More substantive concerns about the intro physics course:
Algebraic representations are the dominant medium students are taught to use for doing anything with kinematics. Students do learn a little about graphs, but they learn it separate from thinking and problem-solving. They simply learn that you can graph data and that an instructor could ask you to interpret a graph either on a test or as a game. They are never asked to use graphs to help organize their thinking or to be their abacus when solving problems. They are also asked to do a few exercises with strobe diagrams, but once again, they are isolated exercises divorced from organizing one’s thinking about phenomena and solving problems. They are just another kind of question an instructor could ask you. Divorcing kinematic representations from each other and also divorcing representations from problem-solving is a big concern here. But my central concern is that the representations are not taught as representations of phenomena. They are all just things that an instructor could ask you interpret. Here’s a graph-interpret it. Here’s a strobe diagram-interpret it. Divorcing representations from their authentic epistemological function is a serious problem in terms of teaching scientific literacy or problem-solving. This is on top of the fact that the algebra is also not taught as a representation, but merely a set of four equations one should learn how to pick, rearrange, and plug numbers into.
No Quantitative-Conceptual Understanding
I want students to have a conceptual understanding of kinematic relationships that allows them to think quantitatively. One litmus test I use to assess students’ understanding of acceleration is this one: “An object accelerates from rest at 10 m/s per second. How fast is it going in three seconds?” If a student goes to grab an equation, I know something is wrong. There are other litmus tests such as, “A car steadily speeds up from 50 mph to 70mph, what was it’s average speed?” I’d like students to be able to say 60 mph quickly and confidently without grabbing an equation. If students don’t have ways of thinking about these questions conceptually and quantitatively, then the fact that they can plug numbers into equations should hold no weight in an assessment of their understanding of physics. I don’t care if they can do algebra problems pretending to be physics, if they don’t know any physics at all. Many of our students can’t do algebra problems pretending to be physics, and almost none of them know any physics. There are a couple reason for this:
- The curriculum spends no time developing the concept of constant velocity. Rather it just harps on the difference between average speed and average velocity.
- The curriculum spends no time helping students to understand the concept of instantaneous velocity, and how it is different from constant and average velocity. Without instantaneous velocity, acceleration is bomb shell.
- The curriculum divorces the concept of average velocity from accelerated motion. All they get is a list of equations.
After 1D kinematics, the curriculum goes to 2D kinematics. From 2D kinematics, we move to 2D forces. Both pretty much jump into finding components, again making the preferred tool algebra. We don’t spend any time in class talking about 1D forces, or talking about what forces do and why. Thus, students don’t understand the most basic idea of Newton’s laws, which is this: Pushing an object with 80N, is the same as pushing it with 100N when someone else is pushing back with 20N. Yeah, I said it, this is the most important concept for understanding forces. It’s not Newton’s 1st, 2nd, or 3rd law. It’s this idea (which I think Hestenes calls Newton’s 4th law): when multiple forces act on an object, wen can think of those multiple forces as having a combined effect that is a equivalent to effect of a single force which we call the net force. Because they haven’t been helped to make contact with this crucial idea in 1D, they are a total loss for 2D problems, except to follow mindless routines of finding components and writing down sum of forces. They have no idea what we are doing when we sum forces.
A student came to me before class yesterday and said, “I’m going to do well on this exam. I can solve all of these force problems, but I don’t have an understanding of what we are doing and why we are doing it.” All I could say was that I was glad that she could tell the difference between the feeling of understanding and the feeling that you can do what’s been asked of you. When a student can ace your exam and tell you straight-faced that they have no understanding of what they are doing and why, then there is a problem.