Sharing Whiteboards

What to do with student whiteboards? Pick a great one and share it with the school! Here's a display case that I had Operations build to show off whiteboards outside my room:

Some Capstones

A few capstones from the AP class in the first term. I wasn't super-happy with the management of these - not enough revision and discussion - but there were certainly some good ones in there. Here's a smattering of the final reports. Some include VPython programs which are pretty neat, too.

• A capstone where a student writes a VPython program to prove that the freefall time for any tunnel through the Earth (along a chord) is the same
• A capstone where a student write s a VPython program to verify the time for the freefall through the center of the Earth (comparing to the solution for the SHM diff. eq.)
• A capstone where a student calculates the through-the-Earth times for different planets/objects (that was a popular topic this year)
• A capstone where a student analyzes a clip from Toy Story, where the slinky dog dives down, changes mass, and spring back up
• A capstone where a student builds a tricord instrument, predicts the correct mass to tune the string to a chord, and tests the predictions

There were several others, and this is just a selection. There were also lots of cool ideas that fell by the wayside for expediency, which is something that I'd like to avoid happening in the future. Some cool ideas about programming a simulation of the view of the Venus transit from Earth (I couldn't quite get this one to work myself, but it was an awesome idea), simulating the Home Alone bucket swing and crash (this one's totally doable), and a few other really neat ideas unfortunately were lost along the way. Oh, well - two more tries left this year. Lots more good ones to come, I'm sure!

Homework Worth Doing

I posted a few weeks ago about motivating kids to do homework by making it worth doing. That's a pretty heavy gauntlet to throw down, and I did have at least one Twitter response calling me on that. I don't claim to always have the right answer to this, but there are a few things that can take us in the direction of kid-obvious worth, I think:

• The most obvious kind is practice. This is an easy type of HW to give, but the tricky part is making kids see that they need it. Assessments should be framed as an opportunity for the students to find out what they need to work on - as formative, rather than summative, and HW is then the second step in a lot of cases. This is a difficult thing to do, and it requires a lot of frank talking with students in class, particularly at the beginning. I get better at selling this every year, but you'll never have every kid on board. Those kids that you can't ever get probably weren't getting much out of "completing" mandatory HW anyway.
• Deeper applications of concepts that you already know can work, but they can be difficult to pull off. Because of their nature, lots of kids are going to miss a subtle concept in there, and you'll have a few successful solutions waiting around for everyone to catch up in class. Depending on the kids and the culture, you may have a large percentage shut down and come in with something blank. It takes good scaffolding for these, and I'd use them sparingly - this is exactly the sort of thing that class is good for.
• Simulations or calculations can take some of the time-consuming, but not super-difficult bits of lab work outside of class. If kids are following up on a collision lab by calculating the center of mass velocity or change in kinetic energy for each system, that's something pretty easy for them to do, and they won't mind doing it (because it's not mentally taxing), but it'll save you class time. If they're at the point where they're pretty comfortable modeling, you can give them a simulation and have them model the relationship. I do this with universal gravitation (since we can't do the experiment in class anyway) and sometimes with circular motion, depending on how I'm feeling about experimental setup. At this point in the year (early second trimester), they're mostly ready to do that - certainly the design, data-taking, and graphical modeling, and most can do the algebraic modeling as well. We can then wrap up the relationship together and have a good discussion when they're 'fresh,' rather than after they've spent an hour taking data and running fits, etc.
• Another useful kind is new explorations. If they're framed well and have a low barrier to entry, they can be really productive. The first one where some kids obviously didn't do it should bring some helpful peer pressure as well. If you have one where nearly everybody doesn't do it and there's a frustrating day, that's a good candid conversation to have with them (and to remind them of the next time).

In this last vein, I have an example, using this gravity simulator (I just got sidetracked for 10 minutes playing with it while finding the link):

This is basically a way to get the conversation started on elliptical orbits, while reviewing a bit about circular orbits and Newton's laws. The kids come in with all sorts of observations and ideas, and it is a great springboard into the topic. If you do this in class, you end up having to curtail their investigation in the hopes of getting the discussion started, which isn't super fun for anybody. 

Not every assignment worth doing looks like this, but it's a way to start to think about meaningful HW outside of class that isn't practice on old topics. 

Newton's 2nd Lab

I thought that I had posted about this apparatus before, but I guess that I hadn't, so here goes:

I've tried several setups through the years for students to model Newton's 2nd law. Qualitatively (balanced vs. unbalanced, direction on "unbalance" is the same as the direction of acceleration) getting the concept should come first - I have a previous post on that here, but when it comes time for modeling acceleration's dependence on force and mass, the setup can be tricky. Some that I've tried and/or seen:

• Pulling a cart with springs, measuring acceleration with a motion detector; it involves a lot of performance (keeping the spring stretch constant) time and practice that I'd rather have them spend on the analysis, especially with my small number of class days
• Half Atwood machine: you can easily vary the hanging mass to change the force exerted on the cart, but you can't equate the hanging weight to the tension, and you can't solve for it unless you know N's 2nd already. You can change the mass of the cart, but then you're changing the tension.
• Half Atwood machine, analyzed as one system: it's procedurally easier, but mystifying for students. Looking at the whole system means that your vector directions will have to be changed because of the pulley, which seems mysterious to students that haven't done that much force analysis. Keeping the weight of the hanging mass constant while adding mass to the cart is easy, but then they really need to record the total mass of the system, which is a bit conceptually tricky so early on. Keeping the total mass of the system constant when you are changing the hanging mass is similarly black-box for them at this point. It's an elegant setup from our point of view, but doesn't ultimately make much sense to most of them at this point in their physics careers

Here's what I used this year:

Half Atwood machine, with a force sensor screwed to the cart (the string's tied to the sensor). A motion detector helps them find acceleration (from the slope of the v vs t graph):

• The system being analyzed here is just the cart. The force probe measures the tension directly, so no complex analysis or tricky conceptual arguments need to be made. About halfway through, it's good to stop them and ask them to compare the hanging weight to the tension force reading and to explain the discrepancy conceptually.
• Varying the force exerted on the cart just means varying the hanging mass, and varying the mass of the cart is simple, too - no mysteriously motivate shuffle of masses back and forth. The experimental design is completely transparent to them.
• You might want to have them split into two factions: some groups investigate how acceleration varies with force and others investigate the dependence on cart mass. They then present whiteboards and the class can determine the combined model from the two partial models. Don't underestimate the reasoning leading from the two individual models to the combined model.

Everything seemed to go quite smoothly (that last conversation's still a bit difficult - I need a better angle on that, because it happens frequently), and my students this year have become stronger conceptually and computationally than with the setups that I've tried in the past, while moving at a faster pace. This one seemed to work quite well.

Spring Wave Speed Lab

My first lab with the spring wave speed used to be a prescribed method of stretching the spring, then keeping the length the same, but not using all of the spring, using the unstretched spring amount as a stand-in for tension, etc. ... It became more about direction-following and less about understanding than I wanted, and I had to dismiss the possibilities of amplitude, etc. affecting the wave speed. At the end of it all, they still didn't have the main idea (that wave speed only depends on properties of the medium) in mind very well.

I've gone to a more open-ended WCYDWT-style lab:
"Here's a slinky: look at these cool wave pulses. What do you think might affect their speeds?"

Take down the list dutifully - this year's ideas:
First section:
- Spring tension
- Amplitude
- Carpet vs. tile floor
- Horizontal vs. vertical pulses
Second section:
- Spring stretch
- Amplitude
- Frequency (this was a fun one to test. There was a metronome involved, and it was tricky to measure the speeds of the lower frequency waves, but it was a good experience for the hearty)

They did a much better job of experimental design, whiteboarding, and presentation than in the past. I'm still having to answer too many questions/guide Socratically too much about what should be on the axes and what the order of the axes should be, but the Honors classes are much better in that regard. Time will hopefully improve this situation for both. Everybody's getting the experience of designing and analyzing, and of calculating the wave speed, too, regardless of their question.

The whiteboards:

Question Boards and Answer Boards

I've been taking pictures of student whiteboards for a while, uploading them to our online classroom on our school's website. When the problems are different, they can be a source of extra practice (complete with solutions) for students.

When the framework is WCYDWT (What can you do with this?), the problems are definitely all different, because they're generated by the students. Today, I had them shoot a launcher straight up in the air, and then they had to develop and answer a question when the launcher was at some other angle. They determined the initial velocity from the first shot, and then came up with a variety of other scenarios for the 2D shot, including simple range equation angle and distance determinations, all of the way up to firing a ball into a moving CVPM buggy.

I structured the whiteboard sharing a little differently this time, though. I had each group write up a nice solution on their big whiteboard, just like normal, but I also had them use a small whiteboard.  On the small whiteboard, they made clear what their question was and included only raw data. This is the "question" board, and the big one is the "answer" board. This makes the process of using these as practice problems more practical and more like "flying solo."

Here's an example:

Collision!

Today was the day for the collision practicum! I set up the air track, cart, and pendulum like this:

I released the cart from the top - 4.8 meters away - and they could time how long the trip took (3 trials).  I also let the pendulum swing for a while, and they could measure whatever they liked. I assigned each group a number of cycles which the pendulum must go through from the time when they release the cart until the cart reaches the bottom of the ramp. They must calculate the location at which the cart must be placed in order to make that happen. There's a piece of magnetic track from my son's train set that makes noise when the magnet attached to the bottom of the pendulum swings just above it - this signals success.

My tests before school were all very successful, so I was hopeful before class about their success.

I had each group write up a whiteboard that just needed data plugged in, and we began the data-taking with about 30 minutes left in class.

In the first class, almost all of the runs looked extremely close, but we couldn't get the sensor to trip - downer. :(  In the second class, I adjusted the sensor setup, and two out of four were successful. One of the others had a good method, but was just a touch off in execution and/or measurement.

Success!

Whiteboards: