Days 48-52: Model Summaries & Final Exam

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We are on trimesters, so this week was the end of tri 1. We usually have a special schedule for final exams the last two days of the trimester, but, due to bussing issues, we followed our normal schedule. We also had a change in our grading policy to do away with cumulative final exams.

I still opted to give a modified practice AP exam covering what we’ve done in class so far. I usually spend 45 min on each half of the exam, so that made it easy to split the exam over two days with our standard 55 min periods. To meet the modified grading policy, I gave my students some points in the formative category of our gradebook for completing the practice exam. This is more in line with how I use the first practice exam, anyway. At this point, I mostly care about students seeing what a test is like and trying their endurance on something longer than our usual quizzes. I also use it to get a sense of what my students are doing well so far and what I need to make sure we keep working on. Even though their grades would not be impacted by how they did, my students took the practice exam seriously and I’m very pleased with how they did.

The practice exam is a good opportunity to review what we’ve done so far, and my favorite approach is model summaries. I gave each group a model that we’ve used so far this year, and asked them to put a scenario on their whiteboard where they could apply their model. Then, I had students add as many diagrams and representations of their scenario as they could. I explained this exercise to students as each model is a toolbox, and we were going to use these whiteboards to remind ourselves what tools come in each box. There were at least two groups whiteboarding each model, which worked out nicely since it’s pretty common that different groups will make use of different tools from the model, so we get a more complete summary with two groups.

Now on to trimester 2! Due to ongoing staffing issues, I’ll be adding two sections of regular physics to my current teaching load of one section of AP. I think a major theme of the next few weeks for me will be figuring out how to balance additional teaching with my responsibilities as a content specialist.

Days 46-47: Conservation of Momentum

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We made it to Thanksgiving break!

This week we wrapped up conservation of momentum. I’ve been liking doing this before impulse since collisions give us a clear reason to make use of conservation of momentum, but I ended up introducing momentum by just giving students the formula and telling them to calculate it for a bunch of collisions, which worked, but I wasn’t thrilled with. I want to keep thinking about how I could better introduce momentum with this sequence (though in theory I won’t be teaching next year…).

On Monday, I had students work through an activity I’m working on for Pivot Interactives where they switch between thinking in terms of two exploding gliders as a single system and thinking of the gliders as separate systems. I was really pleased with how my students did switching between those two types of thinking after the limited intro to impulse we’ve had. I am wishing we’d spent a bit more time on calculations with momentum before our quiz this week. I usually give students two in-class assessments over every learning target, so I’ll have to make sure we get some more practice before our retake.

Days 41-45: Conservation of Momentum & Newton’s 3rd Law

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This week we developed conservation of momentum. Previously, I started with impulse and momentum of single objects, then built up to conservation in systems. I’ve never been thrilled with my storyline, so this year I am trying putting conservation of momentum first, then we will work toward impulse. Once we’d done a lab with some collisions and talked about momentum bar charts, we did Kelly O’Shea’s multiple representations of momentum card sort to incorporate mathematical representations. The card sort really helped my students feel confident with the bar charts and to make sense of the mathematical representations.

We ended the week with Newton’s 3rd Law. I feel like this law fits better with my momentum storyline than my forces one, so this was their first introduction to the 3rd Law. I had students predict how the forces would compare on two carts for a variety of collisions, then we actually tested the collisions out using some force sensors with hoop springs. This is a very rare time that I ask students to make a prediction that I think they are likely to have wrong, so was very intentional in talking to students about my goal of pulling out their existing ideas so we could contrast with the accepted physics. I also made sure we talked about what useful thinking lead them to the incorrect predictions and what physics their predictions showed they know. There was a fantastic moment partway through where a student articulated that both the forces we were measuring came from the same interaction, so it made sense for the size of the force to be the same. She also realized the cart she expected to experience a bigger force did have a bigger change in motion, which was a great opportunity to validate the thinking that lead to that prediction. It was a great note to end the week on.

Days 37-40: Unbalanced Forces

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This week was a little funny because we had Tuesday off for elections.

On Monday, I gave a quiz over unbalanced forces that didn’t go as well as I’d hoped. The big thing students seemed to struggle with was sketching and using free-body diagrams and vector addition diagrams. I decided to put off starting momentum to spend a little extra time working on force diagrams. We started with a card sort with unbalanced force diagrams. Including the motion maps gave me a chance to emphasize the net force is in the same direction as the acceleration, which I hadn’t done a great job of before. This card sort also includes two sets of similar scenarios, which lead to some good conversation comparing and contrasting the similar scenarios. After the card sort, one student told me that she has found card sorts in general to be a really useful tool in helping to visualize what diagrams should look like. I realized one of the benefits of card sorts is they students the visual they are after when they ask me to do example problems on the board, but kept the bulk of the sensemaking on students. We have a lot of card sorts made for our physics courses, but I don’t use them consistently in AP in an effort to keep to a fast-moving pace. This week was a good reminder that it is worth it to make time for card sorts.

After the card sort, we moved into doing some problems, both calculations and conceptual, and students were much more confident and doing much better than earlier in the week.

