The Coulomb Train Revisited (Part 2)

In this post, we will look at understanding potential difference (or voltage) using the Coulomb Train Model.

This is part 2 of a continuing series. You can read part 1 here.

The Coulomb Train Model (CTM) is a helpful model for both explaining and predicting the behaviour of real electric circuits which I think is suitable for use with KS3 and KS4 students (that’s 11-16 year olds for non-UK educators).

To summarise what has been discussed so far:

Modelling potential difference using the CTM

Potential difference is the ‘push’ needed to make electric charge move around a closed circuit. On the CTM, we can represent the ‘push’ as a gain in the energy of the coulomb. (This is consistent with the actual definition of the volt V = E/Q, where one volt is a change in energy of one joule per coulomb.)

How can we observe this gain in energy? Simple, we use a voltmeter.

Kudos to for the lovely circuit diagrams

On the CTM, this would look like this:

What the voltmeter does is compare the energy contained by two coulombs: one at A and the other at B. The coulombs at B, having passed through the 1.5 V cell, each have 1.5 joules of energy more than than the coulombs at A. This means that the voltmeter in this position reads 1.5 volts. We would say that the potential difference across the cell is 1.5 V. (Try and avoid talking about the potential difference ‘through’ or ‘of’ any part of the circuit.)

More potential difference measurements using the CTM

Let’s move the voltmeter to a different position.

On the CTM, this would look like this:

Let’s make the very reasonable assumption that the connecting wires have zero resistance. This would mean that the coulombs at C have 1.5 joules of energy and that the coulombs at D have 1.5 joules of energy. They have not lost any energy since they have not passed through any part of the circuit that actually has a resistance. The voltmeter would therefore read 0 volts since it cannot detect any energy difference.

Now let’s move the voltmeter one last time.

On the CTM, this would look like this:

Notice that the coulombs at F have 1.5 fewer joules than the coulombs at E. The coulombs transfer 1.5 joules of energy to the bulb because the bulb has a resistance.

Any part of the circuit that has non-zero resistance will ‘rob’ coulombs of their energy. On this very simple model, we assume that only the bulb has a resistance and so only the bulb will ‘push back’ against the movement of the coulombs and cost them energy.

Also on this simple model, the potential difference across the bulb is identical to the potential difference across the cell — but this is not always the case. For example, if the wires had a small but non-negligible resistance and if the cell had an internal resistance, but these would only come into play at A-level.

The bulb is shown as ‘flashing’ on the CTM to provide a visual cue to help students mentally model the transfer of energy from the coulombs to the bulb. In reality, instead of just one coulomb transferring a largish ‘chunk’ of energy, there would be approximately 1.25 billion billion electrons continuously transferring a tiny fraction of this energy over the course of one second (assuming a d.c. current of 0.2 amps) so we wouldn’t see the bulb ‘flash’ in reality.

How do the coulombs ‘know’ how much energy to drop off?

This section is probably more of interest to specialist physics teachers, but all are welcome.

One frequent criticism of donation models like the CTM is how do the coulombs ‘know’ to drop off all their energy at the bulb?

The response to this, of course, is that they don’t. This criticism is an artefact of an (arguably) over-simplified model whereby we assume that only the bulb has resistance. The energy carried by the coulombs according to this model could be shown as a sketch graph, and let’s be honest it does look a little dodgy…

But, more accurately, of course, the energy loss is a process rather than an event. And the connecting wires actually have a small resistance. This leads to this graph:

Realistically speaking, the coulombs don’t lose all their energy passing through the bulb: they merely lose most of their energy here due to the process of passing through a high resistance part of the circuit.

In part 3 of this series, we’ll look at how resistance can be modelled using the CTM.

You can read part 3 here.

Physics Six Mark Calculation Question? Give it the old FIFA-One-Two!

Batman gives a Physics-Six-Marker the ol’ FIFA-One-Two,

Many students struggle with Physics calculation questions at KS3 and KS4. Since 40% of the marks on GCSE Physics papers are for maths, this is a real worry for their teachers.

The FIFA system (if that’s not too grandiose a description) provides a minimal and flexible framework that helps students to successfully attempt calculation questions.

Since adopting the system, we encounter far fewer blanks on test and exam scripts where students simply skip over a calculation question. A typical student can gain 10-20 marks.

The FIFA system is outlined here but essentially consists of:

  • Formula: students write the formula or equation
  • Insert values: students insert the known data from the question.
  • Fine-tune: rearrange, convert units, simplify etc.
  • Answer: students state the final answer.

The “Fine-tune” stage is not — repeat, not — synonymous with re-arranging and is designed to be “creatively ambiguous” and allow space to “do what needs to be done” and can include unit conversion (e.g. kilowatts to watts), algebraic rearrangement and simplification.

The FIFA-One-Two

Uniquely for Physics, instead of the dreaded “Six Marker” extended writing question, we have the even-more-dreaded “Six Marker” long calculation question. (Actually, they can be awarded anywhere between 4 to 6 marks, but we’ll keep calling them “Six Markers” for convenience.)

The “FIFA-one-two” strategy can help students gain marks in these questions.

Let’s look how it could be applied to a typical “Six mark” long calculation question. We prepare the ground like this:

FIFA-one-two: the set up. (Note that since the expected unit of the final answer is given, this is actually a five marker not a six marker; however, the system works equally well in both cases.)

Since the question mentions the power output of the kettle first, let’s begin by writing down the energy transferred equation.

Next we insert the values. It’s quite helpful to write in any “non standard” units such as kilowatts, minutes etc as a reminder that these need to be converted in the Fine-tune phase.

And so we arrive at the final answer for this first section:

Next we write down the specific heat capacity equation:

And going through the second FIFA operation:


I think every “Six Marker” extended calculation question can be approached in a productive way using the FIFA-One-Two approach.

This means that, even if students can’t reach the final answer, they will pick up some method marks along the way.

I hope you give the FIFA-One-Two method a go with your students.

You can read more about using the FIFA system here: ‘Using the FIFA system for really challenging GCSE physics calculations‘.

Talk from Chat Physics 2021

FIFA for the GCSE Physics calculation win

Student: Did you know FIFA is also the name of a video game, Sir?

Me: Really?

Student: Yeah. It’s part of a series. I just got FIFA 20. It’s one of my favourite games ever.

Me: Goodness me. I had no idea. I just chose the letters ‘FIFA’ completely and utterly at random!

The FIFA method is an AQA mark scheme-friendly* way of approaching GCSE Physics calculation questions. (It is also useful for some Y12 Physics students.)

I mentioned it in a previous blog and @PedagogueSci was kind enough to give it a boost here, so I thought I’d explain the method in a separate blog post. (Update: you can also watch my talk at ChatPhysics Live 2021 here.)

The FIFA method:

  1. Avoids the use of formula triangles
  2. Minimises the cognitive load on students when approaching calculations.

Why we shouldn’t use formula triangles

Formula triangles are bad news. They are a cognitive dead end.

Screenshot 2019-10-27 at 15.34.54

During a university admissions interview for veterinary medicine, I asked a prospective student to explain how they would make up a solution for infusion into a dog. Part of the answer required them to work out the volume required for a given amount and concentration. The candidate started off by drawing a triangle, then hesitated, eventually giving up in despair. […]

They are a trick that hides the maths: students don’t apply the skills they have previously learned. This means students don’t realise how important maths is for science.

I’m also concerned that if students can’t rearrange simple equations like the one above, they really can’t manage when equations become more complex.

— Jenny Koenig, Why Are Formula Triangles Bad? [Emphases added]

I believe the use of formula triangle also increases (rather than decreases) the cognitive load on students when carrying out calculations. For example, if the concentration c is 0.5 mol dm-3 and the number of moles n required is 0.01 mol, then in order to calculate the volume V they need to:

  • recall the relevant equation and what each symbol means and hold it in working memory
  • recall the layout of symbols within the formula triangle and either (a) write it down or (b) hold it in working memory
  • recall that n and c are known values and that V is the unknown value and hold this information in working memory when applying the formula triangle to the problem

The FIFA method in use (part 1)

The FIFA acronym stands for:

  • FINE TUNE (this often, but not always, equates to rearranging the formula)

Lets look at applying it for a typical higher level GCSE Physics calculation question

Screenshot 2019-10-27 at 16.04.29.png

We add the FIFA rubric:

Screenshot 2019-10-27 at 16.13.00.png

Students have to recall the relevant equation as it is not given on the Data and Formula Sheet. They write it down. This is an important step as once it is written down they no longer have to hold it in their working memory.

Screenshot 2019-10-27 at 16.18.15.png

Note that this is less cognitively demanding on the student’s working memory as they only have to recall the formula on its own; they do not have to recall the formula triangle associated with it.

Students find it encouraging that on many mark schemes, the selection of the correct equation may gain a mark, even if no further steps are taken.

Next, we insert the values. I find it useful to provide a framework for this such as:

Screenshot 2019-10-27 at 16.27.41.png

We can ask general questions such as: “What data are in the question?” or more focused questions such as “Yes or no: are we told what the kinetic energy store is?” and follow up questions such as “What is the kinetic energy? What units do we use for that?” and so on.

Screenshot 2019-10-27 at 16.35.54.png

Note that since we are considering each item of data individually and in a sequence determined by the written formula, this is much less cognitively demanding in terms of what needs to be held in the student’s working memory than the formula triangle method.

