Are change in momentum and impulse the same thing?
I’ve been playing around with the 20 minute pulse check thing we’ve been doing at school and I’ve been playing around with various prompts, but still one of my favorites is “what question do you still have?”
When I first did this, we collected all the questions, and tried to summarize a general question to tweet. The thing that was interesting is that we didn’t answer any of the questions. Part of me thinks this is a good thing—I want students to start to see that they simply forumlating a question can be a huge positive step, and thatthey have the ability to answer their own questions.
But at the same time, some questions have been so good, or some students seem to be so confused that I have decided to on occasion, begin to answer their questions. So I have the kids write questions on notecards, and then write a short reply on the notecard and return it the next day.
One of the most frequent comments I hear from students is “but I don’t have a question” and this can come with either two flavors: 1. I think I’ve got it so well I have no questions, or 2. I’m so confused I don’t even know what to ask. Both of these are problematic to me, and I’ve been trying to get students to see that you should always have a question in mind to guide your thinking. If you don’t have a question, it’s a sure sign you don’t understand as well as you think you do, and if you don’t even know what to ask, its a sign to me that you need to build your confidence that it’s ok to ask those most basic questions that students are so afraid to share.
This week, as we are studing momentum and impulse, I got a number of variations on the following question:
Since impulse is the same thing as change in momentum, why do we need the name impulse? Why not just use change in momentum?
This is a very interesting question, since it shows some of my students’ conceptions of mathematics are still a bit naive (which is to be expected).
I’ve avoided using the symbol for momentum just to avoid adding another symbol to their brains. They all know how to show the equivalence of impulse and momentum using N2:
We’ve discussed before the various meanings of an equal sign in physics, and this time we came back to this idea and talked about how change in momentum and impulse are two different human defined quantities that turn out through experiment to be measurably the same, and that we can see this equality through N2, but that it isn’t any more correct to say they “are the same” than it would be to go around talking about the of a circle instead of circumference.
I need to find a way to assess whether my students are developing a deeper understanding of what an equation is trying to say as relationship. This is the heart of the modeling curriculum, and certainly all sorts of proportional reasoning questions help students to see that equations are really just very short, precise summaries of relationships between various quantities. We also spend a lot of time exploring when a particular model is valid; still I think when students see an equation, they find it very hard to resist the urge to think “what do I plug into this thing?” without asking “what is this thing trying to say about how the world works.”