## Circuits: find out now or leave it hanging?

I had a really fun class today. It was a review day, like every Friday, and I started out with a pretty innocuous clicker question (though I don’t use clickers). Go ahead, give it a try. The correct answer changes to bold when you hover over it.

The initial vote turned out to have a pretty even mix of the 3 realistic answers (rarely do batteries explode). I was a little surprised because 1) it’s not that hard of a problem compared with some of the complicated circuits we’ve been doing, and 2) I knew it wasn’t as hard as a similar question about R2. But because they were showing their confusion with their vote, I decided to really have all three answers be fleshed out.

For each answer, I asked for someone willing to be a public advocate. I got these three arguments:

1. The current doesn’t change because all of it still needs to flow through R1
2. The current increases because there are now more paths for the current to flow through
3. The current decreases because the total resistance is now larger so the battery doesn’t have to work as hard.

For each a student first articulated their thoughts and I said it back to them with some clarifications to make sure I had the argument right. After the three arguments had been laid out, I told them that 2 of them were wrong. So I had them share with their neighbors some more and this time I wanted them to vote an argument “off the island.” In other words, don’t vote for the correct answer, instead vote for the argument that you are most sure is wrong.

The vote was basically even once again!

Ok, here was the cool part. I looked at the clock and realized that we had already spent 10 minutes on a question that I thought would only take us 2 minutes. So I asked them which of the following would help their learning the most:

2. Leave them hanging
3. Let them talk it out some more with their classmates

Interestingly, as I gave the options for the vote, right away a vocal minority shouted for a combo of “tell us now” and “definitely don’t leave us hanging.” So I asked this question:

Are you voting for what you want now or what will help you learn this for next week’s oral exam?

I thought it was interesting that a few of them really seemed to get that they would vote two different ways based on the answer to that question. So, after a brief talk about what I meant by that question, we voted again and it was resounding for “let us talk some more about it.”

So I told them that I’d put them in three groups to hash it out. I asked if they wanted the groups to be made up of people who liked the three different possibilities OR if they wanted the groups to be made up of people who really disliked one of the possibilities. They voted overwhelmingly for the latter, which surprised me. But I went with it.

So they got into their groups and I told them to make sure everyone in their group understood their main arguments and that I would randomly select a person from each group to present the argument. It’s interesting that I made the mistake of asking “are you ready” before making it clear that I would randomly pick someone. Before that clarification they said they were ready. After the clarification there was a strong sentiment that they needed more time.

Here were the three counter arguments:

1. It can’t stay the same because V=IR and R is clearly changing.
2. It can’t increase because the equivalent resistance goes up.
3. It can’t decrease because the charges aren’t psychic (they have no idea that there’s a change ahead when they’re in R1).

Ok, I thought, let’s get into positive groups (groups that are separated by the original answers). Again I told them to have an argument ready.

1. It stays the same because of the psychic argument (which I now called interestingly wrong).
2. It increases because the equivalent resistance goes down (and here’s a chalkboard with a numeric example).
3. It decreases because the equivalent resistance goes up (and here’s a whiteboard with a symbolic approach).

I thought the juxtaposition of the last two was really interesting.

Alright, at this point we had been working on this for 30 minutes! But the energy in the room was great! The next thing I did was follow up with what one student (by himself) had started to do on another whiteboard:

$R_\text{equivalent}=R_1+\frac{R_2 R_3}{R_2+R_3}=R_1+R_2\left(\frac{R_3}{R_2+R_3}\right)

There were a few “aha’s” at that point so I did an oral vote and now everyone was pretty convinced of the correct answer (the current increases).

So I thought it was fun. I liked how they asked to spend more time on it, neither wanting to be left hanging nor just being given the answer. I also really liked the different modes of argument (arguing for an answer versus arguing against an answer).