Note also that on many mark schemes, a mark is available for the correct substitution of values. Even if they were not able to proceed any further, they would still gain 2/5 marks. For many students, the notion of incremental gain in calculation questions needs to be pushed really hard otherwise they will not attempt these “scary” calculation questions.

Next we are going to “fine tune” what we have written down in order to calculate the final answer. In this instance, the “fine tuning” process equates to a simple algebraic rearrangement. However, it is useful to leave room for some “creative ambiguity” here as we can also use the “fine tuning” process to resolve difficulties with units. Tempting though it may seem, DON’T change FIFA to FIRA.

We fine tune in three distinct steps (see addendum):

Screenshot 2019-10-29 at 12.17.55.png

Finally, we input the values on a calculator to give a final answer. Note that since AQA have declined to provide a unit on the final answer line, a mark is available for writing “kg” in the relevant space — a fact which students find surprising but strangely encouraging.

Screenshot 2019-10-29 at 12.16.46.png

The key idea here is to be as positive and encouraging as possible. Even if all they can do is recall the formula and remember that mass is measured in kg, there is an incremental gain. A mark or two here is always better than zero marks.

The FIFA method in use (part 2)

In this example, we are using the creative ambiguity inherent in the term “fine tune” rather than “rearrange” to resolve a possible difficulty with unit conversion.

Screenshot 2019-10-27 at 17.20.42.png

In this example, we resolve another potential difficulty with unit conversion during the our creatively ambiguous “fine tune” stage:

Screenshot 2019-10-27 at 17.33.05.png

The emphasis, as always, is to resolve issues sequentially and individually in order to minimise cognitive overload.

The FIFA method and low demand Foundation tier calculation questions

I teach the FIFA method to all students, but it’s essential to show how the method can be adapted for low demand Foundation tier questions. (Note: improving student performance on these questions is probably a more significant and quicker and easier win than working on their “extended answer” skills).

For the treatment below, the assumption is that students have already been taught the FIFA method in a number of contexts and that we are teaching them how to apply it to the calculation questions on the foundation tier paper, perhaps as part of an examination skills session.

For the majority of low demand questions, the required formula will be supplied so students will not need to recall it. What they will need, however, is support in inserting the values correctly. Providing a framework as shown below can be very helpful:

Screenshot 2019-10-27 at 17.47.24.png

Also, clearly indicating where the data came from is useful.

Screenshot 2019-10-27 at 17.55.45.png

The fine tune stage is not needed, so we can move straight to the answer.

Screenshot 2019-10-27 at 18.01.07.png

Note also that the FIFA method can be applied to all calculation questions, not just the ones that could be answered using formula triangle methods, as in part (c) of the question above.

Screenshot 2019-10-27 at 18.06.16.png

And finally…

I believe that using FIFA helps to make our thinking and methods in Physics calculations more explicit and clearer for students.

My hope is that science teachers reading this will give it a go.

You can read about using the FIFA system for more challenging questions by clicking on these links: ‘Physics six mark calculation? Give it the old FIFA-one-two!‘ and ‘Using the FIFA system for really challenging GCSE calculations‘.

PS If you have enjoyed this, you might also enjoy Dual Coding SUVAT Problems and also Magnification using the Singapore Bar Model.

*Disclaimer: AQA has not endorsed the FIFA method. I describe it as “AQA mark scheme-friendly” using my professional own judgment and interpretation of published AQA mark schemes.


I am embarrassed to admit that this was the original version published. Somehow I missed the more straightforward way of “fine tuning” by squaring the 30 and multiplying by 0.5 and somehow moved straight to the cross multiplication — D’oh!

My thanks to @BenyohaiPhysics and @AdamWteach for pointing it out to me.

Screenshot 2019-10-27 at 16.58.23.png

The Twelve Physics Pracs of Gove (Part Two)

A true-devoted pilgrim is not weary
To measure kingdoms with his feeble steps

–William Shakespeare, The Two Gentlemen of Verona


A picture [of reality]  . . .  is laid against reality like a measure  . . .   Only the end-points of the graduating lines actually touch the object that is to be measured  . . .   These correlations are, as it were, the feelers of the picture’s elements, with which the picture touches reality.

–Ludwig Wittgenstein, Tractatus-Logico-Philosophicus 2.141-2.1515


What they say of disc jockeys is also true of teachers: that someone, somewhere will remember some of your words forever; or, at least, for the duration of their lifetime. The downside is, of course, that you never know which of your words are going to be remembered. The wittily-crafted, near-Wildean aphorism pregnant with socratic wisdom — probably not. The unintentionally hilarious malapropism that makes you sound like a complete plonker — almost certainly.

