Category Archives: Education

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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Filed under Education, physics, Uncategorized

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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Filed under Education, Humour, physics, Uncategorized

Assessment Will Eat Itself

Seemingly a lifetime ago I remember writing about the worst mark scheme ever written. Jon Tomsett recently wrote a searing blogpost about a more recent version.

Laura then took me to her classroom, where piles of coursework were strewn across every table, and showed me what she has to mark. She has 29 students’ work to assess, having to write comments to justify her marks in 7 boxes for each student. That is 203 separate comments with minimal, if any, support from OCR. Page after page of assessment descriptors without any exemplar materials to help Laura, and her colleagues across the country, make accurate interpretations of what on earth the descriptors mean.

This is an example — pure and simple — of assessmentitis.

“-itis” is the correct medical suffix since the assessment system is, indeed, inflamed. Distended. Bloated. Swollen. Engorged. Puffed up.

How did it come to this? When you meet people who work for the examination boards, they are — by and large — pleasant, normal, well-adjusted and well-intentioned people, at least as far as I can judge. How can they produce such prolix monstrosities?

Dr Samuel Johnson made the telling observation that “Uniformity of practice seldom continues long without good reason.” The fact that all the exam boards tend to produce similar styles of document indicates that they are responding to a system or set of pressures that dictate such a response.

I suspect that, at its heart, the system has at least one commendable aim: that of fairness, and that of ensuring that everyone is making similar judgements.

In answer to the age-old question: “But who is to guard the guards themselves?” they have attempted to set up an impenetrable Wall of Words.

But here’s the thing: words can be slippery little things, capable of being interpreted in many different ways. Hence the need to add a comment to give an indication of how one interpreted the marking criteria. It has been suggested that “expected practice” (“best practice” to some) is to include phrases from the marking criteria in the comment on how one applied the marking criteria . . .

This is already an ever-decreasing-death-spiral of self-referential self-referring: assessment is eating itself!

Soon we will be asked to make comments on the comments. And then comments on the comments that we made commenting on how we applied the marking criteria.

But here’s another thing: if the guards are so busy completing paperwork explaining how they are meeting the criteria of competent guarding and establishing an audit-trail of proof of guarding-competencies — then, at least some of the time, they’re not actually guarding, are they?

Who is to guard the guards themselves? In the end, one has to depend on the guards to guard themselves. Choose them well, trust them, and try to instil a professional pride in the act of guarding in them.

Pride and honest professionalism: they are the ultimate Watchmen.

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Filed under Assessment, Education, POAE

Teaching Magnification Using the Singapore Bar Model

He was particularly indignant against the almost universal use of the word idea in the sense of notion or opinion, when it is clear that idea can only signify something of which an image can be formed in the mind. We may have an idea or image of a mountain, a tree, a building; but we cannot surely have an idea or image of an argument or proposition.

— Boswell’s Life of Johnson

The Singapore Bar Model is a neat bit of maths pedagogy that has great potential in Science education. Ben Rogers wrote an excellent post about it here. Contrary to Samuel Johnson’s view, the Bar Model does attempt to present an argument or proposition as an image; and in my opinion, does so in a way that really advances students’ understanding.

Background

The Bar Model was developed in Singapore in the 1980s and is the middle step in the intensely-focused concrete-pictorial-abstract progression model that many hold instrumental in catapulting Singapore to the top of the TIMSS and PISA mathematical rankings.

Essentially, the Bar Model attempts to use pictorial representations as a stepping-stone between concrete and abstract mathematical reasoning. The aim is that the cognitive processes encouraged by the pictorial Bar Models are congruent with (or at least, have some similarities to) the cognitive processes needed when students move on to abstract mathematical reasoning.

Applying the Bar Model to a GCSE lesson on Magnification

I was using the standard I-AM formula triangle with some GCSE students who were, frankly, struggling.

Image from https://owlcation.com/stem/light-and-electron-microscopy

Although most science teachers use formula triangles, they are increasingly recognised as being problematic. Formula triangles are a cognitive dead end because they are a replacement for algebra, rather than a stepping stone that models more advanced algebraic manipulations.

Having recently read about the Bar Model, I decided to try to present the magnification problem pictorially.

“The actual size is 0.1 mm and the image size is 0.5 mm. What is the magnification?” was shown as:

Screen Shot 2018-03-18 at 11.35.05

From this diagram, students were able to state that the magnification was x 5 without using the formula triangle (and without recourse to a calculator!)

