One thing I’ve been trying to do in intro physics this year is get students working on problems that are more challenging that what they’ll see on the exam. Typically our first exam  has a back-and-forth problem where each stage is constant velocity, an acceleration problem that has no back-and-forth aspect, and a free-fall problem where there is a turn-around point.

In my class, we’ve been doing more horizontal acceleration problems that include turn-around points (e.g., using fan carts along a track). This gives students more practice thinking about direction of velocity and acceleration, instead of just memorizing that for free-fall that acceleration is down.

We’ve also been doing more multi-stage problems where parts of it are constant acceleration and others parts of it are constant velocity (e.g., a car speeds up, maintains a speed, and then slows down). This gets students practicing identifying when they need to apply a constant acceleration model or constant velocity model, and also thinking about how to string them together (e.g., the final velocity in stage one is the constant velocity in stage two).

We’ve also been doing more problems involving multiple moving objects (e.g., where or when will two objects meet?). These problems are really the only problems that get students distinguishing among position, distance, and displacement in my mind.

One of the things I like about this is that it means students will be evaluated at level below where I’ve been helping them get to.  However, it has had some interesting negative consequences for exam preparation. Before, students just had to memorize three kinds of problems–back-and-forth, 1D acceleration, and free-fall. They could get by just memorizing, “On these kinds of problems you do this, and one those kinds of problems you do that.” For example, students would know to use multiple stages only on the back-and-forth problem, not on 1D acceleration or free-fall, where they should just set up their variables and plug into one of the equations. Since I’ve been having them practice lots of mixed problems, where there are multiple stages of constant velocity and constant acceleration, students can’t rely on just memorizing. They actually have to make sense of the problem and thinking about what to do.

In this context, I’ve seen students struggling or making “mistakes” I’ve not seen before.

For example, a problem will say, “A fan cart is given a quick push to right, such that it starts with an speed of 12 cm/s. The fan is oriented such that the cart immediately starts slowing down. Three seconds later, it’s moving to the left with a speed of 3 cm/s.”

I’ve seen more students trying to figure out the kinematics of how it go up to 12 cm/s, or thinking that it maintained that 12 cm/s for some amount of time. Or, because the problem doesn’t explicitly use the word acceleration (it’s inferred based on the context and the fact that we’ve been observing fan carts in class a lot), some try to treat it as a back-and-forth problem where it had a constant velocity of 12 cm/s for a while, and then a constant velocity of 3 cm/s for a while. It certainly could be I’m writing ambiguous questions. The thinking and struggling they are doing is fine, and it’s productive for them to be struggling with this. But I fear this may hurt them on the exam–instead of just launching into a quick procedure, based on “which of three possible problems is this”, they’re going to be actually thinking on the exam. It’s not necessarily true that you do better on tests when you do more actual thinking. Tests often favor over-practiced routines. I think I’ve been preparing students to be more adaptive, at the expense of having over-practiced a small number of routines.

While I do want my students to learn meaningfully, I also want them to feel like they’ve been well prepared for the exams, especially the first one. It gives them confidence, and leads them to trust me and what we’ve been doing in class to learn even more. Maybe all my concerns are overblown, but I guess we’ll have to see.