To this day, I still remember Dr Prys’ sharp and appropriate response to a flippant comment (possibly from the callow 6th form me) about whether the scientific constants listed in the data book were truly trustworthy: “Look,” he said, “people have dedicated their whole lives to measuring just one of these numbers to one extra decimal place!” True devoted pilgrims indeed, mapping out the Universe step by tiny step, measurement by measurement.

I have written before on what I consider to be the huge importance of practical work in Physics education. Without hands-on experience of the hard work involved in the process of precise measurement, I do not believe that students can fully appreciate the magnificent achievement of the scientific enterprise: in essence, measurement is how scientific theories “touch” reality.

I am encouraged that parts of this view seem to be shared by the writers of the Subject Content guidance. (All hail our Govean apparatchik overlords!)

Of course, this has to be balanced with the acknowledgement that (as I understand it at least) teacher-assessed practical work will no longer count towards a student’s final exam grade. Many are concerned that this is actually a downgrading of the importance of practicals in Science and thus a backward step.

Sadly, they may turn out to be right: “We have to have this equipment for the practical/controlled assessment!” will no longer be a password for unlocking extra funding from recalcitrant SLTs (and from the exam budget too — double win!)

And, undoubtedly, some “teach-to-the-test” schools will quietly mothball their lab equipment (except for the showy stuff — like the telescope that no-one knows how to use — that they bring out for prospective pupil tours).

That would be sad, and although the DfE have, to be fair, nailed their pro-practical colours to the mast, we all know that the dreaded Law of Unintended Consequences may have the last laugh.

I would say it all depends on how the new A levels are actually put together. I will be attending some “launch events” in the near future. I will blog on whether I think we can expect an Apollo 11 or an Apollo 13 at that time.

In the meantime, I will be setting practicals galore as usual, as I’m old-fashioned enough to think that they give a lovely baroque feel to a scheme of work…

Look at me, I design coastlines, I got an award for Norway. Where’s the sense in that? None that I’ve been able to make out. I’ve been doing fiords all my life, for a fleeting moment they become fashionable and I get a major award. In this replacement Earth we’re building they’ve given me Africa to do, and of course, I’m doing it will all fjords again, because I happen to like them. And I’m old fashioned enough to think that they give a lovely baroque feel to a continent. And they tell me it’s not equatorial enough…
–Slartibartfast, from The Hitch-Hikers Guide to the Galaxy by Douglas Adams


The Twelve Physics Pracs of Gove (Part One)

It’s not often that a DfE publication makes me feel like Kent Brockman, the newsreader from The Simpsons.

I’d like to remind them that as a trusted TV personality, I can be helpful in rounding up others to toil in their underground sugar caves.
Kent Brockman: “I, for one, welcome our new insect overlords.”

This feeling stems from reading the “Use of apparatus and techniques – physics” section from the DfE’s April 2014 Subject Content for AS and A level Biology, Chemistry, Physics and Psychology publication (p.23).

I had the rather novel feeling that it’s actually a sound list: and I, for one, welcome this intervention from our Govean-apparatchik overlords.

Why do I welcome this? Well, I feel that all too often we lose sight of the fact that, at its heart, Physics is, and must remain, a practical subject, the foundation of so much of the modern world.

Miroslav Holub’s poem “A Brief Reflection on Accuracy” paints a haunting and disturbing picture of what could be described as an entirely postmodernist, deconstructed and relativist (rather than relativistic) universe:

A certain soldier

    had to fire a cannon at six o’clock sharp every evening.

    Being a soldier he did so. When his accuracy was

    investigated he explained:

I go by

    the absolutely accurate chronometer in the window

    of the clockmaker down in the city.

   [ . . . ]

Oh, said the clockmaker,

    this is one of the most accurate instruments ever. Just imagine,

    for many years now a cannon has been fired at six o’clock sharp.

    And every day I look at this chronometer

    and always it shows exactly six.

[ . . . ]

So much for accuracy.
And fish move in the water, and from the skies
comes a rushing of wings while

Chronometers tick and cannons boom.

Without the grounding supplied by the art and science of measurement, I believe that we would all inhabit a castle-in-the-air universe as outlined above by Holub (whose experiences as an immunological research scientist are said to have influenced much of his poetry).

Is Holub’s nightmarish scenario even a remote possibility? Would we ever be in a world where “chronometers tick and cannons boom” but no-one actually checks the actual time by, say, looking out of the window to see if it’s daylight or not?

As with most nightmares, it’s probably closer than you think: “The sleep of reason brings forth monsters” as Goya suggested, and the steps that produce the monsters are often small, seemingly-harmless compromises of apparently little consequence.

