Category Archives: Education

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.



Filed under Direct Instruction, Education, Physics, Siegfried Engelmann

The Pedagog Teaches PRAD

Queen Mary made the doleful prediction that, after her death, you would find the words ‘Philip’ and ‘Calais’ engraved upon heart. In a similar vein, the historians of futurity might observe that, in the early years of the 21st century, the dread letters “R.I.” were burned indelibly on the hearts of many of the teachers of Britain.

In a characteristically iconoclastic post, blogger Requires Improvement ruminates on those very same words that he adopted as his nom de guerre: R.I. or “requires improvement”.

He argues convincingly that the Requirement to Improve was, in reality, nothing more than than a Requirement to Conform: the best way to teach had been jolly well sorted out by your elders* and betters and arranged in a comprehensive and canonical checklist. And woe betide you if any single item on this lexicon of pedagogical virtue was left unchecked during a lesson observation!

[*Or “youngers”, in many cases.]

But what were we being asked to confirm to? Requires Improvement writes:

It was (and to an extent, still is) a strange mixture of pedagogies which probably didn’t really please anyone.

It wasn’t (and isn’t) prog; if a lesson has a clear (and teacher-defined) success criterion, it can’t really be progressive. Comparing my experience as a pupil in the 1980’s with that of the pupils I teach now, they are much better trained in what to write to pass exams, and their whole school experience is much more closely managed than mine was. 

Equally, it wasn’t (and isn’t) trad; if the lesson model is about pupil talk, or putting generic skills above learning a canon of content, it can’t really be traditional teaching.

I think that Requires Improvement has hit the nail squarely on the head here. What we were being asked (and in many schools, are still are being asked) to do is teach a weird hybrid Frankenstein’s monster of a pedagogy that combines seemingly random elements of both PRogressive and trADitional pedagogies: PRAD, if you will.

As C. P. Scott said of the word television that no good could come of a word that’s half Latin and half Greek, I feel that no good has come of the PRAD experiment.

While many proponents of PRAD counted themselves kings of infinite pedagogic space, congratulating themselves on combining the best of progressive and traditionalist ideologies, the resulting unhappy chimera in actuality reflected the poverty of mainstream educational thought.

But though our thought seems to possess this unbounded liberty, we shall find, upon a nearer examination, that it is really confined within very narrow limits, and that all this creative power of the mind amounts to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience. When we think of a golden mountain, we only join two consistent ideas, gold, and mountain, with which we were formerly acquainted.

— David Hume, An Enquiry Concerning Human Understanding (1748)

Rather than a magical wingèd lion that breathes fire, PRAD is a stubby-winged mishmash that can’t fly, can’t lay golden eggs, and that spends its miserable days hacking up furballs. It is time to put it out of its misery.


Filed under Education, Philosophy, Society

Starting From Here

It’s a variation on a classic Celtic joke which I’m sure that you’ve heard before, but here it is anyway.

Motorist: Can you tell me the way to Llanpumsaint please?

Welshman: Why yes, but I wouldn’t start from here if I were you…

I wouldn’t start from here. The joke, of course, is that we rarely have a choice of where we start from. We start from here because here is where we are.

David Hammer (2000) in “Student Resources For Learning Introductory Physics” offers a fascinating perspective on the varied points that students start from as they begin to learn physics. He likens a student’s preexisting conceptual structures to the computational resources used by programmers. These conceptual resources inside our students’ heads can be (loosely) compared to “chunks of computer code”, if you will. He goes on to point out that:

Programmers virtually never write their programs from scratch. Rather, they draw on a rich store of routines and subroutines, procedures of various sizes and functions . . . Those who specialize in graphics have procedures for translating and rotating images, for example, which they use and reuse in a variety of circumstances. And, often, a programmer will try to use a procedure in a way that turns out to be ineffective.

Hammer argues that although many teachers have an instinctive but unspoken understanding of the conceptual resources that students possess, all-too-often it is assumed that any preconception is automatically a misconception that must be rooted out and replaced. Hammer suggests that a more productive approach is to understand and use the often detailed knowledge that students already possess.