Screen Shot 2018-03-18 at 11.41.43.png

Magnification question.

The above question was presented as:

Screen Shot 2018-03-18 at 12.02.57

 

Note that the 1:1 correspondence between the number of boxes and the amount of magnification no longer applies. However, students were still able to intuitively grasp that 100/0.008 would give the magnification of x12500 — although they did need a calculator for this one. (Confession: so did I!)

More impressively, questions such as “The actual length of a cell structure is 3 micrometres. The magnification is 1500. Calculate the image size” could be answered correctly when presented in the Bar Model format like this:

Screen Shot 2018-03-18 at 12.22.21

Students could correctly calculate the image size as 4500 micrometres without recourse to the dreaded I-AM formula triangle. Sadly however, the conversion of micrometres to millimetres still defeated them.

But this led me to think: could the Bar Model be adapted to aid students in unit conversion? I’m sure it could, but I haven’t thought that one through yet…

However, I hope other teachers apply the Bar Model to magnification problems and let me know if it does help students as much as I think it does.

 

 

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Corinne’s Shibboleth and Embodied Cognition

You can watch a bird fly by and not even hear the stuff gurgling in its stomach. How can you be so dead?

— R. A. Lafferty, Through Other Eyes

In modern usage, a shibboleth is a custom, tradition or speech pattern that can be used to distinguish one group of people from another.

The literal meaning of the original Hebrew word shibbólet is an ear of corn. However, in about 1200 BCE, the word was used by the victorious Gileadites to identify the defeated Ephraimites as they attempted to cross the river Jordan. The Ephraimites could not pronounce the “sh” sound and thus said “sibboleth” instead of “shibboleth”.

As the King James Bible puts it:

And the Gileadites took the passages of Jordan before the Ephraimites: and it was so, that when those Ephraimites which were escaped said, Let me go over; that the men of Gilead said unto him, Art thou an Ephraimite? If he said, Nay; Then said they unto him, Say now Shibboleth: and he said Sibboleth: for he could not frame to pronounce it right.

Judges 12:5-6

The same story is featured in the irresistible (but slightly weird) Brick Testament through the more prosaic medium of Lego:

Shibboleth

Sadly, the story did not end well for the Ephraimites:

Then they took him, and slew him at the passages of Jordan: and there fell at that time of the Ephraimites forty and two thousand.

This leads us to Corinne’s Shibboleth: a question which, according to Dray and Manogoue 2002, can help us separate physicists from mathematicians, but with fewer deleterious effects for both parties than the original shibboleth.
Corinne’s Shibboleth

Screen Shot 2018-02-16 at 10.39.11.png

Screen Shot 2018-02-16 at 10.40.05.png

Mathematicians answer mainly B. Physicists answer mainly A.

This is because (according to Dray and Manogoue) mathematicians “view functions as maps, taking a given input to a prescribed output. The symbols are just placeholders, with no significance.” However, physicists “view functions as physical quantities. T is the temperature here; it’s a function of location, not of any arbitrary labels used to describe the location.”

Redish and Kuo 2015 comment further on this

[P]hysicists tend to answer that T(r,θ)=kr2 because they interpret x2+ y2 physically as the square of the distance from the origin. If r and θ are the polar coordinates corresponding to the rectangular coordinates x and y, the physicists’ answer yields the same value for the temperature at the same physical point in both representations. In other words, physicists assign meaning to the variables x, y, r, and θ — the geometry of the physical situation relating the variables to one another.

Mathematicians, on the other hand, may regard x, y, r, and θ as dummy variables denoting two arbitrary independent variables. The variables (r, θ) or (x, y) do not have any meaning constraining their relationship.

I agree with the argument put forward by Redish and Kuo that the foundation for understanding Physics is embodied cognition; in other words, that meaning is grounded in our physical experience.

Equations are not always enough. To use R. A Lafferty’s picturesque phraseology, ideally physicists should be able to hear “the stuff gurgling” in the stomach of the universe as it flies by….

Dray, T. & Manogoue, C. (2002). Vector calculus bridge project website, http://www.math.oregonstate.edu/bridge/ideas/functions

Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5-6), 561-590.

