Last February, I had a conversation with my first-year students that changed me.
On quizzes, I had been asking questions about what physically caused this or that. The responses had a weird random quality that I couldn’t figure out. On a hunch, I drew a four-column table on the board, like this:
I gave the students 15 minutes to write whatever they could think of.
I collect the answer for “cause” a write them all down. Nine out of ten students said that a difference of electrical energy levels causes voltage. This is roughly like saying that car crashes are caused by automobiles colliding.
Me: Hm. Folks, that’s what I would consider a “definition.” Voltage is just a fancy word that means “difference of electrical energy levels” — it’s like saying the same thing twice. Since they’re the same idea, one can’t cause the other — it’s like saying that voltage causes itself.
Student: so what causes voltage — is it current times resistance?
Me: No, formulas don’t cause things to happen. They might tell you some information about cause, and they might not, depending on the formula, but think about it this way. Before Mr. Ohm developed that formula, did voltage not exist? Clearly, nature doesn’t wait around for someone to invent the formula. Things in nature somehow happen whether we calculate them or not. One thing that can cause voltage is the chemical reaction inside a battery.
Other student: Oh! So, that means voltage causes current!
Me: Yes, that’s an example of a physical cause. [Trying not to hyperventilate. Remember, it’s FEBRUARY. We theoretically learned this in September.]
Me: So, who thinks they were able to write a definition?
Students: [explode is a storm of expostulation. Excerpts include] “Are you kidding?” “That’s impossible.” “I’d have to write a book!” “That would take forever!”
Me: [mouth agape] What do you mean? Definitions are short little things, like in dictionaries. [Grim realization dawns.] You use dictionaries, right?
Students: [some shake heads, some just give blank looks]
Me: Oh god. Ok. Um. Why do you say it would take forever?
Student: How could I write everything about voltage? I’d have to write for years.
Me: Oh. Ok. A definition isn’t a complete story of everything humanly known about a topic. A definition is… Oh jeez. Now I have to define definition. [racking brain, settling on “necessary and sufficient condition,” now needing to find a way to say that without using those words.] Ok, let’s work with this for now: A definition is when you can say, “Voltage means ________; Whenever you have ___________, that means you have voltage.”
Students: [furrowed brows, looking amazed]
Me: So, let’s test that idea from earlier. Does voltage mean a difference in electrical energy levels? [Students nod] Ok, whenever you have a difference in electrical energy levels, does that mean there is voltage? [Students nod] Ok, then that’s a definition.
Third student: So, you flop it back on itself and see if it’s still true?
Me: Yep. [“Flopping it back on itself” is still what I call this process in class.] By the way, the giant pile of things you know about voltage, that could maybe go in the “characteristics” column. That column could go on for a very long time. But cause and definition should be really short, probably a sentence.
Students: [Silent, looking stunned]
Me: I think that’s enough for today. I need to go get drunk.
Ok, I didn’t say that last part.
When I realized that my students had lumped a bunch of not-very-compatible things together under “cause,” other things started to make sense. I’ve often had strange conversations with students about troubleshooting — lots of frustration and misunderstanding on both sides. The fundamental question of troubleshooting is “what could cause that,” so if their concept of cause is fuzzy, the process must seem magical.
I also realized that my students did not consistently distinguish between “what made you think that” and “what made that happen.” Both are questions about cause — one about the cause of our thinking or conclusions, and one about the physical cause of phenomena.
Finally, it made me think about the times when I hear people talk as though things have emotions and free will — especially high-tech products like computers are accused of “having a bad day” or “refusing to work.” Obviously people say things like that as a joke, but it’s got me thinking, how often do my students act as though they actually think that inanimate objects make choices? I need a name for this — it’s not magical thinking because my students are not acting as though “holding your tongue the right way” causes voltage. They are, instead, acting as though voltage causes itself. It seems like an ill-considered or unconscious kind of animism. I don’t want to insult thoughtful and intentional animistic traditions by lumping them in together, but I don’t know what else to call it.