Refining “Raw Intuitions”

For example, Hammer summarises the work of Andrew Elby who suggests a strategy for refining the raw intuitions that students have.

A truck rams into a parked car, which has half the mass of the truck. Intuitively, which is larger during the collision: the force exerted by the truck on the car, or the force exerted by the car on the truck? That most students responded that the truck exerts a larger force on the car than the car exerts on the truck is not surprising; this is a commonly recognized “misconception.”

In other words, students fail to apply Newton’s Third Law correctly to the situation, which would predict that the forces acting on two such objects are equal and opposite.

However, all is not lost as Elby believes that his students do have a fundamentally correct intuition about the situation. They rightly intuit that the car will respond twice as much as the truck. The problem is to refine this intuition so that it is consistent with the laws of Newtonian physics. Elby posed a follow up question:

Suppose the truck has mass 1000 kg and the car has mass 500 kg. During the collision, suppose the truck loses 5 m/s of speed. Keeping in mind that the car is half as heavy as the truck, how much speed does the car gain during the collision? Visualize the situation, and trust your instincts.

The students, thus guided, came to the conclusion that because the truck lost 5 m/s of speed, the car gained 10 m/s of speed. Since the mass of the car is half the mass of the truck, the car gains exactly the amount of momentum lost by the truck. Since the exchange occurred over the exact same time period, the rate of change of momentum, and hence the force acting on each object, is equal.

In other words, Elby used the students’ intuition that “the car reacts twice as much as the truck” as the raw material to build a correct and coherent physical understanding of the situation.

Hammer then makes what I think is a very telling point: like computer subroutines, intuitions are neither correct or incorrect. They become correct or incorrect depending on how they are used.

In this way, a resources-based account of student knowledge and reasoning does not disregard difficulties or phenomena associated with misconceptions. Rather, on this view, a difficulty represents a tendency to misapply resources, and misconceptions represent robust patterns of misapplication.

As teachers, we do not have the luxury of selecting our starting points. Often, I think that talk of student misconceptions resembles the “I wouldn’t start from here” joke. The misconception has to be eliminated before the proper teaching can start.

As teachers, we don’t have the luxury of selecting our starting points. We start from where our students start. We’re teachers: we start from here.


Elby, A. (2001). Helping physics students learn how to learn. American Journal of Physics69(S1), S54-S64.

Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics68(S1), S52-S59.


Filed under Education, Physics

The p-prim path to enlightenment…?

The Duke of Wellington was once asked how he defeated Napoleon. He replied: “Napoleon’s plans were made of wire. Mine were made of little bits of string.”

In other words, Napoleon crafted his plans so thay they had a steely, sinewy strength that carried them to completion. Wellington conceded that his plans were more ramshackle, hand-to-mouth affairs. The difference was that if one of of Napoleon’s schemes broke or miscarried, it proved impossible to repair. When Wellington’s plans went awry, he would merely knot two loose bits of string together and carry on regardless.

I believe Andrea diSessa (1988) would argue that much of our knowledge, certainly emergent knowledge, is in the form of “little bits of string” rather than being organised efficiently into grand, coherent schemas.

For example, every human being has a set of conceptions about how the material world works that can be called intuitive physics. If a ball is thrown up in the air, most people can make an accurate prediction about what happens next. But what is the best description of the way in which intuitive physics is organised?

diSessa identifies two possibilities:

The first is an example of what I call “theory theories” and holds that it is productive to think of spontaneously acquired knowledge about the physical world as a theory of roughly the same quality, though differing in content from Newtonian or other theories of the mechanical world [ . . .]

My own view is that . . . intuitive physics is a fragmented collection of ideas, loosely connected and reinforcing, having none of the commitment or systematicity that one attributes to theories.


diSessa calls these fragmented ideas phenomenological primitives, or p-prims for short.

David Hammer (1996) expands on diSessa’s ideas by considering how students explain the Earth’s seasons.

Many students wrongly assume that the Earth is closer to the Sun during summer. Hammer argues that they are relying, not on a misconception about how the elliptical nature of the Earth’s orbit affects the seasons, but rather on a p-prim that closer = stronger.

