Today, we whiteboarded some of the homework. I’m really glad we did, because although the students were able to regurgitate some information, there were some heavy misconceptions.
Thought: The position is decreasing as the velocity is decreasing. The object is not accelerating because it is slowing down. Although the position is decreasing, it is still going in the positive direction.
We proved how the object, although decreasing in speed, continues to move in a positive direction. A student was able to show that the position was increasing, but I erased the photo of the explanation. He drew arrows to show that for each second, the position has increased from its previous place.
Thought: The acceleration is decreasing as the velocity is decreasing.
It was really hard to convince the students that this graph was showing constant acceleration. During this very heated discussion, a student remembered that in the last unit, we had a straight line on our x-t graphs. That shows a constant velocity. Even though the position was changing, the velocity stayed the same. Here, it was way more difficult to convince them of that the rate of change of speed is staying the same, even though the speed is changing. I guess that concept is pretty difficult to digest, but I need to figure out a better way to show it to them.
These two students did a great job with their whiteboard. I asked them to send me the photo of their work since they were taking a picture of it. To their credit, they answered all my crazy questions:
- How do you know it’s going in a positive direction?
- It seems as though since the velocity graph is showing a positive slope, that the car would slow down going up the ramp. (They thought I was crazy…but I know there’s probably a student or two out there thinking it.)
- In a position-time graph, if it’s slowing down, can it be going in a positive direction?
- What does a negative acceleration mean?
- What does a positive velocity mean?
I thought all the students did a wonderful job today, despite it being a Friday afternoon….VERY warm afternoon.