Tips on communicating science to a class

Yes, I am still alive.

My wife and I just returned from a long hiking and climbing trip out in the western states. It's tough readjusting to normal life after having been on the road for a month, but I've managed to slowly get back into the world of science while I wait out the visa application process for Switzerland.

Today I came across an interesting article in Wired called "A Media Guide for Physics" by Rhett Allain. In the article, Rhett gives a few tips for producers of science TV shows that would help them communicate science better. His tips are

1. don't be wrong;
2. it's better to say nothing than to be wrong;
3. don't be misleading;
4. [don't focus] on comparisons and numbers;
5. don't get out of control crazy.

I agree with Allain on all these points, especially the last one. Though this example is not from TV, I've noticed that graduate students (myself included) will tend to describe the minutiae of their research to lay people because they don't want to be wrong and because they've been so immersed in it that they forget what other people know and don't know.

The article also got me thinking about what tips teachers and educators should use when communicating science to their students. The list must necessarily be different because the audience is different. What follows is my own list of tips that I think are valuable to college professors when communicating concepts to a class.

1. Don't assume that students are well-grounded in the "background" material and concepts.
2. Don't gesture too much while lecturing. When you gesture, you're referring to an image in your head that only you can see. At least put that image on the board.
3. Present ideas visually and verbally before going into derivations.
4. Include a little history behind the concept you're about to teach if there's time. The reasons for why a concept is important are often found in the history of the development of the idea. For example, Newton's laws seem obvious now, but philosophers had some very muddy ideas about motion before Newton formulated them. And all of thermodynamics arose out of a need to understand how newly invented engines and devices worked. If you start a class by talking about molecules in a box, the relevance is lost.

The list is obviously not exhaustive, but I've seen many professors violate one or more of these to the detriment of their students' understanding. What other tips might be included?

The Reynolds number: A case-study about a simplified concept

Lately I've been re-reading some older papers on random walks in colloids to prepare for my dissertation proposal. One such paper from a 2007 PRL issue is entitled "Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk." The first sentence reads

"The directed propulsion of small scale objects in water is problematic because of the combination of low Reynolds number and Brownian motion on these length scales."

This struck me as particularly interesting because I had never considered the Reynolds number as useful for describing particle transport within a fluid; rather I always imagined it as a number that somehow answered the yes-or-no question "is this bulk fluid turbulent when flowing?" This conceptualization of the Reynolds number comes from my fluid and thermal systems class in the sophomore engineering curriculum at Rose-Hulman. Since I am so much wiser now than I was then, I decided to re-examine this number and its importance.

After consulting Wikipedia, I now understand the Reynolds number as a dimensionless ratio of the magnitude of the inertial forces transmitted by the fluid to the viscous forces. In other words, higher Reynolds numbers means that the fluid molecules will all move in more-or-less the same direction for longer periods of time and over larger domains. If something perturbs a region of the fluid at very large Reynolds numbers, the perturbation is transmitted by a large-scale, correlated motion of the molecules. This is because the dissipation of the fluid does not suffice to damp this motion.

Going further, this picture explains why scientists who study complexity and emergence love turbulence. If a system can not quickly dampen a fluctuation (in this case a small pocket of correlated motion within the fluid), it grows chaotically into a large-scale turbulence. Often, ordered patterns of fluid motion emerge from this chaos, like in Benard cells. So the Reynolds number leads to much more than a simple answer to a yes-or-no question; the physics behind it describes the chaos and complexity of turbulence itself.

This introspective exercise also demonstrates the short-comings of over-simplifying a concept when teaching it to others. I was blind to the connections between Reynolds number, the microscopic behavior of a turbulent fluid, chaos, and emergence for so long* because I only considered the yes-or-not question above, not the concept behind the number.

*It's been 8 years since I took that class. Yikes, I'm getting old.

Teachers vs. students: when interests don't coincide

I recently had a discussion with a close friend who is not a physicist by training but is very interested in many popular physics ideas. I was attempting to explain several paradoxes and non-intuitive scenarios such as Schroedinger's cat, the twins paradox, and the relativity of simultaneity. However, my friend was not impressed by some of these ideas, like Schroedinger's cat, and proclaimed them as "stupid."

I was of course exasperated by her failure to appreciate these concepts. Out of frustration I refused to explain any further ideas despite her questioning. As you could imagine, my refusal angered her; she interpreted my actions as pompous and arrogant. Fortunately, we are both open-minded to our own faults and quickly apologized to one another.

This bout made me realize that a teacher can't always convey why a topic is interesting. Interest is, after all, a personal attribute that varies between individuals. This mismatch of interests can cause a great deal of friction between a teacher and student and should be recognized by both sides for education to be successful.

Teachers must concede that sometimes students just aren't interested in a topic. A good teacher will be patient, even with difficult students, when they encounter a lack of interest. Eventually, the student will show interest in something that the teacher can help them learn about. Students should acknowledge when they are uninterested but still respect their teachers' enthusiasm. More importantly, they should not interpret their lack of interest as a failure to understand subtleties of a topic.

What's not so clear to me is with whom the greater responsibility for learning should lie. I'm inclined to place the greater burden on the student.

A hierarchy of concepts

Richard Feynman, in his Lectures on Physics, had a habit of discussing both the philosophical and practical issues of the science that he taught. One such issue was on the idea that waves could possess particle-like properties, such as momentum and position. As he notes in his Lectures, Vol. 3,

"Only measurable quantities are important to physics. This is false. We need to extend current concepts to unknown areas and then test these concepts. It was not wrong for classical physicists to extend their ideas of momentum and position to quantum particles. They were doing real science, so long as they then checked their assumptions."

What I believe is of value in this statement is the idea that understanding new phenomena is achieved by applying concepts from already well-understood processes and things. So what if a wave didn't traditionally possess momentum or a position? These two concepts (waves and particles) could at least be used to further our understanding of quantum entities, which possess both wave and particle-like properties but do not act entirely like one or the other of these classical constructs.

The same idea I think can be applied in teaching. First find a concept that students are familiar with, then show how this concept can be extended to describe a new phenomenon. However, to be self-consistent and complete, a discussion of how the concept fails to completely describe the phenomenon is required as well. Momentum and position obviously can't describe quantum interference of particles. In this manner, a knowledge of the world is built up of a patchwork of prior understanding.

Addendum
I found this statement particularly enlightening:

"When a data set is mutilated (or, to use the common euphemism, ‘filtered’) by processing according to false assumptions, important information in it may be destroyed irreversibly. As some have recognized, this is happening constantly from orthodox methods of detrending or seasonal adjustment in econometrics. However, old data sets, if preserved unmutilated by old assumptions, may have a new lease on life when our prior information advances."