## Standards-Based Grading in AP Physics C

I learned about standards-based grading from the best. This blog post is my take on how to do SBG in AP Physics C. My APC students took AP Physics 1 and AP Physics 2 as a double-period, year-long course as juniors. They're taking APC as seniors—first semester Mechanics, second semester Electricity & Magnetism. This class is about taking the models we learned with algebra and making them more powerful.

I use a scale of Mastery, Proficient, Approaching, and Beginning. Mastery is NOT perfection; the problems in AP Physics C are often too difficult for 97% of APC students to solve in such a short amount of time without talking to other students. I ask difficult questions that I don't expect students to get 100% right. Mastery means that the student understood the problem, used the correct model, and was on the right track. Most of the time, when I have the time, I have students check their own work and assess themselves against the standards. They are usually a little bit harsher than I would be, but I've learned to believe them when they say they deserve a "beginning."

My standards come from reading the AP Physics C Course Description. My standards are focused on the AP Exam even if my teaching isn't always focused. Here are my standards:

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## Brute-Forcing a Sphere as a Gaussian Surface

I'm not going to bury the lede. The blog post below describes my experience programming; a later post will explain how I'm going to use the program next year. The program shows the flux as brighter or dimmer shades of red (flux out of the surface) and blue (flux into the surface). Play with it. Zoom in and out. Rotate the sphere. Edit and break the program. (I tried to write a lot in the comments, so hopefully you can change a number or two and see what happens.) Give me suggestions. (My students like running it in fullscreen. Find that in the menu at the upper left of the screen.) Here you go:

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## Day 18: The SOS Diagram

So, after a day of learning that the slope of the momentum-time graph is the force, and another day when we figured out the area of the force-time graph gives you the change in the momentum, we were ready to put this model to use.

I know that lots of people use momentum bar charts, but I'm not 100% sold on them. I could be convinced, and I know that energy bar charts are A-MA-ZING. I wanted to play around with momentum bar charts that made the focus more on the motion of the objects and less on the blocks.

So, following in the footsteps of the LOL diagram, I use the SOS diagram. The name will make more sense a little later.

Remember, my students have done balanced forces yet. They only know that a force is a push or a pull and is the slope of the momentum-time graph. I start by introducing interaction diagrams.

First, we make our first interaction diagram together as a class. We use the setup in lab as our situation. (I took a picture of the setup and posted it at the beginning of this post.) We start by listing all the objects we care about and putting them in bubbles. Then we connect the objects that interact with lines. Usually, to interact with an object in a physics sense, that is, to put a force on it, you have to be touching it. There seems to be only one exception we have right now, and that would be the Earth. It seems to push everything around, even when we're not touching the Earth. I mean, that's why babies are FASCINATED by dropping objects from high chairs. "Look!" they seem to scream. "This object is being pushed around and NOTHING IS TOUCHING IT." We aren't usually as impressed nowadays that we're older, but we should be. Anyway, here's what the interaction diagram looks like:

At this point, what interaction or interactions are changing the motion of the object do we care about? Really only the spring on the cart. That's the one that changes the car's momentum. Wait! This diagram shows what changes a car's momentum! Cool! So I can draw the picture before that interaction and after that interaction and put a (simplified version of the) interaction diagram in the middle:

The first diagram represents pᵢ, the second diagram represents ∆p, and the third diagram represents the final momentum (there's no Unicode for subscript f. That makes me mad.)

So, we have our equation here, in picture form: Initial momentum + change in momentum = final momentum. Or, since change in momentum is the area of the force-time graph, and the simplest way to calculate that area would be a rectangle where the base was the time and the height was the average force for the situation, we can write it as...

Initial momentum + average force * change in time = Final momentum.

So why is it an SOS diagram? The O is for the system schema in the middle (which I call an interaction diagram, because 'system' is used differently by the AP, and I don't want to confuse my students), and the two S's are for sketch. It also is a cry for help when you're using the momentum model.

