On Fridays we do a review of the two new standards for the week. This time it was about tops/gyroscopes and simple normal mode systems. I set up two problems and two groups to work on them:
- Consider a spinning top balanced perfectly. What happens when a ball hits it from the side?
- Consider two weakly coupled mass/spring systems. Describe how the energy seems to go back and forth between them.
The groups worked hard. Their first assignment, due 5 minutes into the work, was to report any questions they had. Those ranged from “What’s the mass of the top? (whatever you want)” and “Are the two main springs identical? (if you want)” to “Will it tip? (good question)” and “Is this the same math we developed on Wednesday? (What do you think).” They then worked hard trying to figure out what was relevant and what they could do to spice it up (to make it 4-worthy in my system).
But then the inevitable happened. Both groups developed enough that they wanted to see what would happen if we modeled it in Mathematica. Group 1 wanted to see if the top truly would tip at a 90 degree angle to the trajectory of the ball and group 2 wanted to see a Fourier transform of the motion of the masses for various settings of the springs. And both of those sounded like a lot of fun to set up and to play with. However, there wasn’t time left in class for both. How to decide? That’s what I wanted to get down in this post. Not an answer, mind you, but how our discussion went.
At first we tried to figure out which project was harder. The Fourier transform stuff had them a little worried, as we hadn’t done that in this class at all. But figuring out how to the ball impact was difficult too. The problem was, there wasn’t consensus on whether “hard” meant that it should be done in class where they could ask questions, or done in a screencast (by me) outside of class where they could watch it and rewind etc.
One student really liked the latter argument, saying that they were worried that the subtle details would come too fast if I did it in class. I said that maybe I should do the hard one in class to make sure we figured out what was hard for them.
In the end we did what I thought would be the easiest one in class, though it’s finny that even that one proved too difficult to do in class. Here’s the two scasts I made for them after class if you’re interested.
So what do you think. What should be done in class and what should be an out-of-class resource? Here’s some starters for you:
- I’m in this class and I like that you ask us our opinions about this. I like tailoring my learning that way.
- I’m in this class and I hate the way you waste time asking us what we should do. You’re the expert, so teach!
- This is cool. Do they change what types of things they ask for as the class goes on?
- This is dumb. You shouldn’t put them in two groups if both of the problems are things they should learn.
- This is cool. What happens when you do what they ask for but you don’t quite finish?
- This is dumb. You should promise to do both as scasts and then just spend class time having them predict what’ll happen. That way they’re motivated to watch the vids.
- This is cool. Do you just have the vote be democratic or do you always wait for consensus?
- This is dumb. The whole class should work this way, not just the end.
- This is cool. I’m really surprised at how the top moves. Maybe doing the impact as a temporary gravity adjustment is wrong.
- This is dumb. Doing everything in Mathematica is stunting their growth, stop it.