Effort:Impact Ratio – 1 – Mental Models for Education

6 years ago Joe Kirby decided to leave a lucrative career working for a social venture capital fund, take a massive pay cut, and join Teach First.

As we talked about how we were going spend the year nervously preparing for what was to come, Joe talked about the use of ratios in finance to build a rough picture of what is happening with an investment, good enough to make reasonable decisions from.

He proposed three possible ratios that might serve a similar function for us in teaching.  One, I can no longer recall.  Another, was equally the brain child of Doug Lemov, and found its way into Teach Like a Champion literally called ‘Ratio.’  This was the teacher:pupil work ratio, which is reasonably common in education.

For me, though, the most enduring and powerful of the three ratios Joe proposed was effort:impact.

The idea is simple: teachers should invest time in things that are low effort, but high impact.  The lower the effort, and higher the impact, the better.  The greater the effort, and lower the impact, the worse.

Although these things are difficult to quantify in the education world, you can develop a feel for ‘acceptable effort:impact ratio.’  If the effort just feels too high for the associated impact, don’t do it!

Would I have spent time fine-tuning the position of images in a PowerPoint so that they were all precisely placed, had I considered the actual impact of all that effort?  I felt that pupils in school deserved access to the kind of quality that we’re all used to receiving from commercial companies, like Google, Apple and Microsoft.  But just because I felt that something was important, did that make my decision a good one?

This is an important question, because while our feelings can, and most certainly should, inform our decisions, we often allow ourselves to be slaves to them.

Are comments in marking really worth it?  How about double or triple marking?!  Some people will say that it’s worth it because it has an impact; yes, but for how much effort?  Are there ways you can achieve the same impact for less effort?  If so, do that instead.


Illustrative only

Joe has since helped to establish a Free School, and, as for me, effort:impact has been the one ratio that truly endured above all others, now taking a central place in the school’s strategy.

The result is extraordinary.  The number of traditional school activities that Joe and his team have shown the confidence to reconsider would shatter the nervous system of most senior leaders.michaela-tweet


Initiativeitis – Scourge of School Leadership

Everyone wants to be seen to be making their mark on a school, whether driven by vanity alone, or a real sense of purpose.

A few years ago a friend, recently appointed to head of department, expressed her frustration that her team showed no enthusiasm for the changes she wanted to make.  From her perspective it was all about the kids, and would make a difference to their lives.  The first thing I asked her was if any of her new initiatives would result in her team having to spend more time working.  “…yes,” was the response I got.  My next question was whether any of their other work would be removed or reduced by the initiatives.  “…no.”  There’s the problem.  What at first might look like an assemblance of lazy no-gooders of Goveian nightmare were perhaps instead just a team of mortal humans already worked to their limit.

The unconscious desire to leave our mark can leave us pray to Action Bias, and what we don’t realise is that at the back of our minds it’s justifiable because the action is also good for us.  As the leader initiating the initiative, if it works, we take the credit, so there’s a bit of extra incentive there for us which doesn’t carry through to the whole team.  Whether we realise this consciously or not, it’s always there, it’s unavoidable, and if we don’t realise it consciously, we still know it subconsciously.

One lens, one filter, one mental model to rule them all, Effort:Impact ratio.

That one simple idea has meant not only that the Michaela leadership say no to any new initiative that won’t return enough impact for the effort of its team of teachers, but it led them to jettison what was, until recently, a cornucopia of received wisdom and sacred cows.


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Overview – 0 – Mental Models for Education

Decision making is tough.  We are riddled with cognitive biases, from action bias to the halo effect and sunken cost fallacy.  They seem contrived only to make us terrible decision makers.

Teachers, HoDs, Heads, all need to make decisions.

Shall I tick ‘n flick those books?  Or write comments?  Or do neither and go to bed?

Should the department invest most of Year 7 studying number, or dedicate equal time to geometry, algebra and stats?  Shall we study Skellig, or Oliver Twist?

Should I implement that new initiative, or not?  Should I spend money on one experienced hire, three trainee teachers, or four teaching assistants?

Mental models: you could call them strategies, or lenses, or filters, or heuristics – whatever you call them, they are simple tools designed to aid decision making.  As I moved through the last five years in education there were times I desperately wished some mental models I’d encountered in my former life were widely known and understood in education.  Once known, the absurdity of some of the decisions we make is revealed.  If not the absurdity, then the very real costs, or the risks, that otherwise remain hidden, and go unnoticed.

So I’m going to chuck a few out there, and see what people make of them.  Some you will have heard of, others will probably be new.