Needless to say, this year I explicitly taught the class what I meant by “physical cause” at the beginning of the year. I added a metacognition unit to the DC Circuits course called “Technical Thinking” (a close relative of the “technical reading” I proposed over a year ago, which I gradually realized I wanted students to do whether they were reading, listening, watching, or brushing their teeth). Coming soon.
wakalix! This post reminded me of the wakalix. (I’m going to make you google that if you don’t know what that is because it’s reading)
*grin* I’m guessing you mean the neologism Feynman coined to describe a thought process where “there is no knowledge coming in,” not the technique for mapping the mathematical relationships between just and equal tuning…
Maybe it is. Is the wakalix “cause” or is it “voltage”? (If it’s both, does that make it a superwakalix?) What disgusted me about the whole process was how long I was oblivious to it.
On the other hand, maybe it’s not like a wakalix. “Cause” didn’t seem to be a placeholder for a nonsense syllable — it had a small number of highly repeatable implications, notably “definition,” which I suspect is related to “what caused you to decide that.” (e.g. “The definition of what voltage *is* caused me to decide that something did or did not fall into that category,” which is a perfectly reasonable line of thinking).
Incidentally, you probably already know this, but Brian Frank tames wakalixes and takes them for walks on his blog. They’re quite friendly once you get to know them.
wrt talking about objects as if they have agency/intentions/emotions: the philosopher Daniel Dannett calls it “the intentional stance”…educational psychologists have called it “intentional causality” and “personification” among other things. At times it can be productive in science and science learning…for instance it can sometimes be a good shorthand, and unpacking that shorthand can lead to a useful line of inquiry: (e.g., how does the battery ‘know’ to send out more current when the bulbs are in parallel). It doesn’t sound to me like your students were *really* thinking that voltage causes itself. It does sound to me like they could have used some more time making sense of the mechanisms of what goes on in circuits rather than focusing on definitions & equations…btw I have also noticed learners interpreting cause to mean “what caused you to believe that” instead of physical causation, even adults (even science teachers!)
Thanks for the new words — helpful. I agree that these ideas can be generative — I was frustrated with myself for not noticing that they were happening, and missing those opportunities. I’m a fan of anthropomorphising, myself… especially getting students to pretend to be electrons or compilers. A mission for this year: notice this more often.
I also agree that my students don’t actually think that things cause themselves — although I do wonder what it means when they say “that’s just the way it is” (another mission for this year: find an opportunity to unpack that). Although they probably don’t think it, they sometimes act as though they think it. It’s something I’m trying to get better at noticing and describing.
RE: making sense of mechanisms rather than focusing on definitions… I don’t have much patience for students memorizing definitions. But I’ve got lots of time for students doing the work of defining — and it seems like it is part of the process of sense-making. What is a description that has just the right scope to include all things we want to include, while also excluding all the things we want to exclude? Do we even understand the mechanism well enough to attempt this? When we try to define something and come up with competing definitions, how do we decide what else we need to research or measure in order to resolve the apparent contradiction?
Being able to do this means that we need a shared way to talk about “the description that includes just the right things and excludes just the right things.” We also need to have some criteria against which to judge the goodness of a definition. Working on it…
Glad to know I’m not the only one noticing “What caused you to believe that” vs. “What caused that to happen.” It’s a pretty subtle distinction, so an interesting thing to explore. One piece of good news about this: it’s close in meaning to “how does your conclusion follow from your premises,” something I struggle to articulate to students, so finding a way that students already think that way could help us find some common ground.
Spent some time exploring this with the second-year students this week (the same group I describe above), because it was tricky for them to articulate why they considered open-loop gain to be a differential or common-mode gain, as opposed to why it was. Our (now-) shared vocabulary about causality allowed us to discuss that difference, so I guess I can lay off the booze…
Nice blog, by the way. Liked the eyebrows 🙂
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