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Teaching Electric Circuits? Climb On Board The Coulomb Train!

I’ve said it before and I’ll say it again: teaching electric circuits is hard.

Providing your students with a conceptual model can, in my opinion, be immensely helpful. In recent years, I have used what I call the Coulomb Train Model (CTM). It is essentially a variation on the “stiff chain”-class analogies that some researchers have argued as being particularly useful in developing students’ understanding.

One reason why I like the CTM is that it provides a physical picture to aid students’ comprehension of many of the electrical equations needed at GCSE.

Of course, any analogy or model will have its flaws, but on the whole I think the CTM has fewer than many of its rivals!

Essentially, the CTM pictures an electric circuit as a continuously moving chain of postively-charged “trucks” called coulombs that carry energy from the cell to (say) the bulb. In the diagram below, they should be pictured as moving clockwise.

Charge flow = current x time

Charge flow = number of coulombs that pass a given point in time.

Current = number of coulombs that pass by in one second (i.e. current = charge flow / time).

In other words, an ammeter counts the coulombs passing by in one second. The ammeter only “sees” the coulombs and does not register how much (or how little) energy each one contains. Therefore current I1 and current I2 are equal.

The ammeters are shown as being semi-transparent in order to provide a visual cue that they are low resistance devices.

Energy transferred = charge flow x potential difference

On the CTM, potential difference can be pictured as energy being added to, or removed from, each coulomb.

For example, if one joule is removed from each coulomb as they pass through the bulb, the potential difference across the bulb is one volt. If one joule is added to each coulomb as they pass through the cell, then the potential difference (or e.m.f.) across the cell is one volt.

The total energy transferred from (say) ten coulombs passing through the bulb would be charge flow (10 coulombs) x potential difference (1 volt) = 10 joules.

The white gloves on the voltmeter are intended to be reminiscent of the white gloves of a snooker referee.

The intention is to disrupt the flow of the coulombs as little as possible and so this is a visual reminder that a voltmeter is a high resistance instrument.

To emphasise the fact that potential difference is an “energy difference”, challenge students to predict the reading on this voltmeter.

The potential difference V3 is, of course, zero since there is no transfer of energy to or from the coulombs.

Current in Series and Parallel Circuits

I think the CTM can be really effective in allowing students to a see a comprehensible physical analogue of the circuits.

For example, I3 = I4 = I5 = 0.5 amps; I6 = I11 = 2 amps; and I7 = I8 = I9 = I10 = 1 amp.

Potential difference in series and parallel circuit

Equally, I think the CTM can give a comprehensible physical picture of the situation.

In this case (assuming the the cell has a p.d. of 1 V and the bulbs are identical), V4 = V5 = 0.5 V.

In the parallel circuit, each bulb tranfers one joule of energy from each bulb, and so the potential difference across each bulb is one volt.

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Ohm From Ohm

Amongst the myriad inconveniences and troubles of a Physics teacher’s life, the choice of the symbols commonly used to represent voltage, current and resistance, must surely rank in the top ten.

V is for voltage in volts, V

Well, OK, that’s sensible enough. On a good day, I may even remember to call it “potential difference”. The sage advice of “Never use two words when one will do” is widely accepted. However, as a profession Physics teachers have decided to go it alone and completely ignore it. One can only hope that everyone got the memo.

R is for resistance in ohms, Ω

R for resistance? That’s fairly sensible too.

“But what’s that weird squiggly thing, Sir?”

“Ah, you mean the Greek letter omega? Because Physics is soooo enormous that the measly 26 letters of the Latin alphabet ain’t big enough for it…”

I is for current in amps, A

“WTφ? Are you taking the πΣΣ, Sir?”

“I know, I know! Look, if it helps, think of it as short for intensité du courant . . . Wait, don’t leave! Stop, I have many more fun Physics facts to teach you! Look, here’s a picture of Richard Feynman playing his bongo drums — nooooooooo!”

Ohm’s Law: or is it more a sort of guideline?

Let’s start with a brief statement of Ohm’s Law:

V = I R

Except, that’s not Ohm’s Law; it’s actually the definition of resistance:

R = V / I

There is not a single instance where it is not true by definition. The value of resistance will always be equal to the ratio of the potential difference and the current.

Think of it like this. At room temperature, 1 V of potential difference can push (say) 0.5 A of current through the wire in a filament bulb. (I just love that retro 1890s tech, don’t you?)

This means it has a resistance of 1/0.5 = 2 ohms. However, bump up the potential difference to 6 V and the current is (say) 0.75 A. This means that is has a resistance of 6/0.75 = 8 ohms. Its resistance has changed because it has become hotter. In other words, its resistance is not constant.