To start with, I’m going to try to cover the following, over the next few weeks:

  1. Effort:Impact Ratio
  2. Opportunity Cost
  3. Money Value of Time
  4. Cost-Benefit Analysis
  5. The 80:20 Principle
  6. Objective Oriented Mindset
  7. MECE (pronounced Mee-See)
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At a past Michaela debate I heard Peter Hyman describe a desire for education ‘…with a smile, not a SLANT.’  The implication was not only, bizarrely, that the two are mutually exclusive (Bright Face is another technique taken from Lemov’s Teach Like a Champion) but that ‘SLANT’ is somehow not desirable.


The acronym stands for Sit up straight, Listen, Ask and answer questions, Nod your head, and Track the speaker.

It’s largely a ‘child’s guide to active listening.’

…super hard to wrap my head around what’s egregious about this.


In my experience, some of these, like ‘nod your head,’ tend to fall away quite quickly, and SLANT becomes more of a shorthand for how you expect pupils to sit: straight backed, eyes on the teacher, and with hands interlocked, or arms folded.

This last part’s the interesting bit.

If you struggle to picture it, you can see Colleen Driggs use a hand gesture to remind a child to return to a ‘hands interlocked’ position in this video (the others are already there.)  You have to be pretty quick to see it, mind.  The whole thing takes only a second or two, and Colleen doesn’t break her flow for it at all.

I’ve been in a few trainee teacher classrooms recently where I saw something strange.  When they counted down to silence, they got it pretty quickly.  When they were speaking, the pupils were largely silent.  Maybe they did, but I couldn’t remember my classes going that well in the first couple of months.  Despite this, I noticed something else… I couldn’t for the life of me focus on what the teacher was saying!  Despite the relative quiet, I was constantly distracted by a cacophony of ruler waving pen tapping hand stomping fidgeting that was endemic in the classroom.

What’s a teacher to do?  At most, I expect you could ask that the trainee focus on a firm expectation of ’empty hands.’  That has two problems.  The first is that it doesn’t really deal with the hand stomping or finger tapping.  The second is that… well you know what it’s like, we will all sometimes mindlessly pick things up and play with them when we’re trying to focus for a period of time.  Not just *low level* disruption; this is, for the most part, likely, completely *unintentional* disruption on the part of pupils, yet disruption it is.  I couldn’t focus and I was trying really hard!

How could children focus in this environment?  Truth is most couldn’t.  Yes there was quiet, but there wasn’t a high degree of attention being given in most the classrooms I saw, and I couldn’t blame them – distractions abound.  As lessons drew on, the relatively high level of respectful quiet that the trainees had initially commanded began to wane, I suspect, in direct relation to how much pupils felt they weren’t really learning.

And so I was met with a newfound love and appreciation of SLANT;  at least, that part of it that asks not only that pupils ‘sit up straight,’ but that gives a clear expectation of what to do with their hands during teacher instruction so that they don’t accidentally disturb those around them, and so all have the opportunity to think deeply about the content.

In schools that make use SLANT or similar, I’ve seen this expectation around ‘folded hands’ fade with older pupils.  Despite this, I also saw those pupils exhibit more of the typical ‘mature adult’ mistake – far fewer of the class were wont to fiddle and fidget in general, and those who did needed only a quick, gentle reminder, and they immediately emptied their hands, a little embarrassed, pretty much any of us do when we realise we’ve accidentally started clicking a pen or tapping something that might distract those around us.

So, long live SLANT!

(or some version of it.)

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When is a mathematical process not a process? This changes everything.

When it’s a concept*.

The best example I have so far to explain this distinction, and its importance, is expanding single brackets compared with double brackets.


The type of concept at work here, in Engelmann’s taxonomy, is a transformation.

There is an input, the transformation concept is applied to it, resulting in some output.  For this to be conceptual rather than procedural it should be possible to directly infer the transformation that is taking place by exposure to carefully chosen examples of input followed by output.


The transformation is the hidden concept we want pupils to infer from observation the changes from inputs to outputs


Concept: Distribution

I used to think of expanding a bracket as a process.  There are many ways of communicating it, but one might be:


However the lines are drawn, however the working is set out, and whether you go for this or a grid method, or a variation of that which links it to rectangle areas, it will still largely be communicated as a step by step process.

Here’s why I don’t think it is a process.  Consider the following as an alternative method of instruction, the one I would probably opt for now:


Ideally these would be written on a whiteboard, with pupils able to witness which numbers you rub out and change, and which stay constant

By chance, I actually did something very close to this with my Year 7 bottom set class in my second year of teaching.  The sequence, language and examples were less carefully chosen, and I didn’t use the identity symbol, but the principle was the same: rather than treating this as a process, I used a few examples from which they were able infer what was happening.  This was a group of poorly behaved children who barely knew their times tables, but still they could see that I was multiplying the first number by the other two, 100% success.

