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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When Harold Met William

Legend has it that in 1988, U.S. Presidential candidate Michael Dukakis opened an election rally in front of a huge crowd in a red state with the ringing words: “This joke will appeal to the Latin scholars amongst you…” He went on to lose decisively to George H. W. Bush.

On that note, this joke will appeal to all the Physics teachers (and other aficionados of the dot-and-cross convention).

Harold

For the non-physicists amongst you, this is an illustration of the dot-and-cross convention, which allows us to represent 3D objects on a 2D diagram. The dot represents a vector emerging out of the plane of the paper (think of an arrow coming towards you) and the cross represents a vector directed into the plane of the paper (think of an arrow going away from you).

520px-VFPt_Solenoid_correct2.svg

A solenoid (electromagnet) represented using the dot-and-cross convention. From http://www.wikiwand.com/en/Solenoid

I’ll get my coat…

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Engelmann (and John Stuart Mill) Revisited

Even for the most enthusiastic and committed of us, Engelmann and Carnine’s Theory of Instruction (1982) is a fabulously intimidating read.

I have written about some of the ideas before, but a recent conversation with a fellow Physics teacher (I’m looking at you, @DeepGhataura) suggested to me that a revisit might be in order.

In a nutshell, we were talking about sets of examples. Engelmann and Carnine argue that learners learn when they construct generalisations or inferences from sets of examples. It is therefore essential that the sets of examples are carefully chosen and sequenced so that learners do not accidentally generate false inferences. A “false inference” in this context is any one that the instructor does not intend to communicate.

Engelmann and Carnine painstakingly constructed a set of logical rules that they hoped would minimise (or, more ambitiously, completely eliminate) the possibility of generating false inferences. These include the sameness principle of juxtaposition and the difference principle of juxtaposition.

However, in 2011 Carnine and Engelmann realised that they had, in a sense, been re-inventing the wheel as the same logical rules had been formulated by philosopher John Stuart Mill in A System of Logic (1843).

They outlined their system using Mill’s terms and language in the book Could John Stuart Mill Have Saved Our Schools? (2011).

 

The Method of Difference (The Difference Principle of Juxtaposition)

How can we use examples to communicate a concept to learners so that the possibility of their drawing false inferences is minimised?

The Method of Difference seeks to establish the limits of a given concept A by explicitly considering not-A.

Imagine a learner who did not understand the concept of blue. We would introduce the concept by showing (say) a picture of a blue bird and saying “This is blue.” We would then show a picture of a bird identical in every respect except that it’s colour was (say) green and say “This is not blue.”

So-far-so-blindingly-obvious, you might say. What you might not immediately appreciate is that applying this simple method rules out a large set of possible misconceptions. Without explicitly considering not-A, a learner might, with some justification, conclude that blue meant “has a beak” or “has feathers”. The Method of Difference rules out these false inferences.

Mind your P’s and Q’s

For a beginning reader, the letters p, q, b and d are problematic since they all share the same basic shape. The difference between them is a difference of orientation. Carnine and Engelmann suggest writing the letter ‘p’ on a transparent sheet and rotating and flipping the sheet to explicitly teach the difference between p and not-p.

PND

PNB

PNQ

Could this be used in Physics teaching?

 

Don’t zig when you ought to zag

Possibly — one recurring problem that I’ve noticed is that some A-level students routinely mix up magnetic and electric fields. They apply Coulomb’s Law when they should be applying F = BIl , and apply Fleming’s Left Hand Rule where it has no business being applied.

It seems reasonable to assume that it is not a lack of knowledge that is holding them back, but rather a misapplication of knowledge that they already possess. In other words, they are drawing the wrong inference from the example sets that have been presented to them.

Could using the Method of Difference at the beginning of the teaching sequence stop learners from drawing false inferences about the nature of electric and magnetic fields?

BandEfields1

BandEfields2

You know, I rather think it might…

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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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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.

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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.

References

Elby, A. (2001). Helping physics students learn how to learn. American Journal of Physics69(S1), S54-S64. http://134.68.135.20/JiTT_NMSU_workshop/pdfs/HelpingStudentsLearn_Elby.pdf

Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics68(S1), S52-S59. http://mapmf.pmfst.unist.hr/~luketin/Physics_education/resources_Hammer.htm


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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.

[p.50]

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.

[p.103]

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?

 

REFERENCES

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

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