfully planned and unengaging that you don’t really blame Yusuf for talking.

Just stop.

Don’t agonise over the past and how it’s gone so far. Just stop. Decide that Monday will be different.

What are your boundaries? Decide. Etch them into your skull and heart and classroom wall. Mine are that you do not make a noise – any noise – when the starter slide is on the board. You SLANT when I am on zero.

As predictably as an electric fence gives an electric shock, you give out a sanction for crossing those boundaries. No matter who it is or when it is.

Yes, some angelic students will end up in detention. Yes, sometimes most of the class will be on your detention list. I’m not going to lie: if your first two weeks have gone badly, most of the class WILL be on your detention list for the next couple of lessons. They are testing the electric fence. It hasn’t really been there the last two weeks.

Gabriel will moan that he doesn’t get detention in any other subject. Lucille might cry. Persist. A detention isn’t a cruel and unusual punishment. They will be OK.

Decide this weekend to put up the electric fence. The sooner you do, the less painful it will be – for you and your students.

Surviving outside the classroom

I loved sparklyfran‘s post on Things she wishes she’d known pre Teach First. In particular, it reminded me of how much happens outside your classroom that you’re not prepared for. So in a very similar vein, here is my list o’ tips. Take from it what you will…

  1. Make friends with repro! And IT support! And reception! Just be nice. Spend an extra couple of minutes talking about football when your photocopying’s being done rather than rushing off. It’ll pay dividends. There’s remarkable correlation between buying wine for Mr Reprographics at Christmas and getting your card sort guillotined and enveloped up for you during Ofsted.
  2. Don’t talk shop in public places. Little Johnny’s parent could be sitting right behind you on that bus.
  3. Stay on top of the little things that make you look in control even when everything’s crazy. Check you buttoned your shirt up right. Reply to emails. Wash up your mug. Try to prevent your workspace from looking like a bombsite. You don’t want to be the eyeroll-worthy Teach First buffoon.
  4. You have two ears, two eyes, and only one mouth. Spend a good long time observing before you make any negative comments about the school or individuals. Things are often more complex than they first appear.
  5. A few days a term, when you’re going through a negative patch, make a conscious decision to make that day super-positive. Wake up and just act for that one day like you’re Ronald McDonald. Fake it. Go all out. All smiles, “good morning!”s and positivity. It’s a good recalibration exercise.
  6. Teach First deign to make it unnecessarily difficult to find out exactly what you need to do for the Leadership Development Programme. Sit down in September and sign up for the necessary events to get it out of the way. Ideally do this with your TF bezzies. You will end up seeing them much less than you think and TF events are actually a good way of keeping in touch.
  7. At subject studies days, people’s anecdotes will either be fantastically positive (“My class are targeted Gs but now they’ve had to create a new A** grade for them because I’m just so outstanding”) or fantastically negative (“I get beaten up every day by students and staff alike. Even the Head had a go yesterday”). Or the absolute worst of those combined (“I teach a class of absolute scoundrels who tear round the school bullying every child they come across. But they’re fantastically well behaved for me, producing A level standard essays for the starter activity”). Just nod and smile. And try not to get sucked into doing the same.
  8. You will have days where you are a nanometre off calling in sick. Go in anyway. On my worst days, I’ve told myself “I’ll go just in and then say I’ve been sick at break”. It gets to break and I tell myself “it’s just my year 7s next, I can cope til lunch and then I’ll go home”. And then someone buys chippy chips for the department for lunch and I think “yeah, I can make it through til 3:20 now”. The satisfaction of getting through those days when you’re dead on your feet is worth it.
  9. Go to the pub with your colleagues on Fridays. I know you’re tired. But just do it. And stay for more than one. All the best bonding happens at the end of the evening.
  10. For the love of all that is holy, don’t date someone in your department.

An addendum on card sorts

I thought I might try to give some vaguely helpful advice for new teachers on the card sorts front. Maths seems to be full of them, especially from the Standards Unit which was the number one cited resource by a long shot at SI 2012.

What I do now is look through the card sort and imagine model keen-bean students (of the ability of the set I’m planning for) trying the card sort. What questions would they have? What categorisations would they quibble over? Where would they disagree? Where’s the cognitive conflict?

For example, in a shape categorisation card sort, whether this is a pentagon or not would be a rich source of debate for my imaginary keen beans:


All too often in a paired card sort activity, they would categorise this without thinking or one student would just overrule the other based on popularity or ego size rather than mathematical debate. The quality discussion which draws out misconceptions happens far less often than the Standards Unit authors would like to think, in my opinion.

Anyway, I generate the list of imagined key discussion points. I put statements or questions associated with (one, or two, or many of) them on my powerpoint.

So I’d put that picture of the pentagon up and write. “This is a pentagon. True or false?” underneath it.

Now we can have a class discussion, or a “think pair share”, or a minute of “everybody writes” specifically focused on that crucial misconception.

Far easier to manage, far easier to focus the children’s thoughts on the key areas, far less time consuming to produce.