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:

# Formulas

abc

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.