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## Speed Group Hangs

I love Whiteboard Speed Dating. I love the cross-pollination of ideas that it requires. I really like how students have to deal with the whiteboard in front of them, the ideas of their partner, and their own ideas when they switch boards.

We were starting unbalanced forces, and it was time for those elevator problems. You know the ones—the elevator is going down at a constant velocity or the elevator is accelerating upwards at 2.5 m/s².

First, I told the students to get rearrange the tables and get into groups of three or four. I have them two minutes to move the furniture and get into their original groups. (I have a small class—only 14 students. I know, I know.) I think groups of three to five would work the best here. I wanted the groups to be big enough to have students who think in different ways and at different speeds.

Once they were in ready, I told them we were going to do something similar to speed dating. Instead of two people on this date, you're going to have three or four. It's not really a date, then, is it? It's more like a group hang.

You're going to start this next question as a group. Try to figure out how you'd approach it. Draw diagrams and do some math. Don't use whiteboards; just talk through your ideas and write them on your packet. But don't get too comfortable. Just like we we did speed dating, you're going switch. You'll get a whole new group.

So, while they were starting the problem of a person accelerating upwards on an elevator, I started giving each student a card with a number on it. I made sure that, in each group, every person got a different number. I listened in as each group came up with strategy, and noticed how each strategy was a little different.

Very quickly, before any group had really finished coming up with their strategy, I had everyone stand up. All the 1's go to this table now, all the 2's here, and so on. (You can see the all the 2's on one table in the picture above.)

When they got together, they had four different approaches to the problem. Each person in the group was an expert in a different way to solve the problem. Some were more elegant; some were clunky. At least one had a fatal flaw. But it didn't matter. They were expert in an idea that was the group's idea, and their job was to express that idea. The four groups then worked until they came up with an answer. All four groups quickly came to consensus.

I did this four or five times during an hour. It went great. I spent a little time asking for a class consensus about what the positive and negative signs mean in Newton's second law. But all the groups got to the same point at about the same time, and once the groups realized that everyone got the same answer, they felt really confident in their thinking.

This method fixes one of the drawbacks of speed dating. What if the students don't get along? Who decides if the two students have wildly different ideas about what to do next? Is just one person writing on the board? Now, everyone is writing on their own paper. And students can listen to opposing ideas and act like the judge. (I saw that happen more than once.) As one of my students said during this activity: "Speed dating is awkward. Speed group hangs are fun."

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## Day 16: Starting the Momentum Model

If you've been following me and read this tweet, you know that I'm going to be defining momentum in a different way this year. We're defining force as the slope of the momentum-time graph. This means we have to define momentum too, which is the hand-wavy part of this unit. Why even come up with this concept? Luckily, we define momentum as "how hard it is to stop something" and "mass times velocity" before anyone was too awake.

Then we went to lab and had a cart bounce off a force probe. We changed the mass of the cart and the spring on the force probe. We graphed momentum-time and force-time graphs. Here's what students noticed in lab:

• The momentum of the cart stayed constant except when it is touching the force probe.
• The force was negative because it pushed in the opposite direction of the initial motion of the cart.
• The momentum of the cart started positive and went negative.
• The force was the largest when the momentum of the cart was zero.
• When we used the springs, the momentum after hitting the spring was the opposite of the momentum before hitting the spring. The two momenta had the same magnitudes.
• When we used the clay, the momentum after hitting the spring was less than the momentum before hitting the spring.
• We could never get the final momentum to be larger than the initial momentum except that one time when the plunger exploded and hit the force probe, but we don't think that counts.
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## Using Haiku for SBG

Giving good feedback takes time. And to read such a long post, you're going to need to gifs, memes, and screenshots. So let's improve this post.

