Day 19: An Equation for Friction

After the test today, we only had time to understand the model of friction we explored yesterday. We realized that the maximum force of friction when you are at rest is smaller than the force of friction once you are moving. We also saw that the slope of the line of the force of friction vs. the normal force had the units of newtons divided by newtons. That's a weird unit.

Day 18: Exploring Friction

After Rosh Hashanah off, we are back. We started by whiteboarding some unbalanced force problems. Replacing the numbers in some questions with variable does make it much harder. We spent some time just thinking through variables. But systems thinking is helping; most everyone tried to solve the Atwood machine using a block-string-block system, which made me proud.

Then it was off to lab to figure out a model for friction. We thought of three things we could test that would affect friction--the speed of the object, the normal force, and the two surfaces. The speed didn't seem to matter, and since we can't quantify the surfaces, we tested the normal forces. We will debrief this lab tomorrow.

Day 17: Whiteboard Speed Dating

We worked on uniform acceleration and unbalanced forces and how you can translate between knowing about the forces on an object to knowing about the motion of an object. We did it using whiteboard speed dating, another thing I learned from Kelly O'Shea. It's great; it forces the kids to move. It makes sure that ideas spread around the room. It requires students to wrestle with how other students represented the work. We did whiteboard speed dating for the entire 100 minutes, and we never got tired of it.

Day 15: Building the UBFPM Paradigm

We found out how the acceleration of our hook-string-cart-mass system changed as the external force was changed. Since we talked about systems earlier, it wasn't as hard as usual to use a modified Atwood machine for this lab. The idea of moving mass from the cart to the hook to change the net external force without changing the mass of the system seemed easier to explain this year.

Since we already had a reason to believe that m/s² and N/kg were equivalent units, when the slope reduced to 1/kg, we had to mass one of the systems. Pro tip: I kept a list of the reciprocals of the masses of the systems in my front pocket during the lab. I knew which group I wanted to bring their system up to the front to be massed.

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.

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."

Day 11: Expanding Our Idea of Objects, Systems, and Situations

We talked about how which forces are internal and which are external change when you change the system boundary. We saw how the many forces of gravity become just one when we make the system larger. We defined the mass of the system and the position of the system (the center of mass). And then we tried our model on two air pucks that were previously filmed. We saw no obvious external forces, but the position-time graph wasn't a straight line; the velocity-time graph was. Turns out the system was on a hill, and we need to explore a new type of motion.

Day 10: Interaction Diagrams for Different Objects of Interest

After going over homework on force pairs and forces at angles, I divided the class into six groups and had each group draw an interaction diagram and a free-body diagram using the situation pictured above. Here's what they came up with:

The interaction diagrams looked different because the objects for the FBDs were different. Each group had a different system of interest, so each group saw the situation differently. This insight allowed us to quickly define internal, external, and negligible forces. 

Then we investigated what point should we track on video analysis to see CVPM for various systems. I'm working with some great friends and colleagues I met at the Ohio Modeling Workshops in Columbus, Ohio, and we're working on a manuscript for the Physics Teacher, so I don't want to go into too much detail here. (I'm already thinking of little tweaks for next time.) But my colleagues and I are trying to develop systems thinking in physics, and so far, so good. My first try with students worked well today.