One of the topics we teach in second semester physics is blackbody radiation. The typical kind of scenario students would be asked about is, given the temperature of a star and information about the size and orbit of a planet, determine how much energy arrives on the planet each second. One of the main difficulties students have is deciding how to use the relationship that intensity = power/ area. There are lots of different energies, areas, and intensities to consider, so students who are used to plug-n-chug can easily fall apart here. Since we introduced the topic two weeks ago, I’ve been starting each day with various discussion (clicker) questions asking student to think about intensity, energy, and power qualitatively. We’ve had lots of good days of discussion stemming from this and progress is certainly being made, but students’ handle on the ideas seem to be quite elusive and fleeting with lots of side-steps and backslides, even for the students who don’t usually struggle.  On Thursday, I asked the following question to start our day, which pulled us into a really good discussion that lasted 15-20 minutes or so:

Assume you know how much energy is emitted from a star each second, Es. You want to find the intensity of the light arriving at a planet. Which calculation should you use? The question included a diagram that showed three distancse: Rs, the radius of the star, Rp, the radius o the planet, and Rsp, the distance between planet and the sun. The four options where.

A. Es/ 4πRp²

B. Es/ πRp²

C. Es/ 4πRsp²

D. Es/ 4πRs²

Students thought to themselves, voted, and then talk in groups. When students re-voted, we were split between B and C, with a few unsure whether it was A or B. We’ve been getting used to these kinds of discussions, so I asked a few students to explain why those chose B.  The basic line of reasoning was that we were interested in the intensity at the planet, so the relevant area had to be the area of the planet, because the planet that was catching the energy with its cross-sectional area.

Instead of letting people voice an argument for C, I said that those who picked C had to explain what they was wrong with B without explaining why they thought C was correct. I motivated this by talking about why so many hot button issues arguments are unproductive, such as abortion rights, whereas everyone just keeps repeating their arguments without listening to the other side.

One really nice argument, which ended up being convincing to most in the class, was this:

– Es/ πRp² says in words that you are taking all the energy from the sun and spreading it over the area of the planet. This can’t be right because not all the energy from the sun gets to the planet. In fact, most of energy misses the planet because it goes off in other directions.

I made sure at least one other student could repeat the argument, and then another argument was made: This argument was about how we could actually “correct” the equation so it did give the intensity at the planet. The argument was that if the “area” you want to divide by is the area of the planet, than the numerator has to be energy arriving at the planet Ep, not Es. Intensity *is* an energy divided by an area, but to get the intensity of the planet using the area of the planet, you have consider the actual energy arriving at the planet, so it would be Ep/πRp².

By the time we got around to asking for arguments for C, most students were convinced it couldn’t be B, but formulating good arguments for C was hard, and it took a bunch of back and forth among the students before a really compelling argument to emerge. The discussion was really juicy and students were really listening, but I had a feeling that while the “class” a whole was getting it, many students still needed an opportunity to pull it together, consolidate. So I had students vote with thumbs up, thumbs side, and thumbs down, whether their understanding was , “I understand the reason why it must be C, and could explain it,” “I think I understand why it must be C, but I’m less confident I could explain it someone else,”, “I’m still not sure I understand why it must be C”. The room was split about half between thumbs up and thumbs to the side. I said if your thumb was to the side you had two options: you could look to a person with their thumbs up and tell them that you want to practice explaining it to them OR you could ask them to explain it to you one more time. I’ve never used that move before (giving the students who are unsure the option to either practice explaining or receive an explanation), but for whatever reason, it was the right move at the right time. The entire class in pairs and groups erupted into conversation and spent a long time explaining to each other–serious, passionate, intellectual talk with gesturing and smiles. I just stood at the front of the room and watched and waited for the talk to subside. It took a long time. I had a few more clicker questions, which we breezed through. Many groups told me that while they were discussing alone, they had actually spontaneously asked of themselves and discussed the questions I had posed.

I wanted to jot down this brain dump, because I thought the two counter-arguments were really fantastic, and I wanted to think about why this particular talk move worked so well. Part of it is that they were just primed and ready to talk about it more, but I think there was something about putting the power in the hands of the person who doesn’t understand. They were in control-they could demand to hear an explanation or demand that someone listen to them.