Category Archives: Physics

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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Filed under Humour, Physics

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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Filed under Direct Instruction, Physics, Siegfried Engelmann

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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Filed under Education, Philosophy, Physics, Science

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

 

 

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Filed under Education, IoP Energy "Newspeak", Physics

IoP Energy: It’s About The Physics, Stupid!

[I]t is ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge;- which certainly had been very much more advanced in the world, if the endeavours of ingenious and industrious men had not been much cumbered with the learned but frivolous use of uncouth, affected, or unintelligible terms, introduced into the sciences

John Locke, An Essay Concerning Human Understanding (1690)

OK, so I was wrong.

In a previous blog, I suggested a possible “diagrammatic” way of teaching energy at GCSE which I thought was in line with the new IoP approach. Thanks to a number of frank (but always cordial!) discussions with a number of people — and after a fair bit of denial on my part — I have reluctantly reached the conclusion that I was barking up the wrong diagrammatic tree.

enoji19

The problem, I think, is that unconsciously I was too caught up in the old ways of thinking about energy. I saw implementing the new IoP approach as being primarily about merely transferring (if you’ll pardon the pun) the vocabulary. “Kinetic store” instead of “kinetic energy”? Check. “Gravity store” instead of “gravitational potential energy”? Check. “Radiation-pathway-thingy” instead of “light energy”? Check.

Let’s look at the common example of a light bulb and I will try to explain.

Using the old school energy transfer paradigm, we might draw the following:

enoji20

In spite of its comforting familiarity, however, there are problems with this: in what way does it advance our scientific understanding beyond the bare statement “electricity supplied to the bulb produces light and heat”. Does adding the word “energy” make it more scientific?

For example, when we are considering “light energy”, are we talking about the energy radiated as visible light or the total energy emitted as electromagnetic waves? It is unclear. When we are considering “heat energy” are we talking about the energy emitted as infrared rays or the increase in the internal energy of the bulb and its immediate surroundings? Again, it is unclear.  In the end, explanations of this stripe are all-too-similar to that of Moliere’s doctors in The Imaginary Invalid, who explained that the sleep-inducing properties of opium were due to its “dormative virtues”; that is to say, sleep was induced by its sleep-inducing properties.

The problem with the energy transfer paradigm is that it draws a veil over the natural world, but it is a veil that obscures rather than simplifies.

The IoP, after much debate, collectively rolled up its sleeves and decided that it was time to take out the trash. In other words, they wanted to remove the encumbrance of terms that had, over time, essentially become unintelligible.

The new IoP model distinguishes between stores and pathways. For example, an object lifted above ground level is a gravity store because the energy is potentially available to do work. Pathways, on the other hand, are a means of transferring energy rather than storing energy. For example, the light emitted by a bulb is not available to do work in the same sense as the energy of a lifted weight. It is, within the limits of the room containing the bulb, a transient phenomenon. Many photons will be absorbed by the surfaces within the room; a small proportion of photons will escape through the window and embark on a journey to Proxima Centauri or beyond, perhaps.

Now let’s look at my well-meaning diagrammatic version of the energy transfers associated with a light bulb:

pathway-bulb

The stores are “leak-proof buckets” holding the “orange liquid” that represents energy. The pathways are “leaky containers” that enable energy to be transferred from one store to another. I have to admit, I was quite taken with the idea.

The first criticism that gave me pause for thought was the question: why mention the thermal store of the bulb? Surely that’s a transient phenomenon that does not add to our understanding of the situation. Switch off the electric current and how long would the thermal store be significant? Wouldn’t it be better to limit the discussion to two snapshots at the beginning (electrical pathway in) and end (radiative pathway out)?

The second question was: what does the orange liquid in the pathways represent? In my mind, I thought that the level might represent the rate of transfer of energy. Perhaps a high power transfer could be represented by a nearly full pathway, a low power transfer by a lower level.

But this led to what I thought was the most devastating criticism: why invent objects and assign clever (but essentially arbitrary) rules about the way they interact when you could be talking about real Physics instead?

Is there any extra information in the phrase “light energy” as opposed to simply the word “light”?