The p-prims perspective does not attribute a knowledge structure concerning closeness of the earth and sun; it attributes a knowledge structure concerning proximity and intensity, Moreover, the p-prim closer means stronger is not incorrect.


diSessa and Hammer both argue that a misconceptions perspective assumes the existence of a stable cognitive structure where, in fact, there is none. Students may not have thought about the issue previously, and are in the process of framing thoughts and concepts in response to a question or problem. In short, p-prims may well be a better description of evanescent, emergent knowledge.

Hammer points out that the difference between the two perspectives has practical relevance to instruction. Closer means stronger is a p-prim that is correct in a wide range of contexts and is not one we should wish to eliminate.

The art of teaching therefore becomes one of refining rather than replacing students’ ideas. We need to work with students’ existing ideas and knowledge — piecemeal, inarticulate and applied-in-the-wrong-context as they may be.

Let’s get busy with those little bits of conceptual string. After all, what else have we got to work with?



diSessa, A. (1988). “Knowledge in Pieces”. In Forman, G. and Pufall, P., eds, Constructivism in the Computer Age, New Jersey: Lawrence Erlbaum Publishers

Hammer, D. (1996). “Misconceptions or p-prims” J. Learn Sci 5 97


Filed under Education, Philosophy, Physics, Science

Room 808

Image credit:

MiniEd: the Ministry of Education, Airstrip One, Oceania

It was a warm but overcast day in late August and the clocks were striking thirteen.

Mr Winston Smith, Principal of the Victory G+MINDSET Academy (formerly the Bogstannard Comprehensive School), woke to find himself lying on something that felt like a camp bed, except that it was higher off the ground and it seemed that he was fixed down in some way so that he could not move. Light that seemed stronger than usual was falling on his face.

He gasped as he realised that the infamous MiniEd interrogator, “Grammar School” O’Greening, was standing at his side, looking down at him intently. At the other side of him stood a man in a white coat, tapping an iPad.

“Tell me, Winston,” said O’Greening gently, but with a chilling undercurrent of steel in her voice, “how many buckets am I holding up?”

Winston swallowed fearfully as he realised that he had been deposited by mysterious forces into the deepest bowels of the dreaded MiniEd. 

“Erm…two?” he quavered. The two buckets had “EBacc”and “More bloody EBacc” scrawled on them in crayon.

There were a couple of muffled metallic clangs as O’Greening did a rapid double take. “Nick!” she hissed furiously through clenched teeth. The other man ran to join her. He groaned as he strained to lift a third bucket. “Why do I always have to do the Maths and English bucket? It’s sodding well double-weighted, you know…” he muttered resentfully.

O’Greening ignored him. “How many buckets, Winston?”

“Three! I see three buckets!”

The man let the third bucket drop with an explosive gasp and rubbed his tired arms. “Thank God for that! We had that Sir Ken Robinson in here last week. Kept claiming that he could see a fourth bucket called ‘Unleashing Children’s Inner Demiurgic Muse’. I thought my arms were going to fall off…”

“Comrade Gibb!” snapped O’Greening. The man lapsed into sullen but acquiescent silence. “Now, Winston,” she said sweetly, “from whom have we taken our maths mastery pedagogy? From whom have always taken our maths mastery materials?”

Winston locked his dry lips nervously. “Eastasia…we get our maths mastery materials from Eastasia…” O’Greening nodded encouragingly​. “… but up until a couple of years ago, of course, we were encouraged — well, ordered, actually — to get them from Eurasia instead…”

Gibb had stuck his fingers in his ears and was humming “La la la! Not listening! La la la!”

O’Greening glowered at Winston. “Lies! Delusion! Comrade Gibb: take him to . . . Room 808!”

“Erm, this is Room 808, ma’am.”

“Oh. Then fetch me . . . the school’s RAISEonline report!”

Gibb placed the iPad so that it filled the trembling Winston’s entire field of vision.

“Currently, I have a ‘good pass’ set to ‘4’,” she said conversationally. Actually, thought Winston, it didn’t look too bad. The screen was mostly green with only the odd patch of blue. 