One of my Y13 students, who has been attending a number of interviews for Physics courses, reports that some university departments have told him that “We spend a lot of the first year teaching students how to write formal laboratory reports as we find many of them have not learned how to do this during their A level courses.

Whaaa-aat? I nearly fell off my lab stool when Sam* told me this. In my opinion, that is unconscionable. “Oh, yeah,” Sam went on, “some of the students there said things like ‘Oh, our A level course content makes it unsuitable for practical teaching’.”

Opinions like that, if they genuinely reflect the views of the schoolteachers involved, are steps on the road to bringing forth monsters. Of course, it may not seem like a big deal to either the students or the teachers who are probably following what they see as a reasonable path of little resistance. But it is a big deal, it really is.

“And what did you say, Sam?” I asked.

“I said that we do a formal write up with a full analysis of experimental uncertainties every lesson.”

“Do we, Sam? Every lesson? Really?”
“Yeah, well,” said Sam with a smile, “I lied about that, didn’t I?”

“Exaggerated, Sam. I think you mean exaggerated.”

“Whatever you say, sir,” said Sam.

More on the 12 pracs of Gove in a later post..

* not his real name

The Physicist’s Eulogy

“You want a physicist to speak at your funeral. You want the physicist to talk to your grieving family about the Principle of Conservation of Energy, so that they will understand that your energy has not died. You want the physicist to remind your sobbing mother about the First Law of Thermodynamics: that no energy gets created in the universe, and none is destroyed. You want your mother to know that all your energy, every vibration, every joule of heat, every wave of every particle that was her beloved child remains with her in this universe. You want the physicist to tell your weeping father that amid the energies of the cosmos, you gave as good as you got.

“And at one point you’d hope that the physicist would step down from the pulpit and walk to your broken-hearted spouse there in the pew and tell him that all the photons that ever bounced off your face, all the particles whose paths were interrupted by your smile, by the touch of your hair — those hundreds of trillions of particles — have raced off like children, their ways forever changed by you. And as your spouse rocks in the arms of a loving family, may the physicist let him know that the photons that bounced from you and that were gathered in the particle detectors that are his eyes, that those photons have created within his brain constellations of electromagnetically charged neurons whose energy will go on forever.

“And the physicist will remind the congregation of how much of all our energy is given off as heat. There may be a few fanning themselves with their programs as she says it. And she will tell them that the warmth that flowed through you in life is still here, still part of all that we are, even as we who mourn continue the heat of our own lives.

“And you’ll want the physicist to explain to those who loved you that they need not have faith; indeed, they should not have faith. Let them know that they can measure, that scientists have measured precisely the conservation of energy and found it accurate, verifiable and consistent across space and time. You can hope that your family will examine the evidence and satisfy themselves that the science is sound and that they will be comforted to know that your energy is still around.

“Because, according to both the First and Second Laws of Thermodynamics, not one bit of you is gone: you’re just less orderly.”

Original author unknown. Quoted by ‘WelshmanEC2’ in The Guardian [accessed 14/2/14].  NB: some minor stylistic amendments made in the version presented here.

Update: the original author is Aaron Freeman who performed it on NPR Radio in 2005. Original transcript here. Audio of performance (with added slideshow) here.

Through Other Eyes

To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.

–William Blake, Auguries of Innocence

Yet another whiny email from a Year 12 student. He requests a special selection of past paper questions on a particular topic. My answer? “Go to the flipping website that I have so laboriously set up for your benefit which has resources galore of that particular ilk and more, as well as digital bells and whistles, you clod!”

I did express the above sentiments somewhat more diplomatically in the email. And, to be honest, I was glad to get even that whiny missive: I feel we might be on the verge of that tipping point where the Year 12s stop being passive GCSE Spongebobs and become a little more independent, a little more grown up, a little more like proper 6th form students. Maybe. Just maybe. It might be a sign. I loved it when I heard him say to the other students in the class that “there’s a lot of good stuff on the website.”

Now I know that the student concerned had seen the website previously. He had even complimented me on it. But he obviously hadn’t seen it properly. And, strangely enough, it started me thinking about how we do not always see the world as others see it.

To my mind, one the finest descriptions and “thought experiments” on this topic comes from a short story by the incomparable R. A. Lafferty:

“It may be that I am the only one who sees the sky black at night and the stars white,” he said to himself, “and everyone else sees the sky white and the stars shining black. And I say the sky is black, and they say the sky is black; but when they say black they mean white.”
— R. A. Lafferty, Through Other Eyes, “Nine Hundred Grandmothers and other stories”

Do we genuinely ever see the world as others see it? The truth is — ultimately at least — we don’t rightly know.

Charles Cogsworth, the scientist in R. A. Lafferty’s short story, invents a machine called the Cerebral Scanner which literally allows its user to see out through other people’s eyes, and to truly see the world as others see it.

