Thursday, March 20, 2008

Physics Curriculum Comment

The bulk of this was posted as a comment in the thread "Uncomfortable Questions: Physics Curriculum" in Uncertain Principles. I'll try to define the context of my remarks, but you might need to look at that to get all of it.

By way of background, my students do not have the 1240+ SAT average they get at Union College. Just looking at my students, the half that do have either SAT or ACT scores (a CC only requires a HS degree and a pulse for admission) are in the 1100 territory. The half that don't are probably not too far below that, but the spread is huge (like from 800 to over 1400). A typical FCI score is pathetic, mainly because the majority have not had any HS physics and half of the rest had a bad class. Foreign HS grads are the main exception to this rule.

Nonetheless, I agree 100% with Chad's main thesis that "My general suggestion regarding reform of introductory physics classes is that the goal should be to make them look less like high school physics." I do that with problem solving and pushing the math envelope whenever possible, usually in the second semester, but also get outside the actual text topics to connect to actual real-world engineering and physics problems.

My comments in his blog, repeated below, were not in any logical order nor do they follow his article in any particular fashion.

Regarding "Only about three percent of students who take introductory physics ever take another class in the subject. That's pretty dismal."

1) Compare the number of BS engineering degrees to the number of BS physics degrees and your 3% number is easy to understand, particularly when you consider the number of electives in a typical engineering program [zero].

2) One way to increase that number is to offer a "concentration" (if not a really minor minor) in physics that only requires a third course in modern physics. This can be popular with EE and computer engineers like you have, also materials science. Heck, *you* could tailor it to modern physics with an emphasis on (a) quantum mechanics, (b) lasers and AMO with a teaser about optical computing, (c) enough nuclear physics to be educated about the difference between a bomb and a reactor, (d) enough relativity to discuss astro topics and/or QED. You ought to get at least one extra major a year out of part b alone.

Regarding this posted comment In particular, it always amazes me how bad quantum mechanics classes are. The math is far easier than in E&M or analytical mechanics, yet students feel as though they are underwater the entire semester.

3) I agree 100% with #1 about QM. I evolved from a math undergrad to a physics grad student because I got hooked by a great freshman QM class that made the subject intuitive (to me, at least). If there is an area that needs reform, that is it. Why should the first "majors" class be intermediate classical mechanics?

Regarding "Most of the students in our introductory classes come in thinking that they're going to be engineering majors, and the just-like-high-school approach doesn't encourage them to change their minds."

In addition to my second remark up above ...

4) I am under no illusion that I am teaching mostly engineers at my CC, and I pitch the class that way, yet I have managed to produce some physics majors ... one of whom is applying to grad school this year. Could it have helped that I don't pretend that I am teaching "real" physics and frequently allude to the things you could work on when you do, as well as the next level problems my engineers will have to solve?

5) One of the other things that hooked me into physics was the nearly miraculous agreement between the solution of a system of coupled DEs for a double pendulum and a demo of same. This was also in the freshman sequence I took (out of the old Berkeley course that I saw used recently at MIT). The key there was a bit of non-trivial math explaining reality (really well) rather than a qualitative demo or 'easy' math problems.

5a) If you want to wake up your class, start out with F=ma and do an un-driven damped oscillator in the second week? Using a complex solution to the DE? Then do the pendulum out to the cubic term in the series? Then do the coupled system of two oscillators, with each of these tested by experiment.

Added comment: Part of the rationale here is to kick them out of their comfort zone. Just as half of the valedictorians at CalTech are suddenly below average, kids at Union should get a sense that more is expected of them than was needed to coast through high school. My challenge is the exact opposite. My students have an inferiority complex and need to realize that they can handle something they don't even dare teach to the university students they will compete with next year. This requires some coaching.

Regarding "while we're hitting them with block-on-an-inclined-plane problems that they've seen before."

Most of mine have not seen it before. Some insist they haven't seen it even after we did it in the lab! That is probably a universal problem.

6) Part of every class coasts through the first part of the 1st semester, but my survival fraction would fall significantly (maybe by a third or more) if we did not spend time on kinematics and problem solving. [My answers to the three questions I posted are quite different from yours, I am sure.] I cannot start with challenging modern concepts when most of they are still being challenged by word problems that generate two equations in two unknowns.

Regarding "might help to show them that physics is more than just memorizing lists of equations."

7) My response to the view that physics is about memorizing equations is to note that it should be about problem solving with a handful of equations. No one should give the "range" formula in a freshman textbook or use the elastic scattering equations. The students will only work from first principles if you do. And it does not hurt to give exam problems that have a symbol or three in the answer rather than just a number from a calculator just to be sure they can solve an equation without graphing it.

Added comment: I fight the "equation grabbing" approach every step of the way. Gauss' Law is not 7 equations for 7 different geometries, it is one equation plus your problem solving skills. Here is one place where I go way out of my way to make it impossible to equation grab to the final answer. One way is to ask for the first part of the solution, not the answer.

Further, since the biggest complaint about a typical sophomore entering engineering is that they can't solve a new problem or do free-body diagrams, I sometimes double up on that by giving them a nasty problem where the only thing I want is the correct free-body diagram. It never hurts to think.

Full disclosure: I knew guys in grad school who only got through the comprehensive exam by memorizing the solution to as many possible problems as they could. This approach is not limited to undergrad engineering majors.


Anonymous said...

I'm incredibly curious how you took an intuitive quantum mechanics class. I thought that was an oxymoron.

When I took QM, the only thing that made any sense was perturbation theory. (Of course, that was a while ago, so none of it makes any sense now.)

BTW, one little niggling thing: small t in Caltech. :-)

Doctor Pion said...

Maybe I should blog about that QM class. The trick was in showing us that everything we knew was wrong (and, since it was a freshman honors course, we thought we knew a lot) and developing a new intuition from day one. Just like when you live and work in a relativistic world doing research, those rules can become very intuitive. It is, after all, a local theory without the weirdness of action at a distance you get with gravity and none of those crazy "jumps" in Bohr's bogus version that is usually taught in 1st year classes.

BTW, I prefer to "camel hump" an abbreviation of the actual name of the CaIofT to using their version of it.

Anonymous said...

I'd be interested in reading about the class. It was one of those things I've always wanted to understand...and if you have a book reference, all the better.

Re: the big long as you've got a reason. I just thought I should warn you before someone really ornery came along. :-D