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.
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.
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.
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.
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