We had to create one of three car crash action sequences for a "movie", and tell our director where to put the camera to film it. (The Academy Award goes to Bryan for his role as the penny-pinching director.) The group I was assigned to had to create a car chase that results in a rear-end crash in front of the camera. (Scenario 2)
Adding to the excitement was the short amount of time we had to figure out where to put the camera.
We didn't have much argument about how to start our work. Everyone jumped right in, setting up a 2 meter distance for the cars to travel and pulling out phones to be stopwatches. There were 4 or 5 of us timing, so we took the average time to use in each calculation of the cars' speeds. We used those speeds to set up motion equations based on the generalized equation we'd come up with earlier.
This is where our group split into two. Some of us graphed the equations to see where they intersected. Others did some math to find the solution for the simultaneous linear equations. Then we checked that our answers matched.
It's funny. You know these two methods will both work, but it's still really exciting to find out other people reached the same answer you did, but in a completely different way. It's confidence inspiring. As a math teacher, I always say that answers are strongest when there are many ways to reach them. But as a physics teacher, I haven't been focusing on the multiple representations (graphs, equations, verbal explanations) as ways to reach a numerical answer. The verbal and graphical representations are for conceptual (qualitative) questions, while the math is how you reach an actual numerical answer. My students have been missing out on that moment of "Yeah, I got that too, but I used the graph." (They do compare numerical answers with each other... but it's just not the same as using a completely different method. They're mostly checking that they can do algebra correctly.)
Anyway, the best part of the practicum was actually testing our solution. Everyone gathered around to watch, and we all rooted for the crash to happen in the right spot, cheering when they crashed. From my vantage point, that crash definitely happened where it was supposed to.
Unfortunately, our "director's" camera disagreed. So close!!
I can appreciate the point Bryan made about failure. It is important to fail sometimes, and have to deal with that failure. Our cars didn't crash on the point we'd marked. We failed.
But... I do wish we'd had time to explore what went wrong. There is instantaneous feedback built into the practicum (did it, or did it not, work), but a failure doesn't mean I don't understand the concepts involved. I'm pretty sure our work was right, and that it was a problem with releasing the cars simultaneously. Releasing the chase car early would account for an early crash. So, as an instructor, I think I'd want to make sure I had time built in to have a conversation with the groups about where their errors happened. And maybe let them try it again to see if they're right about those errors. (Not, of course, to change their "grade" on the practicum.)