Depending on the group, either the initial instruction sequence (the examples) or the later sequence of teacher-led pupil activity can be expanded to include all manner of important variations on that concept, including:

  • Have three or more terms in the bracket
  • Swap the order of the unknown and the constant
  • Include negative terms
  • Include more than one unknown
  • Interleave with index laws
  • Include a term outside the bracket which isn’t multiplied by its contents
  • etc.

So much to cover, so little teacher exposition needed.  The concept is ‘multiplication is distributive over addition,’ and it can be inferred through carefully chosen examples (this declarative specification of the concept can be provided at some later date.)

As a caveat, I think verbally pointing out that ‘Ten times three is thirty, and ten times five is fifty,’ *is* an option, or ‘Ten times three ex,’ if you prefer, but I would suggest waiting until the second expression has been written, and pupils have had a few seconds to read it; explain verbally what happened *after* the fact, rather than while you’re writing it up on the board.  We tend to like doing this because it feels like it helps us manage behaviour.  Having tried both, I felt that silence on my part actually helped draw attention to my writing, while speaking at the same time possibly added to the cognitive load of the explanation; after all, it required reading and listening at the same time, which we all know aren’t possible! (split-attention effect)  So this part of the advice isn’t about silencing the teacher – as so much ‘Ofsted Outstanding’ training is wont to do – so much as it is about judicious use of language – Economy of Language, as Doug Lemov might call it.

Compare this now with expanding a pair of brackets.



First, my above suggestion will not work for a pair of brackets.  The reason is obvious:


It’s barely possible to infer directly how the input – the expression on the left – resulted in the output, the expression on the right.  At a stretch, a small minority might spot the relationship between the terms in the bracket and the first and final term in the right hand expression, but few, if any, will realise where the middle term came from.  If they did, how long would it take them to form that realisation?  It wouldn’t be instant at all.  Indeed, forgetting about the middle term is the classic mistake we see.

So my earlier method won’t work here.  Expanding a pair of brackets is not a concept.

I’m now going to set this out a little differently to how I most often did this, and how I’ve seen most teachers teach this, using neither FOIL, any of the many crossed line set ups, nor grid multiplication.  Instead I’m going to set out clearly the three lines of processing that are actually taking place.


Each of these three steps represents the application of a transformation.  The distributive property is applied twice, albeit in very different contexts, and simplification by collection of like terms is applied once.

This changes everything.

Here’s why this changes everything.

Traditionally I would have simply taught the process for expanding a pair of brackets, step by step.  I would have asked that pupils replicate my steps.  Now I would do something very different.

Each of those three lines I would treat as a separate concept, to be communicated separately.  Each one might take a lesson, more than one lesson, or perhaps two of them would appear in the same lesson.  They might be separated by only one day, or perhaps a hundred days; however this is structured, they are treated as separate ideas and fully explored independently of one another.

One lesson might consist of applying the distributive property to the pair of brackets only once (getting to Step 1, though it wouldn’t be called that yet.)  That first line becomes ‘the answer,’ no more.

Notice that, since each of these lines *does* express a transformation concept, they *can* each be communicated in the same way I outlined for single brackets.  It takes a little more time to see how you get from a pair of brackets to step 1, but not that much more, and importantly it *can* be inferred from carefully chosen examples.  It could be done with three and four term expressions in the brackets, rather than binomials, or with three or four pairs of brackets rather than just two.

The same is true in going from step 1 to step 2, and 2 to 3.

Eventually, once all three concepts are fully explored and embedded they would be ‘chained’ together in one lesson, or if needed, more than one.  Going from a bracket pair through to step 2, or from a given Step 1 to Step 3, or all the way from start to end.

By this point, pupils should be fully able to answer the traditional, slightly boring and pointless ‘expand this pair of brackets’ question on an exam paper, but they will also have a much deeper understanding of the concepts masked by that step by step process, and hopefully be better able to deal with anything an exam paper could throw at them.


What do you think?  What are the limits of this?  What won’t it work for?



* We could get into a discussion about whether or not a better categorisation of this is actually ‘procept,’ discussed here by Gray and Tall.

For the sake of simplicity, I’m not going to do that for now.

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Are you using the right coloured pen?


Red or green pen?

Having had the honour of working at literally the best school in the country has led me to do a lot of thinking of late.  I think about all the things that people worried themselves about in my previous school – which went into special measures not long after I left.  I think about all the advice I heard the teachers there – many of whom had advice to share that I rely on to this day – had themselves received from consultants who’d came and went.

