Today in my honors physics class, I was witness to the awesomeness of my students and the power of modeling. I need to record this so I can recall it clearly. This is a long one, but I want to get it all down.
It’s May and we’ve just started the momentum unit. Momentum has always been a tough unit for me to teach, as it is pretty theoretical. The concept is one step removed from the more concrete idea of velocity and the labs for studying it often require air tracks and other contrived setups. Too often, I’ve reverted to lecture for this topic and I wanted to break out of that mold this year. I took the modeling lab from the momentum unit and modified it for today’s class.
Some brief background first. Over the last two days, I introduced the girls to the concepts of momentum and impulse using Frank Noschese’s videos of cart collisions. We talked about how these concepts influence athletics and safety. They’ve had some homework on calculating the momentum of an object in different scenarios. Pretty standard stuff. I hadn’t mentioned conservation of momentum or the idea of the momentum of a system of more than one particle.
When they entered class today, I asked them how we might measure the momentum of an object. We realized you can’t measure it directly, but you can measure the velocity and mass of the object and calculate its momentum. Great, here’s a motion detector, a balance and a dynamics cart – go determine the momentum of a cart that you’ve pushed. Five minutes later, they came back with the momentum of their carts and looks that said, “Why are you bothering us with this trivial task?”. So then I complicated things.
I gave them a second motion detector and a second cart. They played around with these for five minutes and figured out which graph belonged to which cart. That’s when I asked the following: If you let these carts collide, they’re each going to change their momentum. But how does the momentum of the carts before the collision relate to the momentum of the carts after the collision? Come up with a model that answers this question. And off they went. Carts were colliding, measurements were being taken and the students were working diligently on a sunny May afternoon. Then I approached one group and they blew my mind.
S1: “Tell him what you just said.”
S2: “We came up with this idea called momentum equilibrium.”
Me: “That’s a cool sounding term. What does it mean?”
S2: “Well, we think the carts will each have the same momentum after the collision. The momentum will kind of equalize”
Me: “Interesting. Why?”
S2: “Well, we noticed when we pushed a fast cart into a slow cart, the fast cart wasn’t moving as fast after the collision and the slower one had sped up. So we thought that the momentum distributes itself between the two cars.”
S1: “Also, we remember learning about some type of equilibrium with cells in biology and how when two cells are in contact somethings are moving across the boundary equally.”
Interlude: At this point, I’m realizing that their building their own descriptive model for the transfer of momentum. Their basing it on observations, drawing reasonable conclusions from it and tying it into knowledge from another subject. Despite them being incorrect, I’m awed by these two girls creating this on their own. I’m thinking about how to steer them towards the correct conclusion about conservation of momentum, but then the voice of another Brian rang in my head.
“Their misconceptions are valid. These are reasonable conclusions to draw based on their previous experience. If you just tell them that they’re wrong, they’ll believe you, commit conservation of momentum to memory based on your authority as their teacher and never understand it.” 
So, instead of jumping in, I simply said, “That’s an intriguing idea. I’m impressed that you are developing a theoretical explanation for what you are seeing. Make sure you gather a large amount of data so that you can be confident about your conclusion.” And then I walked away. The girls excitedly returned to their work.
I circulated around the room and after fifteen minutes or so, found myself near the group mentioned above. As I listened in, I heard the following:
S1: “I don’t know, these aren’t looking the same. They are definitely different from each other.”
S2: “Yeah, maybe…but look this one went down by about the same amount the other one went up. What if its the change in momentum that’s the same instead of the initial or final momentum?”
A quick calculation later…
S1: ::audible gasp:: “They’re the same! I mean really close, like 0.05 apart. They’re really the same thing.”
S2: “Check the others.”
Huddled together, they compare their other data and then I hear one say in an excited whisper…
S1: “Oh my god, I think we just discovered a law of physics.”
I was so damn proud of them. With zero prompting, they had discovered the law of conservation of momentum. With nothing more than their own senses and brains, they uncovered a secret of the universe and claimed that knowledge for their own. They did it. Not me. Not some textbook writer or famous dead white guy. These two young women did it on their own. I can’t imagine ever going back to a classroom or pedagogy that denies young women this power, this ownership, over their knowledge.
 – This is the voice of Brian Frank who spoke at last nights Global Physics Department meeting about student misconceptions and his research around them. I recommend checking out the notes from the session. And by the way, super smart cosmologist Sean Carroll will be at next week’s meeting. Register here and stop by.