Monthly Archives: May 2018

Crossing Cognitive Chasms With P-prims

Crossing a cognitive chasm . . .

Apparently, roughly 10% of humans still believe that the Earth is larger than the Sun. Do they believe this because they haven’t been properly educated? Possibly. Do they believe this because they’re stupid? Probably not.

In fact, the most likely explanation is that the individuals concerned just haven’t thought that much about it. The Earth looks big; the Sun looks like a small disc in the sky; ergo, the Sun is smaller than the Earth.

The individuals are relying on what Andrea diSessa (1988) would call a phenomenological primitive or p-prim: “These are simple abstractions from common experiences that are taken as relatively primitive in the sense that they generally need no explanation; they simply happen.”

What is a p-prim (phenomenological primitive)?

A p-prim is a pattern of thought that is applied across a range of contexts. For example, the “Ohm’s Law” p-prim — the idea that increased “effort” invariably leads to a larger “outcome” and that increased “resistance” always yields a smaller “outcome” — is routinely applied not just to the domain of electrical circuits, but to the physical world in terms of pushing and pulling objects, and not least to the domain of psychology in the context (say) of persuading a reluctant person to perform an action.

Examples of other p-prims would include:

  • The “Father Dougal” p-prim: things that look small really are small; large things always look bigger than small things.
  • The “More Is Better” p-prim: that more of any quantity is invariably better than a smaller amount.
  • The “Dynamic Balance” p-prim: equal and opposite competing “forces” or “influences” can produce an equilibrium or “static outcome”.

P-prims are not acquired by formal teaching. They are abstractions or patterns extracted from commonplace experiences. They are also, for the most part, primarily unspoken concepts: ask a person to justify a p-prim and the most likely answer is “because”!

Also, p-prims exist in isolation: people can easily hold two or more contradictory p-prims. The p-prim that is applied depends on context: in one situation the “Ohm’s Law” p-prim might be cued; in another the “Dynamic Balance” p-prim would be cued. Which p-prim is cued depends on the previous experience of the individual and the aspects of the situation that appear most significant to that individual at that particular time.

The KIP (Knowledge in Pieces) Model

diSessa integrates these p-prims (and many others) into a “Knowledge in Pieces” model:

[I]ntutive physics is a fragmented collection of ideas, loosely connected and reinforcing, having none of the commitment or systematicity that one attributes to theories.

The model is summarised more poetically by Dashiell Hammett (quoted by diSessa):

Nobody thinks clearly, no matter what they pretend. Thinking’s a dizzy business, a matter of catching as many of those foggy glimpses as you can and fitting them together the best you can. That’s why people hang on so tight to their beliefs and opinions; because, compared to the haphazard way in which they arrived at, even the goofiest opinion seems wonderfully clear, sane, and self-evident. And if you let it get away from you, then you’ve got to dive back into that foggy muddle to wangle yourself out another to take its place.

— Dashiell Hammett, The Dain Curse

So, for example, a person might respond to the (to them) out-of-left-field question of “Which is bigger: the Earth or the Sun?” by simply selecting what seems to them a perfectly appropriate p-prim such as the “Father Dougal” p-prim: the Sun looks like a small disc in the sky therefore it is smaller than the Earth. It is important to note that this process often happens without a great deal of thought. The person reaches into a grab-bag of these small units of thought and takes hold of one that, at least at first glance, seems applicable to the circumstances. The person is simply applying their past experience to a novel situation.

Picking Your P-prim

However, as Anne Nelmes (2004) points out, the problem is that often the wrong p-prim is cued and applied to the wrong situation. As science teachers, is there a way that we can encourage the selection of more suitable p-prims?

Nelmes believes that there is:

Analogy has long been used to aid understanding of scientific concepts, both in and out of the classroom. Rather than trying to overtly change the misconception into the scientific conception, it may be as, or more, effective and certainly less time consuming to cue the right idea using analogy on a very low key level, without the pupils even realising that an analogy has been used. The idea of cueing correct ideas comes from work done by diSessa and others on p-prims (phenomenological primitives). These are small knowledge units which are cued to an active state to explain phenomena.

It is hoped the correct p-prim will be cued by use of the analogy and, if cued repeatedly, will strengthen.

One example presented by Nelmes that I find quite persuasive is in the context of students’ difficulty in accepting that good absorbers of heat radiation are also good emitters of heat radiation. A matt black surface will absorb a substantial fraction of the infrared radiation falling on it; however, matt black surfaces are also the most effective emitters of infrared radiation.

aborbers emitters

This seems a concept-change-too-far for many students; particularly as it often follows hard on the heels of good conductor = poor insulator and good insulator = poor conductor. Students find it hard to accept that a substance that is good at one thing can also be good at its opposite.

Nelmes suggests cueing a more appropriate p-prim for this context by the use of low key analogies such as:

  • Effective communicators are good at taking in information and good at giving out information.
  • Effective netball players are good at throwing the ball and catching the ball.

Nelmes’ research suggests that the results from such strategies may be modest but are generally positive. One telling example is the fact that many student answers featured “you” as in “I think this because when you are good at something, radiating, you are usually good at the other, absorbing heat.”

As Nelmes notes, the use of the personal pronoun in such answers suggests that students had, perhaps, absorbed the bridging analogy unconsciously.

Be that as it may, I think the p-prim and bridging analogy strategy is one I will be attempting to add to my teaching repertoire.

References

diSessa, A. A. (1988). Knowledge in pieces. In G. Forman & P. B. Pufall (Eds.), Constructivism in the computer age (pp. 49-70). Hillsdale, NJ, US: Lawrence Erlbaum Associates, Inc.

Nelmes, A. (2004). Putting conceptions in their place: using analogy to cue and strengthen scientifically correct conceptions.