Blackbody2

Efficiency of a bulb: find the total energy emitted as visible light and divide by the total energy emitted as light of all wavelengths.

And that’s when I realised that I wasn’t helping to take out the trash; in fact, I was leaving the rubbish in place and merely spray painting it orange.

Now don’t get me wrong, I think there’s still a long road ahead of us before we become as comfortable with the IoP Energy newspeak as we were with the old paradigm. As a first step, I suggest all those interested should read and contribute to Alex Weatherall’s excellent Google doc summary to be found here. But I honestly believe that it’s a journey worth taking.

Opium facit dormire.
A quoi respondeo,
Quia est in eo
Vertus dormitiva

— Moliere, The Imaginary Invalid (1673)

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Filed under Education, IoP Energy "Newspeak", Physics

IoP Energy: Notes Towards A Diagrammatic Teaching Approach?

After a fascinating discussion led by the excellent Alex Weatherall (click here to participate in his Google doc Physics-fest — and follow @A_Weatherall on Twitter for more), I was thinking on possible teaching approaches for energy.

Although I think the IoP‘s (the UK’s Institute of Physics) approach is conceptually sound (see previous post here) and addresses many of the shortcomings in the traditional and time-hallowed “forms of energy” approach, many Physics teachers (myself included) are struggling to find direct and simple ways of communicating the highly nuanced content to students.

For example, to describe a filament bulb:

A (filament) light bulb is a device that takes energy in (input) through an electrical pathway (the current) to the thermal energy store of the filament (the metal is getting hotter) which transfers the energy through the radiation pathways of light (visible and IR). There is an increase in the thermal store of the room due to transfer via the heating pathway. The less energy transferred by heating compared to visible light the more efficient the light bulb.

I think this is in accordance with the letter and spirit of the “IoP Energy Newspeak” approach; but sadly, I can picture many students struggling to understand this, even though it was written by many hands (including mine) with the best of intentions.

But then I began to think of adopting a diagrammatic “enoji” approach. (See here for suggested energy icons, or energy + emoji = enoji)

 

Diagrams for Stores and Pathways

An energy store is represented by a “watertight” container. For example, the gravity store of a ball at the top of a slope could be represented thus:

gravity-store

Because it is an energy store, the amount of energy (represented by the level of orange liquid) in the store remains constant. Energy will not spontaneously leave the store. Energy stores don’t have holes. The unit we use with energy stores is the joule.

However, energy pathways do have holes. In contrast to an energy store, the energy level in a pathway will spontaneously decrease as the energy is shifted to another store.

pathway

To keep the energy level constant in a pathway, it needs to be constantly “topped up” by the energy from an energy store.

Since a pathway represents a “flow” of energy, the unit we use with an energy pathway is the watt (one joule per second). The “orange liquid level” in the pathway icon could therefore represent the amount of energy flowing through in one second (although I concede that this idea, though promising, needs more thought).

 

“Enoji Energy Shift” Diagrams

Adopting this convention, the “enoji energy shift” diagram for a ball rolling down a slope might look like this:

pathway2

An energy store does not have any holes — unless it is linked to a pathway, like the gravity store above. Energy will move in the direction indicated by the energy pathway icon.

Simplified in a student exercise book, it could be represented like this:

simplepathway1

The small upward and downward arrows are an attempt to indicate what happens to the energy level over time.

 

The Filament Lightbulb “Enoji Energy Shift” Diagram

This could be represented in a student exercise book like this:

pathway-bulb

Since there are no small up and down arrows on the pathway or thermal store enojis, this indicates that the energy levels are relatively stable (provided we have a constant input of energy from the power station). However, the energy level of the thermal store of the surroundings just keeps on going up…

 

And finally…

Please note this is a work in progress.

I fully expect many teachers will think that the suggested set of conventions may well prove more confusing for students.

However, what I am attempting to do is to give students a set of simple, coherent yet serviceable analogies. In other words, this might provide a conceptual “tool kit” of physical representations of very abstract processes involving energy.

I hope readers will agree that it offers some scope for further development. Comments, criticisms and suggestions would be most welcome.

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Filed under IoP Energy "Newspeak", Physics