Days 32-36: Using Newton’s 2nd Law

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This week, our big focus was on using Newton’s 2nd Law. Students were very successful at using vector-addition diagrams with unbalanced forces and did a nice job playing around with different systems on problems involving Atwood’s machines. We wrapped up the week with an extremely open-ended lab practical. I tasked students with finding the mass of a dynamics cart with a force sensor attached and left it at that. I did ask students to get my okay before they started data collection so I could make sure every group was on a good track. I was really pleased that groups ended up using several different approaches. Some did something similar to our model-building lab with a half-Atwood’s machine, some set their track at an angle to apply a force to their cart, and some manually pulled the cart. On Monday, I want to take a few minutes to make sure we talk about the different approaches, including the different ways uncertainty showed up in each.

Days 27-31: Balanced Force Practical & Newton’s 2nd Law Model-Building

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This week we wrapped up balanced forces with a practical. I used some magnetic hooks to attach spring scales to the whiteboard and let students measure the forces and any angles they wanted. Even though I only had two setups and five groups, different groups ended up taking different approaches, which was great for students to see in some discussion after the practical. We also had some good discussion about uncertainty when we measured the actual mass and students were initially disappointed with how far their calculations were off before, which lead to the realization they’d actually been pretty on target!

After the practical, we started Newton’s 2nd Law with a paradigm lab using the standard modified Atwood’s machine. There was some messiness in the value of the slope that students got, which is pretty typical from when I’ve done this lab. One of these days I’ll figure out how to coach students to really high-quality results! Students did really well at translating the equations for their line of best fit into something that had units and variables that matched the experiment and did a nice job in the board meeting making sense of their slope and intercept.

Days 24-26: Force Diagrams

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This week was only 3 days due to the state union conference held this week.

This week we started working some balanced force problems using vector addition diagrams. I noticed my students were struggling with getting the interaction diagrams and free-body diagrams correct, which then made the rest of the problem trickier. In the middle of the week, we stepped back from the problems to really dig into setting up the interaction diagrams, free-body diagrams, and vector addition diagrams on whiteboards for a range of situations with the hover puck. We got to revisit some important ideas, like the idea that forces must be an interaction, and dig into some things that didn’t come up on previous problems, like how whether you include something like the air cushion under the puck as part of your system can change your diagrams. This day seemed to really help students see the value of some of the thinking I’ve been asking for and to feel more confident in drawing and using these diagrams, which is just what they needed!

Days 20-23: Mathematical Force Models

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This was a short week due to a PD day on Friday.

This week, we focused on building mathematical models for the force of gravity and spring force. My students have taken very nicely to writing equations for lines of best fit in “physics” where they add units to their slope and intercepts as well as use variables that match their experiment. My students are also taking nicely to using “for every” statements like “the force goes up 10 N for every 1 kg of mass” to think conceptually about the meaning of their slopes. Students have also done really well with turning their intercept into statements like “the intercept is the size of the force when the mass is 0 kg” to think about what kind of intercept makes sense.

With the spring force experiment, I had students stretch their springs both vertically and horizontally to see the graph had the same slope in both directions. This usually seems to help address conceptions about the role of gravity in the behavior springs that come up when we get to energy and simple harmonic motion.

Days 15-19: Building a Force Model

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This week was all about starting to build a model of forces. We started by tapping bowling balls with mallets, using a version of the activity based on Frank Noschese’s. Students were quicker than usual to recognize that they had to juts leave the bowling ball alone once it was moving to keep it moving at a constant speed, but I still pulled up an old image I made with motion shot to get some additional evidence. After that, we moved into a version of interaction stations from Kelly O’Shea where students identified forces based on stretch, compression, and shear. Finally, we wrapped up the week with some mistakes whiteboarding with force diagrams. When I introduced system schema and free-body diagrams, I didn’t emphasize enough that the free-body diagram only needs to show forces that cross the system boundary, but that lead to some great conversations during the whiteboarding as students figured out what they needed to include. One student commented that almost all of their mistakes related to including more than they needed to, which lead to some nice discussion about the fact that the hardest part of physics is often figuring out what is relevant.

Days 10-14: Building CAPM

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This week, students did a lab with ramps to start building the constant acceleration of a particle model. Students used Vernier Video Analysis to get their graphs, and I really love how the video analysis tracks set up motion maps for constant acceleration. Students seemed to feel pretty good about some of the math-y skills in this lab, including linearization and “translating” their line of best fit into a version that has variables that match the experiment and units on the slope and intercept. We then did some mistakes whiteboarding with problems translating between different representations of constant acceleration, which my students continued to do fantastic with.

One thing I think is worth thinking about it it feels like because this is our first experience with linearization, the later days of this lab feel very focused on the math. Then, it feels like we set the heavy math aside while working on translating between representations, only to circle back once we are ready to start doing problems. I wonder if there is a way to structure the constant acceleration unit differently to make it feel more coherent. We have the Vernier motion encoder carts, so I wonder if one option could be to start by having students more or less play with carts on ramps to focus on the shape of graphs, then work on translating representations. Then once students are solid on the representations, do the more standard ramp lab to bring in mathematical representations.