Using Desmos for Physics (Part III)

My inspiration for this project was a Twitter tweet from Brian Frank. In that tweet he showed a photo of a graph sketched out on a whiteboard. It was a graph of a collision between two objects, and it showed the velocity and momentum of the objects before, during, and after the collision, as well as the force the objects applied on each other during the collision.

Today was momentum transfer in isolated systems using multiple representations. Here is a look. pic.twitter.com/YHECBOl8fn

— Brian Frank (@brianwfrank) November 2, 2018

When considering collisions, one usually compares the momentum before the collision to the momentum after, demonstrating the conservation of momentum. Rarely does one consider what is happening during the collision (it's complicated). What happens during the collision is usually saved for a discussion of impulse, where it is revealed that during the collision the objects exert equal and opposite forces on each other (and this is why momentum is conserved). What Brian had done that was exciting to me was to present it all in one beautiful set of graphs: momentum, velocity, and force, for both objects, before, during, and after the collision.

I decided to model this in Desmos.

I used as my default view a 6-axis view rather than Brian's 3-axis view. I thought that the 6-axis view would be less confusing for my students. The 3-axis view is more elegant, though, so I built a "switch" into my simulation so you could switch back and forth between views.

I have also added other kinds of interaction: the masses and initial velocities can be changed; the collision can be switched from elastic to completely inelastic and back; the time duration of the collision can be changed (impulse!); and there's an adjustable scale which is helpful when the lines all start to overlap.

I added a collision simulation of two balls at the bottom that is timed with the graphs. When the balls collide, they simply overlap, I didn't try to build a realistic collision model.

Here's the link to the project: https://www.desmos.com/calculator/xtr8shdagl





You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.

Using Desmos for Physics (Part I)
Using Desmos for Physics (Part II)

Using Desmos for Physics (Part II)

Here is a variation on the Desmos graph I created in my last post. This graph is intended less as a demonstration and more as a student exercise. The five dots are moveable, and define the position curve. Then by clicking on the Speed circle at line 4 in the side panel, students can see the speed curve, which is the slope of the position curve. This is useful for students learning to read slope by focusing on key inflection points and trends.

Here's the link to this Desmos project: https://www.desmos.com/calculator/vo4kxervvi





You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.

Using Desmos for Physics (Part I)
Using Desmos for Physics (Part III)

Using Desmos for Physics (Part I)

When I discovered Desmos, I knew that both I and my students would love it. Desmos has been called an online graphing calculator, which is literally true, but a description that barely captures the possibilities. I have come to see Desmos as a programmable simulator, using a programming language called math.

I could see right away that there would be two ways for me to use Desmos in the physics classroom. First, I could create interactive, animated graphs that students could manipulate and play with. Second, students could, with a little scaffolding, create their own animated graphs. These graphs could demonstrate basic graphing concepts, such as finding the slope of a curve, or building a distribution curve for a set of data. They could also demonstrate basic mathematical relationships among various physical quantities.

But first I had to learn how to use Desmos. The fastest way for me was to find existing graphs that I was interested in, study how they had been built, and then modify and adapt them. When I inevitably "broke" a graph, I was able to find enough information online to figure out where I had gone wrong. It was really fun, and the immediate response by Desmos to any changes was addictive. I also quickly realized that my math skills are pretty rusty. I've done a lot of programming, and you can get away with some sloppiness and inelegance, but straight-out math is pretty unforgiving. If you need to brush up on your math skills, Desmos is the most fun way I can think of to do so.

This is my first Desmos project: https://www.desmos.com/calculator/fm6yuykclr





You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.

Go to line 6 on the left panel (Graph of Slope) and click the circle.

This graph is based on a graph I've already had the students draw and analyze. Students commonly confuse position (the height of the curve) with speed (the slope of the curve), so the more tools for visualizing the better. In this case, I'm using Desmos as a demonstration tool, but it's pretty easy to have all the students call up the graph on a laptop and show them things they can change. I try to have them guess what might happen with a given change, and then check their guesses. Each instance of the graph is separate from the other instances, so students can modify the graphs without disturbing my original or each other. They also do not need to create an account, or even log in. Hit the link and play!

Using Desmos for Physics (Part II)
Using Desmos for Physics (Part III)

New Physics Curriculum

I was tasked this year with redesigning the physics curriculum at my school. Our state (MA) just upgraded their framework, so we needed to re-align. For the last decade, the state's framework was nothing more than a shopping cart of physics topics. There wasn't even an attempt to distinguish topics from concepts. The state assessment required students to have key vocabulary memorized, and to know how to pick out the right equation and apply it correctly to word problems. And that was about it.

My physics team has only three members. For good or for ill, we are all well-versed in the old state framework and assessment. The new framework is mostly based on the Next Generation Science Standards, so it’s quite different. I was excited about the change, because I think the NGSS is a worthy approach. But it’s very different from the old approach, and I wanted the team to have the time and opportunity to adapt. The new curriculum I wrote is organized in a way that looks similar to the old curriculum, but introduces and adapts the new framework language. The team already has a strong bias toward hands-on, project-based, team-oriented classwork. I wanted the physics team to continue moving in that direction, but to shift their conception of this project-based classwork from demonstration-of-topic to phenomenon-model-interaction.

To help our team, perhaps other science teams, and even our supervisors, to better understand the NGSS framework, I created a concept diagram. The diagram is not based directly on the NGSS framework, but is instead a representation of the new curriculum I wrote. I think of the new curriculum as a particular instance of the NGSS framework.

The old curriculum thinking was topic first, application second. The new curriculum flips that around to phenomenon first, model second. The basic interaction is that the phenomenon informs the model, and the model makes predictions about the phenomenon. We choose an anchor phenomenon that is sufficiently complex, has relevance to the lives of the students, and is interesting or engaging. As an aid in exploring this phenomenon, simpler and perhaps more accessible related phenomena are introduced.

The model is related to other models, largely through shared concepts such as force and energy. Through these core concepts, students can develop a picture of physics as a consistent viewpoint and approach to understanding the world, rather than merely a collection of topics. The model is represented and expressed in many ways. These multiple representations give students multiple pathways for exploring the relationship between model and phenomenon.

Finally, in keeping with the idea that learning comes from doing, I include a summary of what students could do as they explore the phenomenon-model relationship. This list is broadly in line with the goals stated in the standards of the new state framework.

Cross-posted to Teaching Is . . .