Ohm’s Law is perhaps most simply stated as:

The potential difference is directly proportional to the current over a range of physical conditions (including temperature).

Using standard symbols:

V α I

or, taking R’ as a constant of proportionality:

V = I R’

You do see the difference, don’t you?

In the first example, R is not a constant value for a given range of physical conditions: for example it can get higher as the temperature increases.

In the second, R’ is constant over a range of temperatures and other physical conditions.

And so there we have it: V=IR can be a perfectly valid statement of Ohm’s Law, provided it is specified that R is constant. If one does not do that, then all bets are off…

In the meantime, here’s another picture of Richard Feynman playing the bongo drums. Enjoy!

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Lottie and Lorentzian Length Contraction

@_youhadonejob tweeted this textbook picture with the amusing and sardonic comment “Little girl in this textbook is 5 m tall”.

I liked @jim_henderson60’s take on this when he tweeted: “You see. Physics helps us all grow tall.”

But then I started thinking, what if the 5 m measuring stick was in an inertial frame moving past Lottie’s inertial frame at a substantial fraction of light speed? (In my head, I named the girl “Lottie”, although “Alice” would be more in the more usual tradition of SR* pedagogy, I guess.)

The illustration could represent that single instant at which both ends of the 5 m ruler were precisely opposite Lottie’s head and feet as its inertial frame whizzed by hers…

A quick calculation indicated that Lorentz length contraction could indeed account for the relative measurements on the illustration if v = 0.97c

Of course, Lorentz length contraction is a two way street. From the 5 m ruler’s inertial frame, length contraction would make Lottie appear even shorter than her compact 1.2 m. Given that v = 0.97c, I calculate that she would appear only 0.29 m tall.

Correction: not appear. She would genuinely be only 0.29 m tall when viewed from that inertial frame, just as the 5 m rule would genuinely be only 1.2 m long when viewed from Lottie’s inertial frame.

We live in an universe where everything is indeed relative. However, for most of us that takes a fair amount of getting used to…

*SR = special relativity. My brain is currently too small to handle GR (general relativity).

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Markopalypse Now

AHT VAL: And once you’ve finished marking your students’ books and they have responded IN DETAIL to your DETAILED comments, you must take them in again and mark them a second time using a different coloured pen!

AHT HARVEY: A page that’s marked in only one colour is a useless page!

NQT BENJAMIN: Erm, if you say so. But why?

AHT VAL: It’s basic Ofsted-readiness, Benjamin. Without a clearly colour-coded dialogue between teacher and student, how can we prove that the student has made progress as a result of teacher feedback?

NQT BENJAMIN: But I’ve only got this red biro…

AHT HARVEY GRINS UNPLEASANTLY AND OPENS A CABINET FULL OF PENS OF MANY COLOURS.

AHT HARVEY: In this school we wage a constant battle against teacher sloth and indifference!

(With apologies to The League Of Gentlemen)

I have been a teacher for more than 26 years and I tell you this: I have never marked as much or as often as I am now. We are in the throes of a Marking Apocalypse — a Markopalypse, if you will.

And why am I doing this? Have I had a Damascene-road conversion to the joy of rigorous triple marking?

No. I do it because I have to. I do it because of my school’s marking policy. More to the point, I do it because my school expends a great deal of time and energy checking that their staff is following the policy. And my school is not unique in this.

Actually, to be fair, I think my current school has the most nearly-sensible policy of the three schools I have worked in most recently, but it is still an onerous burden even for an experienced teacher who can take a number of time-saving short cuts in terms of lesson planning and preparation.

Many schools now include so-called “deep marking” or “triple marking” in their lists of “non-negotiables”, but there are at least two things that I think all teachers should know about these policies.

1. “We have to do deep/triple marking because of Ofsted”

No, actually you don’t. In 2016, Sean Harford (Ofsted National Director, Education) wrote:

[I]nspectors should not report on marking practice, or make judgements on it, other than whether it follows the school’s assessment policy. Inspectors will also not seek to attribute the degree of progress that pupils have made to marking that they might consider to be either effective or ineffective. Finally, inspectors will not make recommendations for improvement that involve marking, other than when the school’s marking/assessment policy is not being followed by a substantial proportion of teachers; this will then be an issue for the leadership and management to resolve.

2. “Students benefit from regular feedback”

Why yes, of course they do. But “feedback” does not necessarily equate to marking.

Hattie and Timperley write:

[F]eedback is conceptualized as information provided by an agent (e.g., teacher, peer, book, parent, self, experience) regarding aspects of one’s performance or understanding. A teacher or parent can provide corrective information, a peer can provide an alternative strategy, a book can provide information to clarify ideas, a parent can provide encouragement, and a learner can look up the answer to evaluate the correctness of a response. Feedback thus is a “consequence” of performance.

