I’ve been writing about how well things have been going since September, how inquiry-based learning has transformed my classrooms into little rainbow-coloured explosions of critical thinking and engagement. I haven’t written much about the times I want to cancel class for the day and give up on human reason. Today was one of those days.
Two students were presenting the class’s data on this subject today: Why do the peak-to-peak voltages across circuit components sometimes add up to the total voltage and sometimes not? Is it because of phase shift?
Presenting Students: [presented data that shows that circuits without phase shift have 0-5% error in Vt = V1 + V2. Circuits with phase shift have 3 – 20% error. They clearly draw this out, separating the data into two distinct categories. Then they say they can draw no conclusions.]
Me: So is the phase shift what’s causing the voltages to not add up?
Presenting Students: I don’t know. Why do only the RC circuits have phase shift?
Me: Thanks, I’ll add that to the list of questions. Now what about the voltages adding up — does it have anything to do with phase shift?
Presenting Students: I don’t know.
Me: Well, for the circuits that don’t add up, do they all have phase shift?
Presenting Students: We can’t really tell.
Me: You just went to a lot of trouble to colour code them differently to show that all the circuits that don’t add up have phase shift. Why did you draw our attention to that?
Presenting Students: I don’t think there’s really anything we can add to the model.
Rest of class: Well, this circuit was designed to give us phase shift, so that doesn’t really prove anything. [Note: last week everyone chose their own values, and they decided they couldn’t draw any conclusions because the data sets were all different. This week we picked a standard circuit from the lab book, and they rejected the data because it was “cooked.”]
Me: Ok, what would you need to test to strengthen the evidence?
Students: Why don’t component voltages add up in RC circuits where phase shift is present?
Me: Does anyone else have comments about the data?
Rest of class: *silent*
Me: Does this bring up any questions that we should look into?
Rest of class: *silent*
Note to self
I think this was one of those times when I should have asked “How does the evidence support [idea]? How does the evidence conflict with [idea]?” But honestly, I don’t think it would have helped. We ended up just staring at each other in mutual incomprehension. It might have been more helpful if I had asked them to remind me what they meant by phase shift, or why we were asking this question at all. I think what I actually did was ok: let it go and focus on the thing they’re curious about (why circuits with two capacitors or two resistors don’t have phase shift at all). It just resulted in a gnawing irritation that has blossomed into full-fledged (and uselessly irrelevant) anger now, 10 hours later.
In my mind, the evidence is either conclusive, or there is some question that needs addressing, or there is some flaw in the experiment that needs to be fixed, or… something! I honestly don’t care what the problem is, or whether there’s a problem with the data. But when it’s none of the above, I’m at a loss.
Tentative conclusion about me
I was overwhelmed with a knee-jerk reaction of “appalled” and couldn’t, in the moment, think how it was possible for someone to contradict themselves so blatantly and fail to notice.
Tentative conclusion about the presenting students
They had forgotten what phase shift meant, exactly (they analyzed the data yesterday, and proposed the question last week) so it wasn’t making any pictures in their heads. There are too many new ideas in play for them to be able to hold all of them in their attention at once, and their mental “RAM” was occupied thinking about how capacitors charge up. I know this because, having resisted the temptation to cancel class and go home, we later discussed why a capacitor reads “open” on an ohmmeter. The students unleashed a flood of high-quality questions, like “maybe the ohmmeter can’t measure the resistance because the charged capacitor is fighting the ohmmeter’s current, the way two opposing batteries do.” “Can we put it in a wheatstone bridge to measure its resistance?” and “Can you make a DC supply with a cap? It could charge up and then shoot out steady current to make it steadier.” (connections, cause, clarity…). They’re really into the idea of “charging up” and “discharging” the capacitor right now.
Well, we’re in the middle of reviewing capacitor research, which will help. We’ll definitely measure the things they are interested in, of which there are a million, so there’s no rush on this. I will do some more directive activities about phase shift, I think. I’m thinking along the lines of having them practice adding sine waves graphically (along the lines of Why Kids Shouldn’t Use Components Until They Beg). I will also require students to write down their conclusions and questions on their whiteboard while they are analyzing the data, in the hopes that that will prevent the ideas from getting lost… or at least helping us notice that an idea got away.
Update March 12, 2012
Shortly after writing this, I was bowled over to learn more about how my students were thinking about cause. This conversation may have had more to do with their ideas of what causation is than their ideas of what causes voltages to not add up. More soon.