Image from

“Now observe what happens as I now define a ‘strong pass’ as a ‘5’!” O’Greening twisted the dial from 4 to 5.

Winston screamed as the entire screen turned blue. “Arrgh! Don’t do it to us! Do it to another school! DO IT TO ANOTHER SCHOOL!”

O’Greening and Gibb patted him on the shoulder. “Oh, we will. We most certainly will.”

They left Winston Smith alone in Room 808. Tears ran down his face, but he smiled quietly to himself as he stared at the screen. Students, happiness, staff, well-being, people — none of that mattered any more. He had finally won the battle against himself. He loved Big Data.


Filed under Education, Humour, Satire

Still Working Away In Our Silos (Thank Goodness)

If a thing is worth doing, it is worth doing badly.

–G. K. Chesterton, What’s Wrong With The World (1910)

Why are teachers beavering away in their individual silos, each one of us spending hours reinventing each pedagogic wheel, crafting schemes of work and resources for the new GCSEs?

Wouldn’t life be so much easier and better if we simply shared…?

To which I say: NO!

To be honest, my favourite part of the job is designing, crafting and re-designing resources and teaching approaches. They’re not perfect, of course. I’m reminded of a line from the opening credits of South Park: “All celebrity voices are impersonated . . . poorly.” As Chesterton remarked, if a thing is worth doing, it is worth doing badly.

But the point is, my approaches and resources are a lot less imperfect than they used to be. I flatter myself that, over the years, some of them have become . . . quite good. I believe Michael Stipe once said that in the entire history of the world there were only ever five rock and roll songs; and that REM could play two of them quite well. There’s a parallel in that most teachers have a lesson or two (or three) that they — and they alone — can teach brilliantly.

I often think that, given the right context, most students prefer shabby, bespoke individualism rather than shiny mass-produced perfection.

As teachers, I think we sometimes overestimate the impact that we have on our students. There is no royal road to learning, and neither can all our craft and pedagogic arts construct a conveyor belt either.

As educators, the most we can hope to do is clear a few stones out of the way of our charges as they set out on the rocky path to learning.

In the end, the journey is theirs. Let us wish them well as we watch from our silos . . .

The difficulty of obtaining knowledge is universally confessed [ . . .] to reposite in the intellectual treasury the numberless facts, experiments, apophthegms and positions, which must stand single in the memory, and of which none has any perceptible connexion with the rest, is a task which, though undertaken with ardour and pursued with diligence, must at last be left unfinished by the frailty of our nature.

Samuel Johnson, The Idler, 12 January 1760


Filed under Education, Humour, Philosophy

IoP Energy: Once More Unto The Breach…

Why do we make these analogies? It is not just to co-opt words but to co-opt their inferential machinery. Some deductions that apply to motion and space also apply nicely to possession, circumstances and time. That allows the deductive machinery for space to be borrowed for reasoning about other subjects. […] The mind couches abstract concepts in concrete terms.

— Steven Pinker, How The Mind Works, p.353 [emphasis added]

I am, I must confess, a great believer in the power of analogy.

Although an analogy is, in the end, only an analogy and must not be confused with the thing itself, it can be helpful.

As Steven Pinker notes above, the great thing about concrete analogies and models of abstract concepts is that they allow us to co-opt the inferential machinery of well-understood, concrete concepts and apply them to abstract phenomena: for example, we often treat time as if it were space (“We’re moving into spring”, “Christmas will soon be here”, and so on).

To that end, I propose introducing the energy stores and pathways of the IoP model to KS3 and GCSE students as tanks and taps.

Energy Stores = tanks

Energy Pathways = taps

Tank and taps

Consider the winding up of an elastic band.

tank and taps 3

This could be introduced to students as follows:

tank and taps 2.PNG

One advantage I think this has over one of my previous efforts is that I am not inventing new objects with arbitrary properties; rather, I am using familiar objects in the hope of co-opting their inferential machinery.

Suggestions, comments and criticisms are always welcome.

My propositions are elucidatory in this way: he who understands me finally recognises 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.

— Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1922), 6.54




Filed under Education, IoP Energy "Newspeak", Physics