In our physics department, every physics major has to serve as an undergraduate TA. Most of them get assignments in our algebra-based introductory physics course. Because of the manner in which most of these students were taught (i.e., find an equation and substitute numbers), they can easily find themselves feeling a bit lost in my class, especially if they think they are supposed to be an expert of the content.
For example, here’s a question discussed in class. A bowling ball is dropped from a height of 45m, taking 3 seconds to hit the ground. How fast is it moving the very moment before it hits the ground? The problem is intended to draw out the following answers and arguments, which we hash out.
10 m/s, because all objects fall at the same rate
15 m/s because you can calculate the velocity as 45m/3s = 15 m/s
30 m/s because it gained 10 m/s in each of the 3 seconds
Other more idiosyncratic answers come up as well, but not with high frequency.
The first answer points to the ways in which students haven’t yet teased apart clearly the meaning of acceleration and velocity. The second answer points to the ways in which students haven’t yet teased apart clearly the meaning of average and instantaneous velocity. The third answers is consistent with the idea of constant acceleration. We hear arguments, and counter-arguments, and at some point I help clarify the right reasoning, and what’s both so tempting and subtly wrong about the other answers.
So, here is the way the TA solved it, before class began.
xf = (vf + vi)/2 * t + xi
0 = (vf + 0)/ 2 * 3 + 45
0 = 3/2 v + 45
-45 = 3/2 v
v = – 30 m/s
While the TA could solve this problem, they didn’t have a rich set of ideas for thinking about. It didn’t seem obvious that 30 m/s makes sense, because of the idea that its 10 m/s/s, or because final velocity sould be twice the average velocity (since it accelerated from rest). For other questions without numbers that we discussed, the TA seemed just likely as students to give answers inconsistent with the concept of acceleration. I’m perfectly OK with that, but my suspicion is that the TAs aren’t prepared for this. They aren’t prepared to be wrong about so many things or confused about so many things. I wonder how I can better position them as learners in the class–learners who just know somethings that the first-time students don’t, but not everything.
Of other interesting note is this. In my physics content course for future physics teachers, the students that have had me for a semester or two are pretty rock solid on having a repertoire of ways of think about kinematics problems, and also for avoiding common pitfalls. The others are pretty much falling for all the pitfalls. The difference is pretty striking. The thing that I like is that the range of expertise we have allows for peer-coaching, but also some, “Hey, it’s OK. We were making those exact same mistakes 4 months ago,” and, “Yeah, get used to it. Brian isn’t too into solving problems by putting numbers into equations.”