Charles makes the mistake of using the Scanner to look out through the eyes of his girlfriend, Valery. He is horrified: “she hears sounds that I thought nobody could ever hear. Do you know what worms sound like inside the earth? They’re devilish, and she would writhe and eat dirt with them.”

Valery also uses the Cerebral Scanner to look out through the eyes of Charles, and is equally disturbed. She confronts the hapless Charles:

“You can look at a hill and your heart doesn’t even skip a beat. You don’t even tingle when you walk over a field.”

“You see grass like clumps of snakes.”

“That’s better than not even seeing it alive.”

“You see rocks like big spiders.”

“That’s better than just seeing them like rocks. I love snakes and spiders. You can watch a bird fly by and not even hear the stuff gurgling in its stomach. How can you be so dead? And I always liked you so much. But I didn’t know you were dead like that.”

“How can one love snakes and spiders?”

“How can one not love anything? It’s even hard not to love you, even if you don’t have any blood in you. By the way, what gave you the idea that blood was that dumb colour? Don’t you even know that blood is red?

“ I see it red.”

“You don’t see it red. You just call it red. That silly colour isn’t red. What I call red is red.”

And he knew that she was right.

–R. A. Lafferty, Through Other Eyes

The phrase that has stayed with me over all the years since I first read this story as a callow youth is Valery’s description of what is, to her, Charles’ unforgivable deadness to the wonders of the world: “You can watch a bird fly by and not even hear the stuff gurgling in its stomach.

That is the experience of Physics that I want to communicate to my students. I want them to look at the universe and hear the stuff gurgling in its stomach. I want them to be able to experience their understanding, not just on an intellectual level, but also on a visceral level. This, to my mind, is what makes studying Physics fun.

Do I always succeed? Absolutely not. Do I sometimes succeed? Maybe, sometimes.

Do I have fun in classroom? A significant part of the time, yes. This is why I wanted to become a teacher. This is why I have stayed a teacher. And what about the other rubbish that is constantly being foisted on us?

Well, just for now, I think I’ll let it all go hang. I’ll worry about that on Monday.

National Curriculum Levels: worth keeping?

There is a tide in the affairs of men, or so opined Brutus in Julius Caesar.

Likewise, there is something like a tide in the edu-blogosphere, or at least a prevailing wind. And the prevailing wind right now seems to blowing against the idea of National Curriculum levels (try Joe, Daisy or Keven for their wiser, more coherent thoughts on this issue.)

But here’s the thing: I’ve always quite liked the idea of levels.

There. I’ve said it. Now I feel like Captain Rum in Blackadder:

Aaaaaar! All them other scurvy-bloggers be sayin’ be rid of NC levels! But I says…

Edmund: Look, there’s no need to panic. Someone in the crew will know how to steer this thing.

Rum: The crew, milord?

Edmund: Yes, the crew.

Rum: What crew?

Edmund: I was under the impression that it was common maritime practice for a ship to have a crew.

Rum: Opinion is divided on the subject.

Edmund: Oh, really?

Rum: Yahs. All the other captains say it is; I say it isn’t.

Blackadder II, Episode 3: Potato

Now this is not to say that some schools did some mighty strange things with levels and sub-levels. Like insisting that Key Stage 3 students should progress by two sub-levels per year. And woe betide any teacher that did not achieve this minimal standard of progression, or — horror of horrors! — reported that a student had made negative progress. How dare one cause even the minutest blip on our glorious straight lines on our graphs (drawn in Excel! with colour coding!) of student progression!

And so, for a quiet life, some rascally teachers may have looked at last year’s level, added two sub-levels to it, and entered that.

And, lo, it came to pass that everybody was happy: “Yea, we have numbers, and numbers are scientific. Gosh, some of us even use numbers and letters, which is beyond scientific: I mean, it’s more like advanced cognitive calculus of your learning soul, right? And Ofsted want to see progress over time. Which is shown by our graphs. In Excel. With colour coding. A glorious and undeviating straight line. For every single student. God, we are so good, aren’t we? Outstanding, even.”

That said, I am still in favour of keeping a form of assessment level. No, not the hyperformal “Oh-they’ve-got-to-sit-both-SATS-papers-in-order-to-get-a-reliable-level-and-sublevel” type of level.

What I have got in mind is an approach that was introduced to me many, many moons ago. It was called the CONTROL WORD approach to levels (ring any bells for anyone else yet?)

Level 3: DESCRIBES cause and effect using everyday language (e.g. “The wind blew the door shut”)

Level 4: Uses scientific TERMINOLOGY (e.g. “A force is a push or a pull.”)

Level 5: EXPLAINS cause and effect using scientific terminology (e.g. “The boat slowed because of the drag force of the water.”)

