I’m following up my previous post about warm-ups in Physics 2, where I’ve been trying to use warm-ups as a venue for extracting more value out of class without giving up much time. So far, the experiment seems to be paying off.
But, what do I do on a day when I really don’t have much time to give up to warm-ups and I really don’t have much time to plan a whole activity? For this, my go to move over the past few weeks is to just look at some of the tricky mathematical or procedural aspects of the problems we will be solving and make them warm-ups.
For example, we were doing problems with diffraction earlier this week. I know that students struggle with unit conversions in these problems because the exponents are large. For example, in diffraction problems you are dealing with nanmeter wavelengths, micron apertures, grating densities described in cm or mm, lengths describes in m or cm, and diffraction patterns described in mm. I also know that students do not know or remember anything about the small angle approximation, which comes up in a our lab. So there you go, two warm-ups for the day– a little bit of practice doing unit conversions with a focus on talking about different strategies, and little mini-exploration of how tan, sin, and theta compare for different triangles. I actually pick values for them to practice that show up in my example problem, their problem, or the lab.
During class, I realized another warm-up that we needed was thinking about how to relate “slit density” to “slit spacing”. Not sure exactly what that warm up would be, but that reasoning is always a struggle for students. It’s the same reasoning that shows up elsewhere in physics, so I’ve seen students struggle this and resort to memorization of formulas like T = 1/f.
All and all, the key I think to these “obstacle” warmups is to emphasize the reasoning and strategies, and this alone helps makes them pretty good warm-ups even if how I structure the warmup isn’t all that great. By front-loading some of the obstacles well before they encounter them in the midst of problem-solving, it makes the classroom more manageable. Without warms ups, I’ll often get six of out of eight groups stuck at the same spot at the same time. With warmups, maybe only one or two groups will need some help from me on those areas, and usually it’s just a reminder of the strategies we talked about in the beginning. Students feel a little more equipped to tackle the problem.
I imagine you could certainly go overboard, trying to frontload all the obstacles and that would be a mistake. I think my goal is to front-load the obstacles that obscure thinking about the underlying physics. I could also think about front-loading such obstacles for pre-class assignments, but then I think it would be harder to focus students on the reasoning and strategies.
Note: I think one reason I’ve been thinking about this part of my planning so much is this: I want to be able to circulate around the room and have interesting conversations with my students about their understanding of the physics, but that just doesn’t happen if my students are frustrated, or bogged down in things like unit conversions, or all simultaneously stuck on the same part of the problem. My best attempts at proximal formative assessment (e.g., listening to students, asking good probing questions) get destroyed if I am circulating around the room putting out fires.
I’ve known for a long time that planning has always been the weakest part of my skillset, having written almost 4 years ago:
“I will say that my weakest area is as architect (choosing tasks to use with student as well as deciding how those tasks should be carried out), especially thinking about the design of a whole course. I haven’t had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability.”
I think now that I wasn’t getting away with anything. And I even think my thinking about planning (or warmups more specifically) now is nothing unique or special, and not even particularly great. What I think is amazing is how much even small improvement to my planning (and my thinking about planning) can make a difference.
Teach. Brian. Teach. 
I tried something in class the other day that I don’t think worked well. We were talking about the doppler effect, and we had done a pretty good job with explaining the origin of the effect (simulations, past experience, water wakes, etc). Then we tackled how the effect could be put into math. We worked on how the wavelength shrinks and how the listener affects the apparent speed of the wave. Then I did my new thing: “Here’s the end result (Doppler equation). We have all the physics on the board, the rest is algebra.” What’s interesting is that, as a student, I wouldn’t have been able to handle that. I would have insisted on figuring out the algebra before paying attention again. I asked a student who had a confused look on her face whether she could handle it, and she said “I have faith in you” meaning she trusted that I would show them how to do the algebra in one of my many follow up videos that I make. I thought of this because your point about “putting out fires” is exactly how I feel when I’m helping a whole bunch of students see how to do what is basically “just” algebra.