A big one was around pen colour.  Apparently someone had arrived shortly before my time to help the school spend its money on learning that red was an ‘aggressive’ colour that could upset pupils.  Teachers should all mark in green.  Everyone would be much happier this way.  They’d learn more, one assumes.

The profound philosophical question about whether or not teachers should mark with a red or green pen has plagued schools for a decade now.  The question has proved such an intractable devil that one trainee was driven to make its resolution her ultimate edu-quest.

The debate reached its apotheosis when one senior leader announced a decisive breakthrough: purple and orange pens!  Now, at last, there were no pre-conceived connotations attached to the colour of the pen; lucid and pure, the teacher’s words could shine through on page.

It’s as I prepare training on Lemov’s concept of the Exit Ticket that I find myself jotting down a note about how our pupils might ‘green pen’ a ticket returned to them i.e. correct it with a green pen they are expected to have in their pencil case.  I realise I’ve been writing in red ink now for three years.  I like it; not because I enjoy scrawling angry blood trails across pupils’ work, but because it is the colour that contrasts best against the blues and blacks in which pupils write.  It’s easy to read against a white background, unlike green, making it a solid choice.

And you know what?  It didn’t do our kids any harm.

I almost expect this is why teachers have been marking in red for decades; it’s almost as though this were a natural, sensible, choice, considered and resolved aeons ago.

One wonders… how much time have teachers found themselves wondering long, deep into the night, about things that matter not a jot.  How much nothing has been trumped up into all by people charging a fee.  How much longer will education allow itself to be blustered by changing winds blowing in all directions, before fizzling out to lead nowhere.

Bodil Isaksen’s blog title was obviously wry irony; even a trainee who hadn’t yet set foot into the classroom had been able to see the emperor was naked; why not the rest of us?

There will be ‘the next Brain Gym,’ the next Learning Styles, the next Red or Green pen; my question is how are we so spectacularly taken in by it, time and again.  Why are we allowing ourselves to be humiliated like this?  How long until we develop institutional immunity to nonsense?

At Wellington’s Festival of Education 2014 I argued that teaching needs a codified body of knowledge before we can lay claim to being any kind of real profession.  At the 2016 festival discussed a new model of teacher training and development, and at ResearchED 2016 I flirted with some of education’s historic development.

Not long ago I heard a trainee tell me that their university tutor educated him in learning styles, which is only shocking until you read Howard Jones review of the neuromyths prevalent in education (93% in the UK still thought learning styles were a thing).

We’ve a long, long way to go, but I look forward to us getting there.

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Reading Reconsidered: Two Quick Thoughts


Last week I had the privilege of attending a two day training programme delivered by Erica Woolway, Maggie Johnson, and Doug Lemov.

The training was based on their new book, Reading Reconsidered.

It’s about teaching reading, of which I have no experience, and so the whole experience was packed with learning experiences for me, but two things have stuck out.

I’m not sure I was ever taught how to read

In one section, Maggie ran an extended model of Close Reading, as she would with her pupils.  She began by asking us to read the opening paragraphs of Grapes of Wrath.

TO THE RED COUNTRY and part of the gray country of Oklahoma, the last rains came gently, and they did not cut the scarred earth. The plows crossed and recrossed the rivulet marks. The last rains lifted the corn quickly and scattered weed colonies and grass along the sides of the roads so that the gray country and the dark red country began to disappear under a green cover. In the last part of May the sky grew pale and the clouds that had hung in high puffs for so long in the spring were dissipated. The sun flared down on the growing corn day after day until a line of brown spread along the edge of each green bayonet. The clouds appeared, and went away, and in a while they did not try any more. The weeds grew darker green to protect themselves, and they did not spread any more. The surface of the earth crusted, a thin hard crust, and as the sky became pale, so the earth became pale, pink in the red country and white in the gray country.

In the water-cut gullies the earth dusted down in dry little streams. Gophers and ant lions started small avalanches. And as the sharp sun struck day after day, the leaves of the young corn became less stiff and erect; they bent in a curve at first, and then, as the central ribs of strength grew weak, each leaf tilted downward. Then it was June, and the sun shone more fiercely. The brown lines on the corn leaves widened and moved in on the central ribs. The weeds frayed and edged back toward their roots. The air was thin and the sky more pale; and every day the earth paled.

Then asked us to summarise the main idea of the passage.  I wrote:

That a severe drought has struck, causing all the plants, crops, and even weeds to die.

She then ran through her series of activities, and asked us to again summarise the main idea of the passage.  This time I wrote:

The sun has changed its nature, and now a losing battle is fought between a powerful and murderous sun, and the remaining, beleaguered, forces of nature still dedicated to life.

