This semester I’m trying to flip my flipped approach. Here’s a quick description. Today was the best day so far doing it this way. It was the fourth day of class, and the others had been ok but not great, in my opinion. The first day we spent time on the Euler equation (complex numbers), vector calculus review, and linear algebra basics. I farmed out different things for each person to do and then they presented. It was a little fragmented and I don’t think everyone got a lot out of it. The second day we focused on Maxwell’s equations, again farming each one out to them. Again I felt it was a little disjointed, though, since it was mostly review, I wasn’t too worried about it. The third day went pretty well as we talked about what plane waves are. But today felt really good, so I want to describe why.

The topic was the index of refraction. The “daily question” was “Does light slow down in glass even though the speed of light is the same in all inertial frames?” Instead of jumping right on that question, I started by having them think about the trajectory of a single charged particle exposed to a plane wave. After working for ~5 minutes, I asked what some thought and got the answer that the particle would head in the direction of the field and then turn around and go back to where it started. We kicked that around a while and then I quickly coded it in Mathematica:

sol=First[NDSolve[{y”[t]==Sin[t], y[0]==0, y’[0]==0}, y, {t,0,10}]];

Plot[y[t]/.sol, {t, 0, 10}]

And they saw that they were wrong (have you put some thought into it yet?). What was cool was that their prediction matched a plot of the speed of the particle, just not the displacement.

So after we were ok with the trajectory, I asked whether that charged particle would emit any light. We went back to this great PhET simulation to see, after they put some thought into it themselves. They seemed pretty happy with the idea that a monotonic, though herky-jerky, motion would produce pulses of light.

So next I asked them to think about what would happen to lots of charges. After that we talked about atoms with heavy nuclei and light electrons. We came around to the notion of the electrons effectively behaving like they were attached to springs. So then we started playing around with this great resonance PhET simulation. It took a while, but I kept asking if they thought the mass oscillated with the same frequency as the driver, and whether it was in phase (or how much it was out of phase). Eventually we put these ideas on the board:

- charged particles will oscillate with the same frequency as the light
- They are most likely out of phase with the light
- They are accelerated charged particles so they emit light
- The light they emit is the same frequency as the shaking
- Therefore the emitted light frequency is the same as the original light frequency
- The emitted light is most likely out of phase with the original light
- Particles further on in the material will experience the combined light of the original plane wave and the scattered light from the other particles.

Finally we were able to get their thoughts about the daily question. I asked whether the interpretation of bending light as a manifestation of light slowing down is wrong, if Einstein’s theory somehow didn’t apply, or something else. It was a cool discussion, involving ideas about how glass might not be inertial and how light might zigzag on its way through glass.

So here I did a little bit of lecture, talking about how multiple out-of-phase fields added, showing that the sum can lead to a total field with a slightly different phase. That phase shift happens over and over again at each scattering point, making the wavelength appear to shorten. Here’s the vid we analyzed:

Basically, a single quick phase shift only places a single phase jump in an otherwise smooth sine wave. However, as you can see in that cartoon, lots of them together makes the wavelength appear to be shorter.

Where does that lead us? Well, if the wavelength appears shorter but the frequency is the same (see list above), then the speed appears slower! It’s an optical illusion! (get it?) In fact, it’s a remarkably powerful illusion. No photon travels slow. They don’t zigzag (because only the forward direction shows constructive interference for randomly placed particles), and they don’t pause during the scattering (it’s been confirmed to take less than ~10 attoseconds). They all cruise through at the speed of light. But the locations of constructive interference (the peaks in that cartoon) move at a different speed. Cool, huh?

So, that was a lot of fun, and they really asked some great questions. So why did I think this was a good example of flip the flip? Because if they had really read the book ahead of time, they would not have engaged as much with this conversation. How do I know? Because I’ve taught this many times. If they read the book, they’re stuck in Maxwell equation this and Polarization that (which is also important, of course).

Here’s the kicker. After all that, then we engaged with the book, following these steps:

- light makes the charges slosh around
- we assume they slosh at the same rate as the light
- We assume that they slosh in a fashion linearly related to the amount of light
- We plug in those assumptions into the wave equation (with a sloshing source term)
- We see that it all works out as long as we let the index of refraction be related to the constant of proportionality in (3).
- Ahhh! but the constant is complex because of the phase shift
- therefore absorption has to happen

Now, 1, 2, and 3 were much better to work with my students on compared to previous times I’d taught this class because of the work we did ahead of time. Then I talked about the typical calculations/derivations I wanted to hold them responsible for and they asked me to provide a few screencasts to help them out. You can see them all here.

So I thought it went well for these reasons:

- They all engaged with a similar background right away
- They hadn’t seen what the trajectory of that first charged particle was, and their mistakes helped them learn
- They went on the speed-of-light tangent with me because they didn’t know it was a tangent
- The derivations were more fun to go over because they could see the physical explanations behind them
- I felt the whole day went better than the two previous attempts: 1) flipped with lots of homework due each day, and 2) flipped with standards based grading.
- The resources (scasts) that I made for them were completely tailored to their needs.

Ok, what do you think? Here’s some starters:

- I’m in this class and I really thought that speed of light thing was cool. However, this sucked: …
- I’m in this class and I was totally lost. I really wish I had read the material before I came.
- I like this way of talking about the speed of light. Does it work in this situation . . .?
- That’s not how light propagates at all! You should teach them this instead . . .
- I think you lectured too much. It’s not flipped at all! Here’s what you should do . . .
- I think you could do an even better job by . . .

I like the way you are describing things. The flipped classroom is great because you can spend time in class helping them understand a concept that solves a problem, but the flip-the-flip classroom is great because it can convince students that there is a problem to be solved.

I love how you phrased that at the end. I want my students to engage and see that there’s something cool but complex here. Then I want them (in a perfect world) to be curious how to model it, mathematically, philosophically, and numerically.

On Tue, Feb 18, 2014 at 8:53 PM, SuperFly Physics wrote:

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It’s great when your posts make me reconsider how I think about and understand various topics.

I like that the activity seems to be built around playing with various ideas and building up a collection of observations/conclusions that you can then use to help you interpret a new theory. This seems more physical and less intimidating than saying ‘here’s a new theory, let’s use it to draw a bunch of conclusions.’

As an anonymous student in your class, I liked this approach. However, here is where I am confused. How does the Mathematica code represent the situation you present? Could you explain what the code means a little more and how it reflects the situation? For me it would be helpful if you give more explanation when you use Mathematica since otherwise I feel like I am taking it on faith that your code indeed reflects the situation properly.

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