## Day 8: What Students Think About When Using Motion Detectors for Carts Down Ramps

Here are the issues my students thought about when they used the motion detectors to look at carts speeding up and slowing down on ramps:

• Is the position-time graph for an object going down a ramp starting at rest an exponential or a parabola?
• How can the slope of the velocity-time graph be negative when all the velocities we measured were positive?
• So, when the velocity is negative, the acceleration is always negative, right?
• So, when the object is moving in the negative direction, the acceleration is always negative, right?
• So, if the object is slowing down, the acceleration is always negative, right?
• So, if the velocity is decreasing, the acceleration is always negative, right?
• So, if velocity is a slope and acceleration is a slope, they have the same shape, right?
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## Day 14: I should've stayed quiet

I've been modifying some classic modeling problems to take the numbers out and replace them with variables. I like variables in physics when the students have enough fluency with algebra to then be able to talk about the relationships—what would happen if a increases? How could I change Δx to make t smaller? I also want them to be ready for the AP exams.

The students did a great job with the uniform acceleration problems with numbers. I couldn't stump them with any questions. There was one problem left to do in the packet, one I had modified: what is the acceleration of rocks that start from rest and then travel 2x meters in t seconds?

They struggled. Groups formed and disbanded. And I wanted to butt in. I can't remember my reason, but I bet it was a combination of "it shouldn't take this long," "I know a great hint," and "I can teach something important in very little time if I do this right." I tried to get my class back together as a group, but they fought me.

As they should. They knew the problem. They had the background knowledge. What could I do at that point, with the whole class, that would help? Nothing. I would have shut down the debate too early. I would have taken away their sense of accomplishment and the ability to come to their own realizations that'll stick. I'd stop them thinking like scientists and start them thinking like memorizers. And I realized it as I got their attention. So I tried to say as little as possible. That's what my picture is of today. I showed them the choices that were around the room. (My picture doesn't show the third choice, that these two graphs are saying the same thing.) And I let them work.

After almost everyone was done (one group would not stop debating the two graphs!), not everyone had the right answer. But every student had thought through the thinking both graphs showed. Every student could explain why he or she picked which graph. And while they wanted to defend their answers, they all listened to each other and tried to build on each other's ideas.

What more do I want?

Nothing. I started my teaching career lecturing. The more I taught, the more I gave activities, labs, and experiences, but I still kept giving way too many hints. I kept wanting to teach over their thinking. After Modeling Instruction, I realized their thinking is the most important part. I want to change their thinking, their approach to seeing the physical world. The better I get at my teaching now, the more room I give them for their thinking. (That doesn't mean it's all just their own thinking. I create, with well-planned experiences and problems, a path that the students sometimes don't even realize.)

Oh, yeah, we tested to see if objects in free fall follow UAPM. They tested lots of objects and they seem to think, yea, we can model objects in free fall with UAPM as long as we can pick objects where we can ignore air resistance.

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## Day 13: Velocity-time Graphs Rule

We whiteboarded some conceptual questions on the center of mass and uniform acceleration. One student noted that if velocity and acceleration are the same sign, you're speeding up; opposite signs mean you're slowing down. Then I summarized what we've done with a velocity-time graph and said "now, we can solve quantitative problems. Go."

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## Day 12: Defining Acceleration

We are making our own meaning about what acceleration looks like. It was mostly students talking to students today, with me at the end just writing down our class consensus for a definition of acceleration.

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