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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Room 808

Image credit: https://www.flickr.com/photos/costi-londra/3989596804

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 https://johntomsett.com/page/21/?archives-list=1

“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.

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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

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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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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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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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Brownian Motion, Staff Rooms and Bromeliads

Individuals aren’t naturally paid-up members of the human race, except biologically. They need to be bounced around by the Brownian motion of society, which is a mechanism by which human beings constantly remind one another that they are…well…human beings.

— Terry Pratchett, Men At Arms

Happiness is . . . not having an office.

I had a job once where I had an office. It was a quite a nice office. And I had it all to myself. It was a quiet, pleasant little space with a small kitchen nearby. It even had natural daylight through a large window Perfect, you might think.

But I grew to hate that office. You see, I think that teachers — more than anyone, perhaps — need, occasionally, to be “bounced around by the Brownian motion of society”. 

What is Brownian motion? Well, it was first observed by botanist Robert Brown in 1827, who noted that, under a microscope, pollen grains in water seemed to “jiggle” randomly. Brown at first assumed that this motion was due to the “life force” of the pollen grains; however, he dispensed with this idea when he saw particles of stone dust (reportedly taken from the Great Pyramid to make sure they were completely and utterly devoid of life) perform the same drunken, wiggly waltz that came to be known as Brownian motion.

And there the matter rested, for a while. And then in 1905, a young patents clerk, working in his spare time at a kitchen table in a very modest apartment in Geneva, suddenly discovered the explanation — and more, much more.

The patents clerk’s name was, of course, Albert Einstein. His explanation rested on the insight that the visible pollen or dust particles were being buffeted by invisible water particles. His mathematical analysis was not only the first verifiable evidence of the actual physical existence of atoms, but also established their size. Understanding the movement and nature of the unobservable by minute and careful scrutiny of the observable…

Looking back at the job with its own office, I think I missed the simple daily dose of teacherly Brownian motion that you get by simply stepping into a staff room. Are you a little too-full-of-yourself-by-half? Some friendly ego-puncturing banter is usually on tap. At your wit’s end with a difficult student or class? A sympathetic shared eye-roll can work wonders. Plus there might even a few good ideas thrown in for good measure.

A good school staff room is not always synonymous with a “good” school, but a good staff room can make even a “bad” school bearable — enjoyable, even! — and the lack of one can make even an “outstanding” school feel like a souless and joyless treadmill.

If you are being interviewed by more than one school, choose the one that has the beat-up, well-used furniture in the staff room, replete with dirty coffee mugs and tottering piles of unmarked marking whose lower layers are being spontaneously formed into sedimentary rock by the crushing pressure from above.

Sadly, I feel that that this type of staff room is a vanishing phenomenon. I suppose that I am like a dinosaur complaining that bromeliads these days don’t taste as nice as the bromeliads they had in the old days.

Teachers today just aren’t rubbing elbows as much as they used too. H’mmm. Maybe that’s why we don’t have to wear elbow patches any more…

But that does not detract from this universal truth that should, I feel, be more universally acknowledged: if a staff room is suspiciously neat and clean and looks like an airport lounge…RUN AWAY!

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