Maybe you used to love ActiveGrade for Standards-Based Grading. (Or, like John Baunach, you're just starting SBG this year.) And now you're using Haiku Learning Solo Edition. It's OK, but you're not sure how to use it. I'm going to use this post to explain what I'm doing to make SBG work for me on Haiku. I don't feel like an expert at all, but I've bumbled my way to a workable solution for me. It may not work for you. I'd love to hear how you use Haiku as well, and I'll update this post (and give you credit) with your ideas. For example, I give credit to Kelly O'Shea who asked for more pictures and memes. Hopefully, in a year, I'll just delete this whole post and refer you to something better.

Until then, let's get started.

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## Day 9: It's OK to be Wrong, but It's Better to be Confused

We had great discussions today about different situations where objects are accelerating. They were deep and interesting and in each class, students brought up some great ideas.

I took no pictures, though. I feel like a #teach180 rookie.

So, instead, I'm going to focus on how hard it is to be wrong. Students don't want to put up wrong answers. I had a student today who told me he was worried that other students would judge him for not understanding the material. I talk about how important it is to discuss different ideas. I train students to ask questions rather than just point out flaws.

But I feel like I'm still caught up in the right/wrong paradigm. I don't think I'm pushing the conversation from answer-finding (which is all about right and wrong) to meaning-making (which is all about clarity/connections and confusion/disconnections). I need to work on communicating that to students. Instead of, "what do you like or not like about these boards?" (which is my go-to question about whiteboards and is way too vague), I'm going to try other approaches. My ideas so far:

• What connections between the ideas on the board to you see? (Like, how do the position-time and the velocity-time graphs relate?)
• What connections do you see between this problem and the problem where...?
• What makes the most sense to you on this board?
• What did you learn by doing this question? (Or what did you learn from the discussion of this question?)

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## 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 7: What does the P mean in CVPM?

We took our first quiz today about CVPM. But our short lesson today was about the particle in constant velocity particle model.

Mr. Kaar, Mr. Engels, and Ms. Pollack, and I created a unit to explore what "particle" means in CVPM, and how it relates to conservations of quantities in systems. This lesson is the first part of this.

We start with a video of two air pucks connected by balsa wood sliding along the ground. We make sure we know what those air pucks are, and how they seem to move at CVPM. We then learn how to track one air puck. (See awesome gif above. Thanks, gifmaker.me!) Cool, a motion map! That motion map doesn't look like CVPM at all! We look at the position-time graph, and that doesn't look right either. It's way more complicated than a straight line. What should we track? Students usually quickly realize the middle is what we should track. We then do the same thing for three air pucks attached into an equilateral triangle. What should you track now? That's more difficult, because the middle isn't really part of anything. But it still works!

We then give them the two pucks again but this time, when they track the center, it doesn't look right. Why? Because we secretly filmed it on the ramp outside. So that's why the dots on that motion map aren't equally spaced. It seems to be speeding up, which is what we'd expect on a ramp. Guess we'll have to test things on ramps with the motion detectors on Monday...

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## Day 6: Speed Dating in CVPM

We did physics speed dating (see this blog post by Kelly O'Shea if you want to know more) to tackle the most complicated constant velocity representations we'll do. I have to be careful at this time of the year; I can spend a lot of time making sure their model of constant velocity is perfect, but I don't think it really matters for a few reasons:
• We will get a chance (literally in the next unit) to deepen our understanding of these representations.
• It takes a lot of effort to get the last bit of refining. Do I care what they do on motion maps with the last dot? Well, no, not really. If a student decides to draw the position-time graph one more second to what the arrow says will happen next, I'm OK with that. I'm sure other physics teachers have strong opinions about this, but I don't, and more importantly...
• I don't know what we'd get out of having the best constant velocity model. Constant velocity isn't the cornerstone of physics. The next model is. I don't care if there's a small mismatch between my model of constant velocity and theirs.

Still, even with this leeway, we still have some important discussions:

• Where does a position-time graph? Does it ﻿always﻿ start on the vertical axis? Does it ﻿always﻿ start with the first dot?
• What happens between one region of constant velocity and another region? How can the velocity change and no time pass?
• What do the numbers on the motion map diagram represent?

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