This year in AP Physics 1, I began the year with kinematics in 1D. I moved on to a brief coverage of vectors and relative motion before discussing projectiles. I gave a pretty short time to projectiles because these students have had physics before, even if it was three years ago, and I believe the conceptual foundation is still there. The algebra skills are there, certainly. I made sure we did some graph stacks, and that was about it conceptually.
We had a test on kinematics in 1D and 2D, and have since moved on to the kinematics of Simple Harmonic Motion. This is an unorthodox second unit, but last year’s AP1 class experience caused me to think that this would be a very helpful topic to have at the very beginning of the year. Last week I had students do a prelab to graph the force-displacement graph for each of a pair of stretchy springs – Hooke’s Law. I just wanted them to find the “k” value of the springs and to think of that value as nothing more than the slope of the F-vs-delta-x graph. We barely had to talk about what a force is, in order to accomplish this prelab. It went well, and the following day the lab groups used their spring pairs to set up horizontal oscillators on a Pasco track. The springs went on the ends of a Pasco track and were stretched out and hooked onto the track stops. A few quick video captures and position tracking showed the following:
- Hey, it’s a sine wave. Or a cosine. Or a negative cosine I guess. (Okay they’re all sinusoids! That’s a vocab word).
- Hey, changing the amplitude doesn’t cause the period to change. (That’s a vocab word)
- Hey, putting masses in the cart makes the period increase but it’s not a linear relationship. Weird.
That’s all I wanted, so I was very happy with the results. I showed the students the Ts formula on the formula sheet and we did some algebraic acrobatics to verify that we could calculate things from the lab or from test-like questions.
But for me, the real payoff came this week, when I put a SHM position-time graph on the board and I asked the students to walk me through a graph stack to make velocity-time and acceleration-time graphs. I cannot emphasize how wonderful it is to do this with students who are in precalculus or maybe AP Calc AB. They do not yet know the derivative of the sine function, so we actually had to talk it out. Show me all the points where the slope is zero. Now show me where it is the most positive. And what does it do in between the zero and the most positive? They walked me through it and they told me it was easy. That’s the best kind of teaching.
This site was originally intended to note what I have done in my physics classes, but it has not been getting used because I never feel that I have the time to write up a blog post that does justice to the classes. That results in zero blog posts, which really do not do justice to the classes. So that’s got to stop.
The classroom I now inhabit is equipped with four fairly large mobile lab tables and a single, oval-shaped wooden conference table that was probably designed to seat about 14 adults, but manages to fit closer to 20 students when necessary. The table is usually referred to as “Harkness-style”, and I just want to take a moment here to link a blog post from a Chemistry teacher who toured Phillips Exeter Academy in New Hampshire, where the “Harkness Method” of teaching was first developed. As Hans (the blogger I linked) notes, the Harkness Method was developed at Phillips Exeter Academy in the 1930s and has been used in the humanities ever since… but they did not use that method in the science classrooms until the 1990s.
Rhett Alain is an Associate Professor of Physics at Southeastern Louisiana University. He is one of many physics educators who has impressed me by being insightful and funny on Twitter (@rjallain), and at Wired.com Science Blogs.
Recently, Rhett wrote about a brain teaser. Then people on Twitter and in the comments section of his blog told Rhett that he was wrong, and he responded in the way we all should – he admitted he was wrong. I suspect that most people think they would be honest and forthright when their errors are pointed out, but I don’t know that most people actually do that. I always appreciate it when somebody does it correctly.
But that’s not exactly what prompted me to reflect here. The puzzler Rhett wrote about reminds me a bit of another that I heard a long time ago (I have no idea the source):
A man starts at the bottom of a mountain at sunrise and takes all day to hike to the top, arriving at the summit exactly at sunset. He camps at the peak overnight. The next day he starts down the exact same path from the peak, beginning at sunrise and arriving at the bottom exactly at sunset.
Keeping in mind that he’s on the same trail, does it have to be true that at some point, he will be at the exact same place and time on the second day as he was on the first day?
Years ago when I first heard this, I figured the answer would have to be “no”. I’m not sure why – it was just a gut response. Probably the reason I remember the question years later is that my gut response was wrong, and the reason it is wrong was explained very clearly. If I change the way the question is asked, it should become very clear.
One day, a man walks up a trail from the bottom of a mountain to the top. During the same day, a woman walks down from the top of the mountain to the bottom, using the same trail. Does it have to be true that at some point, they will be at the exact same place and time?
Clearly the answer is yes. The rewording of the question didn’t just tell me that the answer is yes – it allowed me to see clearly that the answer must be yes. I think this experience is one of the best parts of learning and of teaching, and I relish every time I am able to help a student see why their gut response is incorrect. It’s almost as good a feeling as when somebody does that for me.
One of the most important things teachers ask students to do is to step back and gain some perspective on what they have been learning. Obviously, teachers must allow themselves the time and space to do the same thing. And as with students, we must seek feedback from others – peers and mentors in the field. I hope I am able to elicit some dialogue on various topics in education and physics. Without reflection and feedback, our ability to grow is compromised – and I would like to avoid that at all costs.