While the activity was heavily guided, and Maggie deliberately drew our attention to key words, phrases and imagery in the text, both the original and final words are my own.

I was struck by how markedly different they are.  In the absence of experience, I have no baseline to measure whether this is typical of all English lessons.  English teachers, please comment.

Important to me is that my first attempt followed my typical ‘reading quickly to get the gist,’ while Maggie’s activities forced us to spend a long time considering many deliberate choices made by the author.  It’s an activity I might suspect English graduates to have ready to execute as second nature, if needed.  For my part I’m not sure if I was ever taught to read like this at school.  It’s certainly not my nature now.


And I probably should have been

One point Doug made early on, both on the day and in the book, is that if you’re going to attempt to access university education, you are probably going to have to comfortable reading, on your own, a lot.  He distinguished between:

Learning to Read


Reading to Learn

Which I like.

As a physicist, I’m not sure I read a single book at university.  Actually, I think I read some for an essay on chaos theory that I wrote once, and maybe I read something on nanotechnology.  Mostly, though, I turned up to lectures, tried out some practice questions, and then did some exams.  Where I did read at all, I often abandoned it not long in – reading about science is hard.

By contrast, my friend had read the Feynman Lectures, and I’m sure took so much more from all of our lectures and study.  How much more could I have learned and understood if I’d done the same?

It got me thinking – perhaps even in subjects that aren’t literature heavy, such as science and mathematics, where you wouldn’t normally expect there to be much reading, or feel a ‘reading week’ a necessity, there is so much to be gained if a person has habituated the idea of learning by reading.  When not presented with materials to read, would they now naturally seek them out?  Would the math’s student reach for Georg Cantor’s work on Transfinite Numbers?

There’s only one school in the country that I’m personally aware of that has attempted anything like this, Michaela Community School.  In this post, Katie Ashford outlines all of the reading that takes place in all of the lessons – 6,000 words during school hours.  That’s 1.2 million per year, and 8.2 million over 7 years, assuming the reading work load doesn’t increase with age.  I’ve seen it in action, a little, and I saw every teacher in every classroom running the same reading strategies with the children.

Despite being averse to the idea of reading about mathematics to learn mathematical concepts – simply because it’s a linear communication system for concepts that rarely lend themselves to linearity – I applaud and admire the dedication to putting reading front and centre in their children’s lives; I feel I could happily give up 200 words a lesson to be part of that, and might even reason that there is value in the idea of reading in maths lessons.

At the training, a science teacher remarked that they can’t ask their children to learn science by reading, since, you guessed it, most their kids can’t really read.  There may be others, and I’ve love to hear about them if so, but this is the only example I’ve heard so far of a school taking that failure seriously, and determining to overturn it.

And while, as with mathematics, there are more effective and efficient methods for learning many scientific concepts at school level than reading, there necessarily comes a point in our lives when one has to read about science to learn more science.

How might I have approached university education differently if I’d spent every day at school reading 6,000 words, expecting to learn from them?

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Education is the lighting of a fire.

Yesterday I re-read this excellent post by Joe Kirby, which featured this quote-by-not-Yeats:

“I wholeheartedly disagree that possessing knowledge improves your ability to think. I’m afraid your criticisms would give way to a ‘filling of a pail’ approach rather than a‘lighting of a fire’ approach.

I was also pointed in the direction of this woefully misguided ode to vapid, where you can see its echo:

“Moreover, teaching a prescribed “core knowledge” instills a culture of conformity and an insipid, passive absorption of carefully selected knowledge among young people. It doesn’t encourage students to think critically about society – nor does it fire a desire to challenge the views they are taught. Schools that adopt this method become nothing more than pipelines producing robotic citizens, perpetuating the vision of a capitalist society and consequently preventing social mobility.”

Of course.  People with knowledge never thought critically.  Critical thinking is in fact magic.  Magic that happens through shear force of passion and sunbeams, and punk rock.  I’m reminded of Tom Bennett’s hilarious dig at the Education Select Committee, when they asserted that Amanda Spielman didn’t demonstrate enough ‘passion’ during their interview:




-> Critical Thinking



Then I realised something funny about that quote: fire needs fuel.

Knowledge is of course the fuel of thought; a bit like kerosene, used to power jet planes and rocket ships amongst other things.  You’re not going to get much in the way of critical thinking if you have nothing with which or to which you can apply your mind, just as much as your well-constructed jet plane ain’t going nowhere if you don’t fill it with fuel.


So there you have it.

If you want to light a fire, fill the pail with kerosene first.


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