What do you think? Here’s some starters for you:

• I’m in this class and I thought it was great. I was confused at first but . . .
• I’m in this class and I just wish you would have given us the answer because . . .
• I’m in this class and you’ve totally misrepresented what happened. Instead this is what happened . . .
• I don’t see the difference between what I want now and what helps me with next week’s oral exam.
• I would have fired up PhET and shown them after the initial prediction (Note that one twitter buddy basically said just that:

• I would have wired up the circuit and shown them.
• I wouldn’t have spent more than your original plan of 2 minutes. This is too easy of a problem to spend 30 minutes on.
• What do you have against clickers? They’re the single greatest technological invention in the last 100 years!
• Do you have students really advocating for themselves when you say you might pick them randomly?
• This class sounds great, how do your students like all these crazy things you do?
• It’s too bad you weren’t asking about R2. That’s a much more interesting problem. Note that another twitter bud of mine characterized that as the pizza problem:

Professor of physics at Hamline University in St. Paul, MN
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### 4 Responses to Circuits: find out now or leave it hanging?

1. bretbenesh says:

This was really interesting.

“I asked if they wanted the groups to be made up of people who liked the three different possibilities OR if they wanted the groups to be made up of people who really disliked one of the possibilities.”

I suppose this could make sense (although it was surprising to me, too) if you focus in on the “really disliked” part of the sentence. Students may have wanted to be put together with people with strong feelings.

And is there a way to arrive at the correct answer “intuitively?” Or do you need to basically do the calculation in order to figure it out?

• Andy "SuperFly" Rundquist says:

I think there are ways to develop intuition about these sorts of circuits. The notion that more possible paths means more overall current works in this case.

2. Mylène says:

So many interesting things here — the original clicker question, the student responses, the creative questions you asked them. A few quick thoughts:

1 — I think that clicker question is algebraically simple, but conceptually difficult. It’s great to hear that the classroom culture is one where students talk about what “what things are like” and their intuitive concepts of heuristics and causes, not just math tricks. The reasons I think it’s tricky are well articulated by your students — the “psychic”-seeming electrons, the ideas that adding a resistor should increase resistance, and the “sequential” way of thinking about electricity that many people use, as if there’s a single starting point where current “comes from”, instead of a nearly-simultaneous motion of electrons that pre-exist everywhere in the circuit. Can’t remember if you already use the DIRECT Concept Inventory — I found the paper that describes it helpful in anticipating students’ initial ideas, and the authors were happy to share the inventory itself.

2 — I’m always wary of replacing students’ causal thinking (“it’s happening because of the number of paths, or the amount of resistance, or the amount of voltage”) with non-causal thinking (“it’s happening because math, because PhET, because the ammeter says so”). “Because math” (my students’ favourite hiding place) is a legitimate answer to “what”, but it’s a circular answer to “why.” I found the causal thinking your students were doing quite exciting — Were they able to carry that causal thinking forward into the correct answer?

3 — I’d love to know what they would say if you asked them to choose an incorrect answer and explain what physically causes it to *not* work that way. Another way to cast this would be to give them a few heuristic explanations and have them choose the best one, or say what was good about each one. I’m imagining things like “before the switch is closed, there are lots more electrons available inside R1, but they’re not flowing yet because there’s a limited number of spaces opening up in front of them. By adding the second resistor, there are more spots opening up for electrons from R1 to flow into.” Or “Adding the second parallel resistor increases the “reach” of the electrical field so that it pulls more strongly on the current.” Or (insert your own non-canonical explanation phrases in heuristic terms here). Any thoughts about what they might say?

3. Andy "SuperFly" Rundquist says:

1. Thanks for the DIRECT link, I’d never seen that!

2. I’m not sure if they were able to carry through their casual thinking. I really wish we had more time to spend on this (or, I suppose, a slightly smaller class – this is a 40 person lecture section).

3. They definitely liked having the opportunity to chime in on why other argument didn’t work, but not many of them (out loud, anyways) really did the kind of musing you’re talking about. Again, more time would have been great.