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Teaching Electric Circuits? Climb On Board The Coulomb Train!

I’ve said it before and I’ll say it again: teaching electric circuits is hard.

Providing your students with a conceptual model can, in my opinion, be immensely helpful. In recent years, I have used what I call the Coulomb Train Model (CTM). It is essentially a variation on the “stiff chain”-class analogies that some researchers have argued as being particularly useful in developing students’ understanding.

One reason why I like the CTM is that it provides a physical picture to aid students’ comprehension of many of the electrical equations needed at GCSE.

Of course, any analogy or model will have its flaws, but on the whole I think the CTM has fewer than many of its rivals!

Essentially, the CTM pictures an electric circuit as a continuously moving chain of postively-charged “trucks” called coulombs that carry energy from the cell to (say) the bulb. In the diagram below, they should be pictured as moving clockwise.

The coulomb is, of course, the S.I. unit of electric charge, so rest assured that there is method in the apparent madness of naming our “trucks” with a word that would be unfamiliar to most of our students.

Charge flow = current x time

Charge flow = number of coulombs that pass a given point in time.

Current = number of coulombs that pass by in one second (i.e. current = charge flow / time).

In other words, an ammeter counts the coulombs passing by in one second. The ammeter only “sees” the coulombs and does not register how much (or how little) energy each one contains. Therefore current I1 and current I2 are equal.

The ammeters are shown as being semi-transparent in order to provide a visual cue that they are low resistance devices.

Energy transferred = charge flow x potential difference

On the CTM, potential difference can be pictured as energy being added to, or removed from, each coulomb.

For example, if one joule is removed from each coulomb as they pass through the bulb, the potential difference across the bulb is one volt. If one joule is added to each coulomb as they pass through the cell, then the potential difference (or e.m.f.) across the cell is one volt.

The total energy transferred from (say) ten coulombs passing through the bulb would be charge flow (10 coulombs) x potential difference (1 volt) = 10 joules.

The white gloves on the voltmeter are intended to be reminiscent of the white gloves of a snooker referee.

The intention is to disrupt the flow of the coulombs as little as possible and so this is a visual reminder that a voltmeter is a high resistance instrument.

To emphasise the fact that potential difference is an “energy difference”, challenge students to predict the reading on this voltmeter.

The potential difference V3 is, of course, zero since there is no transfer of energy to or from the coulombs.

Current in Series and Parallel Circuits

I think the CTM can be really effective in allowing students to a see a comprehensible physical analogue of the circuits.

For example, I3 = I4 = I5 = 0.5 amps; I6 = I11 = 2 amps; and I7 = I8 = I9 = I10 = 1 amp.

Potential difference in series and parallel circuit

Equally, I think the CTM can give a comprehensible physical picture of the situation.

In this case (assuming the the cell has a p.d. of 1 V and the bulbs are identical), V4 = V5 = 0.5 V.

In the parallel circuit, each bulb tranfers one joule of energy from each bulb, and so the potential difference across each bulb is one volt.

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Ohm From Ohm

Amongst the myriad inconveniences and troubles of a Physics teacher’s life, the choice of the symbols commonly used to represent voltage, current and resistance, must surely rank in the top ten.

V is for voltage in volts, V

Well, OK, that’s sensible enough. On a good day, I may even remember to call it “potential difference”. The sage advice of Never use two words when one will do is commonly accepted by everyone; however, Physics teachers have, as a profession, decided to go it alone and completely ignore this tired old saw. Thus, voltage is become potential difference because of — erm, reasons (?)

One can only hope that everyone got the memo . . .

R is for resistance in ohms, Ω

R for resistance? That’s fairly sensible too.

“But what’s that weird squiggly thing, Sir?”

“Ah, you mean the Greek letter omega? Because Physics is soooo enormous that the measly 26 letters of the Latin alphabet ain’t big enough for it…”

I is for current in amps, A

“WTφ? Are you taking the πΣΣ, Sir?”

“I know, I know! Look, if it helps, think of it as short for intensité du courant . . . Wait, don’t leave! Stop, I have many more fun Physics facts to teach you! Look, here’s a picture of Richard Feynman playing his bongo drums — nooooooooo!”

Ohm’s Law: or is it more a sort of guideline?

Let’s start with a brief statement of Ohm’s Law:

V = I R

Except, that’s not Ohm’s Law; it’s actually the definition of resistance:

R = V / I

There is not a single instance where it is not true by definition. The value of resistance will always be equal to the ratio of the potential difference and the current.

Think of it like this. At room temperature, 1 V of potential difference can push (say) 0.5 A of current through the wire in a filament bulb. (I just love that retro 1890s tech, don’t you?)

This means it has a resistance of 1/0.5 = 2 ohms. However, bump up the potential difference to 6 V and the current is (say) 0.75 A. This means that is has a resistance of 6/0.75 = 8 ohms. Its resistance has changed because it has become hotter. In other words, its resistance is not constant.

Ohm’s Law is perhaps most simply stated as:

The potential difference is directly proportional to the current over a range of physical conditions (including temperature).

Using standard symbols:

V α I

or, taking R’ as a constant of proportionality:

V = I R’

You do see the difference, don’t you?

In the first example, R is not a constant value for a given range of physical conditions: for example it can get higher as the temperature increases.

In the second, R’ is constant over a range of temperatures and other physical conditions.

And so there we have it: V=IR can be a perfectly valid statement of Ohm’s Law, provided it is specified that R is constant. If one does not do that, then all bets are off…

In the meantime, here’s another picture of Richard Feynman playing the bongo drums. Enjoy!

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Assessment Will Eat Itself

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

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

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

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

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

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

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

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

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

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

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

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

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

Pride and honest professionalism: they are the ultimate Watchmen.

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