Saturday, September 18, 2010

Physics preconceptions

One of the interesting things about teaching introductory physics students is the weird mistakes they make.

For instance, many people come to class with the preconception that acceleration goes in the same direction as velocity.  You define velocity, and you define acceleration, and they see that they're different.

Then you draw a graph of position vs time and ask which way it's accelerating.  "That way," they say, and they point in the direction of velocity.  "So... the velocity is increasing in this direction over time?"  Confused stares.  Mumbled answers.  The answer is clearly "no," but doesn't that contradict their previous answer?

Later, we do a simple hands-on lab, with a cart on a track.  We tilt the track.  If we push up the cart and let it go, which way is it accelerating as it goes up?  Which way is it accelerating when it stops at the top?  And when it comes down again?  It's clearly changing direction... right, Mr. Miller?

When the track is flat, I ask them to show how they pushed the cart to give it positive acceleration.  They give a short and sharp push and let it roll freely.  See, acceleration!

After all this has been corrected, I ask them why it is we think acceleration is in the same direction as velocity.  Nobody knows.  I say, "I don't know either; I study physics, not psychology."

It's hard for me to sympathize, because I don't remember ever making this kind of mistake.  Maybe I just don't remember it.  But I sure didn't make the mistake repeatedly, having to relearn the same lesson every time the context changes just a little.

In my pedagogy class, we are learning a bit about the cognitive psychology of the naive conceptions brought in by introductory physics students.  We are learning what they are, where they come from, and most importantly, how to deal with them as teachers.

Don't expect me to blog much about this psychology stuff.  I'm quite aware that we only really scrape the surface, to practical ends.

But I will say that this sounds an awful lot like skepticism.  Skepticism is all about the strange things people believe, where they come from, and how to deal with them.  Skepticism is a lot like teaching.

The difference is that the subjects of skepticism are often hostile to it, and skeptics are not in any position of authority.  Come to think of it, this is a really huge difference.  As a physicist would say, this can't be modeled as a small perturbation.  Maybe skepticism is nothing like teaching after all.

Anonymous said...

I just started grad school as well, and am doing TA work. I've also been wondering about the preconceptions the students have, and other problems they might have with understanding physics.

The preconception that acceleration and velocity are always in the same direction is a common one, as you pointed out. I think the origin of this - just as the origin of the idea that force is necessary for motion - is their experience in having to actively apply some sort of effort to move despite friction. In particular, when they drive, the action of the motor turns the wheels; and the fact that pressing the gas pedal is often called "accelerating" even if it isn't increasing the speed of the car relative to the Earth probably doesn't help.

Another strange thing is the way the students put concepts together. I instruct three lab sections, and the answers the students give to homework problems get weirder as the week goes on. There was a recent lab involving Newton's second law and the homework had only one question. Most of my Tuesday section got it right; many from the Wednesday section erroneously brought the third law into their answer; and many from the Friday section started talking about normal forces, static and kinetic friction, etc. in spite of these having nothing to do with the problem. I'm inclined to think that the students are trying to learn the material without really fitting it into an over-arching structure that allows them to know what concepts are necessary for which problems.

Sorry to ramble on in response to your blog, but I felt that this was relevant.