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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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Electrifying Engelmann

It is a long-standing and melancholy truth that, despite the best efforts of many legions of Physics teachers, many students continue to not only dislike electricity, but to hate it with the white-hot intensity of a million suns.

What we have here, I think, is a classic failure to communicate.

A final fact is that samenesses and differences of examples are more obvious when the examples are juxtaposed. This fact implies that the continuous conversion of examples provides the clearest presentation of samenesses and, differences because it creates the changes that occur from one example to the next.

— Siegfried Engelmann and Douglas Carmine, Theory of Instruction (1982) p.46

Looking at my own teaching, I certainly attempt to juxtapose a number of circuits. I really want to highlight the similarities and differences between circuits in order to better develop my students’ understanding. But the problem is that both limited resources and other practical considerations mean that the juxtapositioning cannot happen by continuous conversion, except very rarely.

For example, I would set up (or ask students to set up) a circuit with a single bulb with an ammeter, then I (or we) would disassemble the circuit and rebuild it with the ammeter in a different position, or a second bulb added in series or in parallel . . .

It occurs to me that what we are relying on to thread these juxtapositions together in students’ minds is a sequence of circuit diagrams. I suppose it’s another case of the curse of knowledge writ large: experts and novices think differently.

As a beginning teacher, I remember being genuinely shocked that many students found it easier to interpret a photograph or a 3D drawing rather than the nice, clutter-free, minimalist lines of a circuit diagram.

Without a doubt, many students retain strong visual impressions of many of the circuit diagrams they encounter, but they do not parse and decode the diagrams in the same way as their teachers do.

And that, I think, is the major problem when we are introducing electric circuits.

But what to do?

— R. S. Thomas, The Cure

Can we introduce the important aspects of electrical circuits by continuous conversion of examples?

I think we can. And what is more, I think it will be more effective than the itty-bitty assembly and disassembly of circuits that I have practiced to date.

Conservation of electrical current (and current in parallel circuits) by continuous conversion

Parallel Circuit

This is introduced with a teacher demonstration of the above circuit. Students are invited to note the identical readings on both ammeters and asked to explain why they are identical. They are then asked to predict the effect of adding a second bulb in parallel. The teacher then adds the second bulb by connecting the flying lead. The process is repeated with the third and fourth bulbs, with the teacher testing students’ understanding by asking them to predict the change in current readings as bulbs are added and removed. The teacher also tests students’ understanding of the conservation of current by asking students to predict whether the reading on both ammeters will be the same or different as bulbs are added and removed.

I find it useful to include a bulb that is not identical to the other three. It should be noticeably brighter or dimmer than the other three with the same p.d. so that students do not make the incorrect inference that the current always increases or decreases in equal steps when the circuit is changed.

The teacher could also draw the original circuit on a student whiteboard and ask students to do likewise. The changes that are about to be made could be described and students could be asked could alter the picture/circuit diagram and write their prediction on their whiteboards. They could then compare their version with the teacher’s and their prediction could be quickly tested by making the proposed changes “live” in front of the students.

If resources and time permit, students could then, of course, go on to construct their own parallel circuits as a class practical. However, I think it is important that these vital, foundational ideas are introduced (or re-introduced!) via a teacher demonstration to avoid possible cognitive overload for students.

Series circuits by continuous conversion

Series Circuit

In this demonstration circuit, four of the three bulbs are short-circuited so that they are initially unlit. The teacher asks students to explain only one bulb in the circuit is lit: it is helpful if they have previously encountered parallel circuits and can explain this in terms of electrical current taking the “easier” route (assuming they have not yet encountered the concept of electrical resistance).

Again, the two ammeters allow the teacher to emphasise and test students understanding of the idea that current is conserved.

The teacher then asks students to predict the change in current reading when switch X is opened: will it increase or decrease? Why would it increase or decrease? The process is repeated with switches Y and Z and students’ understanding is tested by asking them to predict the effect on the current reading of opening or closing X, Y or Z.

As before, the teacher would amend her circuit diagram on her student whiteboard and students would do likewise. For example: “I am going to open switch Y. Change the circuit diagram. Show me. What will happen to the reading on the left hand ammeter? What will happen to the reading on the right hand ammeter? Explain why.”

Again, I recommend that at least one out of the four bulbs in not identical to the other three to help prevent students from drawing the incorrect inference that the current will always increase or decrease in identical steps.

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