Level 6: Explain cause and effect using an ABSTRACT concept (e.g. “The bulb became dimmer because the resistance of the circuit increased.”)

Level 7: Uses a scientific MODEL to explain a phenomenon (e.g. “The wire has resistance because the freely moving electrons collide with the atoms of the wire and lose energy.”)

Level 8: Links PHENOMENA using a sophisticated model [or models] (e.g. “The atoms vibrate with greater amplitude at higher temperatures. This means that the freely moving electrons will collide more frequently with them. Thus the resistance of the wire increases with temperature.”)

The sublevels were allocated as follows:

(c) can do this with coaching or with highly structured prompts

(b) can usually do this with some prompting or coaching

(a) can do this relied on to do this independently

I’ve always secretly applied this assessment schema when asked for NC levels, and my rule-of-thumb-pulled-out-of-thin-air level has usually been at least comparable with “two-sodding-SATS-papers-to-bloody-well-mark-just-to-generate-one-number-and-one-stupid-letter approach”, or the T.S.S.P.T.B.W.M.J.T.G.O.N.A.O.S.L Approach, as an educational consultant might call it.

Anyhow, now my secret is out. Please feel free to pile on and criticise.

I shall sign off with what I think is an appropriate quotation from Wittgenstein:

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)

He must surmount these propositions; then he sees the world rightly.

Tractatus Logico-Philosophicus, 6.54

A Letter from Talleyrand: ‘Some Thoughts on Education and Political Priorities’ by Dominic Cummings, aged 39¾

Michael Gove and Dominic Cummings
If Michael Gove can be likened to Napoleon, would that make Dominic Cummings his Talleyrand? (after Charles Maurice de Talleyrand-Périgord 1754-1838, Napoleon’s éminence grise.)

The Duke of Wellington once remarked that the battle plans of Napoleon were made of marble, whereas his own were made of little bits of string. Napoleon’s plans were brilliant and effective, as majestic as a triumphal arch. However, they all shared one fatal flaw: if one little bit went wrong then the whole edifice came crashing down. Wellington said that his own battle plans were different: if one string broke, he would merely knot two other strings together and the plan would continue on.

The pdf what Cummings wrote*  has the feel of man attempting to build a Napoleonic battle plan in order to sort out, once and for all, all the tiresome disagreements about educational policy.

And there’s no denying the man has been busy: he has read a lot. An awful lot. From a very wide range of authors. And it’s quite an interesting and eclectic read.

But it also gives the impression of being no more than an energetic exercise in quote mining, and not a dispassionate investigation of the issues. In other words, I strongly suspect that Cummings read so widely in order to find extracts to support his pre-existing views, rather than thoughts or insights to help form or challenge them.

Reading this document, I was put in mind, more than once, of the fictional doctor, Andrey Yefimitch:

“You know, of course,” the doctor went on quietly and deliberately, “that everything in this world is insignificant and uninteresting except the higher spiritual manifestations of the human mind … Consequently the intellect is the only possible source of enjoyment.”

— Anton Chekov, Ward 6

Cummings laments that “less than one percent are well educated in the basics of how the ‘unreasonable effectiveness of mathematics’ provides the language of nature and a foundation for our scientific civilisation.” That, though true, is not necessarily a reason for lambasting our current education system as “mediocre at best”. For me, this seems a curious priority.

Sir Isaac Newton was roundly criticised by his contemporaries for lacking a solid theoretical foundation for the infinitesimal calculus: Bishop Berkeley accused him of trafficking in “the ghosts of vanished quantities”. A couple of centuries later, the rigorous** notion of a limit laid that criticism to rest. Now of course it is generally better to understand more rather than less, but would learning about the foundational difficulties of the calculus be the most pressing priority of a 18th Century student of Physics? I would argue no, not necessarily.

For my part, I have thought long and hard about the “unreasonable effectiveness of mathematics in the natural sciences” (in Eugene Wigner’s phrase). I have discussed it with students. I think it’s a fascinating issue, and I adore far-ranging, off-spec discussions of this ilk. But is it an educational priority? Not in my opinion.

Other parts of the pdf seem just plain odd to me:

It would be interesting to collect information on elite intelligence and special forces training programmes (why are some better than others at decisions under pressure and surviving disaster?). E.g. Post-9/11, US special forces (acknowledged and covert) have greatly altered … How does what is regarded as ‘core training’ for such teams vary and how is it changing?

— Cummings, p.98

Interesting, sure. These special forces teams are (I presume) made up of already highly-motivated and highly-capable individuals. Cummings overarching priority always seems to be towards the individuals on far right of the “bell curve” (another Cummings hot topic: see pp.13, 20, 67, 224 and others). He genuinely seems to recoil in fastidious horror at the very concept of being “mediocre”.

