What do I add to a first-year university physics class on simple harmonic motion? Anything?
What’s the point of a class on simple harmonic motion?
Why do first-year physics classes exist?
I was thinking about these questions exactly six months ago, pre-pandemic, when I started writing a blog post that seems especially relevant now. I therefore decided to finally finish it.
On that morning (February 17, 2020) I ran a session of a second-quarter, first-year undergraduate physics course, substituting for a colleague who was out of town. As I prepared for it I wondered: Is this a waste of time? Both “yes” and “no” are valid answers, and there are arguments for each that touch on broader questions of what college is for and what faculty are for, especially in an era of abundant information. Many discussions of these topics are rather abstract; I often find it interesting to consider specific situations. Hence, this post.
The topic of the class was an important one: simple harmonic motion, the rhythmic, sinusoidal oscillation shown by a swaying pendulum, a mass hanging from a spring and bouncing up and down, and countless other systems. These systems need not be mechanical, which is why the subject is so crucial — the oscillator can be an electromagnetic field, a chemical concentration, a gene expression level, anything for which there is a force (or something analogous to a force) that pushes back towards an equilibrium state and whose magnitude is proportional to the displacement away from equilibrium (or something analogous to displacement).
The learning goals of the day’s class were that students should understand how to set up and analyze the differential equation governing harmonic motion for the paradigmatic case of a mass on a spring, extracting for example the period of oscillation, and understand the the general lesson that a linear restoring force leads to sinusoidal oscillations.
My own goals were the standard ones, and #1 and #3 especially made up the regular instructor’s class plans:
- To convey the content noted above.
- To motivate the topic and its analysis.
- To answer questions and assess student understanding.
Let’s think about these.
#1 — Content. Not surprisingly, this ground is exceptionally well trod. Not only is simple harmonic motion covered in every introductory physics textbook, but there are nowadays many excellent, freely available videos and online resources, in formats ranging from traditional lectures to animations. Even when I was a kid, there was information out there — in books mainly, but also from other sources. (I used to enjoy watching the Mechanical Universe series on the local public access TV channel.) Nowadays there are hardly any barriers of time, cost, or availability separating a student from high-quality content, at least at the school or first-year-college level. As a consequence, there is absolutely nothing in terms of content that I provided that isn’t readily available elsewhere.
#2. Motivation. I began the class by introducing myself and providing examples of the wide-ranging importance of harmonic motion. Some were standard examples; some were not. I shared a video from my research lab of oscillating membranes (shown below), as a non-obvious example of how analyzing oscillations can reveal the physical properties of interesting materials, like cell membranes. A large part of education consists of motivating students to devote the often considerable effort needed to study the subject; examples of its relevance help. They don’t necessarily need to be examples related to the instructor, but we’re social creatures, and connections to the person talking to us really do help students engage. One student told me after class that she’s interested in my research and would look up my lab’s web page, which was nice to hear.
#3 — Questions and Assessment. An important part of classes is that they give students an opportunity to ask questions. There’s much more of this in smaller or higher-level classes than in large introductory classes; the latter typically have only a few questions. An equally important part of classes is me asking questions, both to spur thinking and to get a sense of what people understand. As is usually the case in such classes, I asked “clicker” questions, surveyed the answers and had students discuss various choices with each other.
Goals and activities revisited
Six months later, amid a pandemic that has put classes like this on-line rather than in-person, how do these statements of goals fare?
Item 1, content, was a feeble justification for standard introductory-level classes to begin with. At best, one might argue that, rather like a concert, there’s something psychologically appealing about 100 people in a room experiencing the same content delivery, even if the delivery isn’t great. Or we can note that students consistently complain when classes aren’t used for content delivery, which tells us that despite its pointlessness we should continue providing our “customers” with what they want. On-line, however, the concert-like appeal is essentially gone, and no one finds a lackluster Zoom lecture preferable to the best of what’s out there seen on exactly the same laptop screen.
Items 2 and 3 are the only features that justify the existence of the standard class. They’re not bad justifications, but we would structure courses differently if both faculty and students were more upfront about what we want from courses. Such conversations would be difficult: universities would have to acknowledge that there isn’t secret knowledge that only their classes can convey, and students would have to acknowledge that being fed material that is easily accessible to them elsewhere is a waste of time. On-line, it’s not clear whether seeing the virtual me on the screen motivating the topic adds anything compared to on-screen recordings of others’ motivations, but even if so, this hardly takes a few minutes. Questions and assessments are, then, the only remaining meaningful feature of a class. (I should write more about assessment more broadly, especially the question of how we can acknowledge the efforts of those who study topics on their own.)
In the pre-pandemic world, we largely ignored these issues. Of course, many of us discussed them and worked to make our courses more centered on active learning, for example, rather than content delivery. But fundamentally, there was little change. Students, to my continual amazement, went along with consistent and stunning tuition increases, year after year, without protest, being charged more and more for increasingly unnecessary educational formats.
Now, however, we (and most universities) charge full tuition for online-only courses. Students can’t tell themselves that their $13,000/year (Oregon resident) and $37,000/year (non-resident) tuition is warranted by some vague “college experience” they get. Faculty are more starkly faced with questions of purpose, though our response to this still seems muddled and self-centered.
The question to ask
Six months ago, I struggled to find meaning in the single day of the intro-level class I taught. If I were to do it again, now online, I couldn’t go through with it in the same way, spending any appreciable class time writing down the diagrams and equations of simple harmonic motion. It would be unconscionable, given the fees students are paying and the better material freely available to them. To transform completely into a flipped or coaching-like model would be a shock to many students, however. As a constructive means of making change possible, I would suggest that every course begin with each student, as well as the instructor, answering the question: Why does this class exist in its current form?, with responses separately addressing the topics of content, motivation, and assessment, and with prior discussion of what aspects of the course content are standard and readily available. This will be hard for the students, many of whom have never thought seriously about the question of what a course should be. It may be painful to discuss. It may take us, however, toward a more productive and engaging form of higher education that can withstand all sorts of disruption.
A zebrafish. Given their importance to my lab’s research, I’ve often thought I should get better at drawing or painting them. This one is ok, but there’s considerable room for improvement.
— Raghuveer Parthasarathy, August 17, 2020