So a textbook, mark scheme or model answer can provide feedback. It does not have to be a paragraph written by the teacher and individualised for each student.

Daisy Christodoulo makes what I think is a telling point about the “typical” feedback paragraphs encouraged by many school policies:

[T]eachers end up writing out whole paragraphs at the end of a pupils’ piece of work: ‘Well done: you’ve displayed an emerging knowledge of the past, but in order to improve, you need to develop your knowledge of the past.’ These kind of comments are not very useful as feedback because whilst they may be accurate, they are not helpful. How is a pupil supposed to respond to such feedback? As Dylan Wiliam says, feedback like this is like telling an unsuccessful comedian that they need to be funnier.

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Whither Edu-blogging?

The task of an author is, either to teach what is not known, or to recommend known truths by his manner of adorning them.

Samuel Johnson, The Rambler, 27 March 1750

I regret to say that, for me at least, blogging has become a habit that has been more honoured in the breach than in the observance. And, judging from a conversation or two on Twitter, I haven’t been alone. A number of edu-bloggers also seem to have hit a dry spell.

Some ask: what’s the point? What have we actually achieved? In a typical school, how many teachers actually read any edu-blogs? Outside the edu-Twitter bubble, has anyone ever changed anybody else’s mind, ever? Humans can generally change their location easily enough, but as Horace observed mordantly many years ago, “Who can change their mind?”

And yet. Reading blogs and engaging in Twitter conversations has changed at least one person’s mind: mine. And one of the most important things it taught me was: I was not alone.

I wasn’t alone in thinking that group work was over-emphasised as a panacea to the point of absurdity. I wasn’t alone in thinking that Learning Styles seemed a bit dodgy. I wasn’t alone in believing that a teacher should, on occasions, be an unapologetic sage-on-the-stage and not a permanently-muted guide-on-the-side.

And, in my opinion, a number of things have indeed changed for the better. Ofsted still has issues but it isn’t the educational Thought Police which brooked no dissent from the One True Path that it was a few years ago. A significant part of the credit for this should go to the edu-blogging pioneers who pointed out that a number of its policies had no clothes, and did this using evidence and reasoned argument rather than merely relying on a set of appeals-to-educational-authority as was the style at the time. I would single out @oldandrewuk, @tombennett71 and @daisychristo as being particularly influential in this regard, but there were many others.

I agree with @larrylemonmaths‘ comment that “When the stonemason hits the rock, the first 99 times, it seems like nothing is happening, then suddenly, on the 100th blow, the rock breaks apart. It’s important to keep blogging and talking and arguing, even if it seems like nothing is happening.”

So if we are to continue blogging, what should we blog about? Whither Edu-blogging? in other words.

If I was to highlight some current issues that I think would benefit from more people blogging about them, they would be:

1. Markopalypse Now: why are most teachers in most schools marking so much? When did insane amounts of over-marking become the new normal? Do people realise that written marking is not the same as feedback and that the majority of marking is being undertaken to comply with school policy and a misguided idea of “what Ofsted wants”.

2. The Bonfire Of The Greyhairs: why are so many experienced teachers leaving the profession? Are some of them being forced out because of budgeting pressures with manufactured “performance issues”? Is there any other profession where the wisdom of long-serving colleagues is not only sidelined as an irrelevance but actively rejected?

3. Accountability Roulette And The Culture Of Fear: research suggests that the “teacher factor” is responsible for between 1 and 14% of educational outcomes. Why, then, are teachers judged as if they are accountable for 100%?

No doubt I will blog on other issues besides the ones above (assuming that I blog at all!), but I will try to contribute to the tap-tap-tap of stonemason’s chisels on the adamantine rock of these problems at least.

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Physics Limericks: Some Classics

The following two are, I believe, by famed textbook writer A. P. French

There was a young fellow named Cole
Who ventured too near a black hole
    His dv by dt
    Was quite wondrous to see
Now all that’s left is his soul!

Ms. Farad was pretty and sensual
And charged to a reckless potential
     But a rascal named Ohm
     Conducted her home.
Her decline was, alas, exponential!

I came across this one recently, and I like its subtle cleverness.

Relatively Good Advice
by Edward H. Green

Dear S’: I note with distress
The length of your yardstick is less
     And please wind your clock
     To make it tick-tock
More briskly. Your faithful friend, S.

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A Classicist Writes

My lovely wife Laurie has started her own blog called A Classicist Writes.

She writes on Ancient Greece and Rome (she has an M.A. in Classical Studies), cats, Ralph Waldo Emerson, more cats, more Ralph Waldo Emerson, and other topics.

Hope you enjoy!

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