This essay is aimed mainly at ~15-25 year-olds and those interested in more ambitious education and training for them. Not only are most of them forced into mediocre education but they are also then forced into dysfunctional institutions where many face awful choices: either conform to the patterns set by middle-aged mediocrities (don’t pursue excellence, don’t challenge bosses’ errors, and so on) or soon be despised and unemployed.

–Cummings p.4

Compare with Dr Yefimitch:

Life is a vexatious trap; when a thinking man reaches maturity and attains to full conciousness he cannot help feeling that he is in a trap from which there is no escape.

— Anton Chekov, Ward 6

Apparently, Mr Cummings plans to leave the DoE and take up the headship of a Free School. Although I have serious reservations about the Free School programme, I welcome this as an encouraging example of a politician putting his money where his mouth is. And I wish him well. I genuinely do.

However, from my own experience I have to say that I do not think his abstract philosophy will be as reliable a guide for navigating the choppy waters of a headteacher’s life as he believes it will be.

I have quoted from Chekov’s Ward 6 already. This masterful short story is the best description I have ever come across of the result of a collision between a man with an abstract philosophy and real life. In a discussion with a lunatic, Dr Yefimitch proposes that: “There is no real difference between a warm, snug study and this [cold, freezing] ward … A man’s peace and contentment do not lie outside a man, but in himself.” However, disaster strikes and he is committed to the asylum:

Andrey Yefimitch was even now convinced that there was no difference between his landlady’s house and Ward No. 6, that everything in the world was nonsense and the vanity of vanities. And yet his hands were trembling, his feet were cold, and he was filled with dread…

Now, I am not suggesting that our Dom will end up in an insane asylum, or even cold, hungry and alone. What I suggesting is that since one Free School head of what might be described as “the-how-hard-can-it-be?” tendency has, sadly, already bitten the dust, Mr Cummings may find that running a school (or just being a plain old teacher for that matter) requires far more than is dreamt of in his philosophy.

Unless, that is, he learns to make his plans out of string rather than out of marble…


* This joke ©Morecambe and Wise c.1972, as are most of the rest of my jokes
** Now where have I heard that word before?

Spongebob Squarepants Explains the Higgs Boson!

Congratulations to Peter Higgs and Francois Englert on their Nobel Prize for their work on the Higgs Boson and the Higgs Field — yay, them!

In a nutshell, the Higgs Field and the Higgs Boson were born to rescue The Ultimate Theory Of How Twelve Particles And Their Interactions Can Explain Pretty Much Everything That Has Ever Happened and Probably Ever Will (Oh, Except For Gravity, That Is); or, as physicists called it, a little more prosaically, The Standard Model.

The Standard Model works really well except that, in its original form, it cannot explain the origin of mass. In other words, it cannot explain why some particles are heavy and others are light. The Higgs Field explains how this happens, and if there is a Higgs Field, there must be a special sort of particle called a Higgs Boson connected with it.

What follows is my attempt to explain some of these concepts in a manner suitable for school students. I call it the Spongebob Squarepants Analogy.

Our Spongebob Squarepants lives, not at the bottom of the sea, but on the steeply sloping side of a mountain (work with me on this!) and for the life of him cannot figure why things like sponges are heavy but un-spongelike things are light.

He comes up with a groundbreaking idea to explain this difference: it’s raining!!!

Its raining, all the time. Everywhere. Invisibly and imperceptibly. Neither Spongebob nor the spongepeople can see the rain, but it’s raining. And it never, ever stops raining.

Spongbob reckons that spongelike things are heavy because they absorb this mysterious, invisible stuff called water. Non-spongelike things do not absorb this water stuff and so they stay light.

The rain represents the Higgs Field.

Now, how can Spongebob tell if he’s right about this water that he cannot see directly?

He predicts that if he bangs two pieces of sponge together with enough energy then they will release enough water to form (sorry, more technical terms here) a puddle.

The puddle will not last a long time because it will start running downhill (remember that our Spongebob lives on the side of a mountain?) The puddle is not stable in Spongebob’s universe. But if Spongebob is very quick and very lucky he might be able to catch a glint of sunlight from the surface of the puddle, and this will prove that he’s right about the water and the rain.

In fact, Spongebob persuades the spongepeople to build what he calls the Large Sponge Collider…but that’s another story.

So, to sum up:

Spongebob Squarepants = Peter Higgs
Rain = Higgs Field
Water = Higgs Mechanism
Puddle = Higgs Boson

My dad would sometimes respond to my more strained and unlikely metaphors in a stern voice, saying: “Son, an analogy is only an analogy!” However, I like to think that he would have enjoyed this one.