e=mc2andallthat

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 Physics, 69(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 Physics, 68(S1), S52-S59. http://mapmf.pmfst.unist.hr/~luketin/Physics_education/resources_Hammer.htm