Phys 87: Thinking Like a Physicist

Meets Wed. 3–3:50 PM in MHA 2623 Fall quarter, 2016

Problems

The Goal

This Freshman Seminar is meant to free the minds of our students so that they approach problems with flexibility, intuition, and quantitative estimates. You think that's π you're smelling?

The Symptom

Students in physics classes often have problems transitioning from the lower division courses into upper division courses. Many reasons contribute, but one observation is that students have developed a habit of solving problems by pattern-matching. This can come in the form of equation-hunting or relying on exposure to essentially identical problems from the past.

Human beings are powerfully adept at pattern recognition, and this versatile tool can get us rather far—all the way to upper-division physics. At this point, concepts begin to rule, and students must have a well-stocked toolbox of mathematical techniques at the ready—and know which tools to grab for the problem at hand. Sure, identifying relevant concepts and applicable tools also constitutes a type of pattern matching, but at a higher, more flexible level.

Observations

Causes

One may only speculate, but here are some thoughts:

The Cure

So let's try re-programming the way students approach problems before reaching the upper-division whiplash moment. That's what this Freshman Seminar aims to do. No guarantees that this will be successful, but let's try building comfort and versatility in thinking about problems so that students have better intuition and alternate ways to sanity-check their answers. Among the approaches, we will:

Some Philosophy

Famous physicists like Fermi and Feynman frequently forged formidable feats 'festimation. Less alliteratively, good physicists tend to have well-developed estimation abilities. Seldom are these skills learned in classes, but "learned on the mean streets," as my colleague George Fuller puts it. Maybe it's a selection effect: those who are good at estimation are more likely to succeed in physics/science.

For me personally, I learned at least as much in my explorations outside of class as I did in the formal classroom. I almost always had some problem I was chewing on, and my eagerness to understand and make progress drove new discovery. What's more, because I had problems in mind (some of which I got stuck trying to solve), when new concepts and tools became available in the classroom, I would think, "Aha! That's the piece I've been waiting for!" and I could return to the problem and do it less clumsily than before. By having context in mind already, I had carved out space waiting to be filled by classes. By exploring the problem before and after new techniques came along, I owned the material. It was personal. It meant something to me.

Examples of problems that occupied me during high school and college appear in the list below (not chronological). I'm sure I am forgetting numerous lesser problems, but these are the ones that stand out in memory. And yes, my tendency to actually carry out these schemes brands me as an experimentalist. But just because kid-me did some stupid things does not mean that adult-me condones these activities!

A word on emulation

The lesson should not be to copy what I did. Emulating a rock star's visible behavior is not effective (and will probably land you in jail!). Countless hours practicing and honing the basic skills is where it's at (which is utterly boring to most people). Concert pianists spent years perfecting excruciatingly uninteresting scales before spinning off masterpiece performances. Emulation is not in itself a likely path to success. Rather, find your own interests and ask your own questions. Let your curiosity guide you. Plunge in to solve problems or go as far as you can while you wait on pieces to fall in place. Don't be afraid to explore. It's stumbling into the dark that lets you build a picture of what you can't see by staring into that darkness.