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When we start investigating a new topic or component, I often ask students to make inferences or ask questions by applying our existing model to the new idea.  For example, after introducing an inductor as a length of coiled wire and taking some measurements, I expect students to infer that the inductor has very little voltage across it because wires typically have low resistance.  However, for every new topic, some students will assume that their current knowledge doesn’t relate to the new idea at all.  Although the model is full of ideas about voltage and current and resistance and wires, “the model doesn’t have anything in it about inductors.”

There are a few catchphrases that damage my calm, and this is one of them.  I was discussing it with my partner’s daughter, who’s a senior in high school, and often able to provide insight into my students’ thinking.  I was complaining that students seem to treat the model (of circuit behaviour knowledge we’ve acquired so far) like their baby, fiercely defending it against all “threats,” and that I was trying to convince them to have some distance, to allow for the possibility that we might have to change the model based on new information, and not to take it so personally.  She had a better idea: that they should indeed continue to treat the model like a baby — a baby who will grow and change and isn’t achieving its maximum potential with helicopter parents hovering around preventing it from trying anything new.

The next time I heard the offending phrase, I was ready with “How do you expect a baby model to grow up into a big strong model, unless you feed it lots of nutritious new experiences?

It worked.  The students laughed and relaxed a bit.  They also started extending their existing knowledge.  And I relaxed too — secure in the knowledge that I was ready for the next opportunity to talk about “growth mindset for the model.”

On network analysis

“At first I didn’t understand why we had to learn these complicated methods when we could just do it the simple way you showed us last semester.  But when you get to these complicated circuits, it makes it so much easier.  I do math every night now, even if I don’t have any for homework, because you have to exercise all the time or you lose it.”

“I got off to a bad start with this, I had the wrong answers for everything, and I really didn’t know how to do it.  I won’t lie.  But now after taking all these measurements, I’m starting to understand.  And I did really bad on that first quiz — I didn’t even know what DC offset was. But I made up some practice problems that are a little bit different from the quiz, and I can do them now.”

On AC voltage, sinusoidal signals, and what the time domain really means

“I just realized that the word ‘electronics’ has the word ‘electron’ in it. ” (x2) (After a conversation about how a sinusoidal signal represents a voltage or current that changes over time)

“Is this why we need DC voltage for electronics — so it doesn’t turn off all the time?”

“In an AC circuit, how to the electrons get their energy back after they’ve lost it?” (I love the insight in this question — the synthesis of ideas, the demand for a coherent cause)

While presenting some routine lab measurements

“How does an electron know how much voltage to drop in each component?” (7 months later, students are suddenly gobsmacked by the totally weird implications of Kirchoff’s Voltage Law)

During a one-on-one discussion of the group’s interpersonal dynamics

“I find no one in this program is looking for someone to give them the answers.  We might text all night long about homework but it’s never ‘Can you send me X,’ it’s always ‘How can I figure out X?’ “

While whiteboarding some AC circuit data

“I don’t like saying that KVL applies to instantaneous voltages, because it applies everywhere.”

“But if you say instantaneous, it applies in a general sense. Have you ever seen an AC circuit where the component voltages didn’t add up to the supply?”

Another whiteboarding session

“Make sure you’re talking about electrons, otherwise it’s not a cause!”

“And that’s supported by the model, because…”

While designing an experiment

“Do you have a 1uF capacitor?” “No, I guess we can use 100uF and scale it…”  (Students making big gains in proportional reasoning)

After discussing how a capacitor’s voltage approaches an asymptote

“I never noticed before how much math relates to life — like the idea that sometimes the closer you get to something, the harder it is to get there.  I guess it’s not surprising — because math comes from life.  Math is everything.”

I expect students to correct their quizzes and “write feedback to themselves” when they apply for reassessment.  The content that I get varies widely, and most of it is not very helpful, along the lines of

I used the wrong formula

I forgot that V = IR

It was a stupid mistake, I get it now.

I was inspired by Joss Ives’ post on quiz reflection assignments to get specific about what I was looking for.  This all stems from a conversation I had with Kelly O’Shea about two years ago, back when I had launched myself into standards-based/project/flipped/inquiry/Socratic/mindset/critical thinking/whatnot all at once and unprepared, that has been poking its sharp edges into my brain ever since:

Me: Sometimes I press them to be specific about what they learned or which careless mistake they need to guard against in the future. It’s clear that many find this humiliating, some kind of ingenious psychological punishment for having made a mistake. Admitting that they learned something means admitting they didn’t know it all along, and that embarrasses them. Does that mean they’re ashamed of learning?

Kelly: How often do you think they’ve practiced the skill of consciously figuring out what caused them to make a mistake? How often do we just say, “That’s okay, you’ll get it next time.” instead of helping them pick out what went wrong? My guess is that they might not even know how to do it.

Me: *stunned silence*

So this year I developed this.

Phases of Feedback

1. Understand what you did well
2. Diagnose why you had trouble
3. Improve

Steps 1 and 3 can be used even for answers that were accepted as “correct.”

This has yielded lots of interesting insight, as well as some interesting pushback. Plus, it gave me an opportunity to help my students understand what exactly “generalize” mean.  In a future post I’ll try to gather up some examples. Overall, it’s helped me communicate what I expect, and has helped students develop more insight into their thinking as well as the physics involved.

How can I help students make causal thinking a habit?  I’ve written before about my struggles helping students “do cause” consistently, and distinguishing between “what made it happen” vs. “what made me think it would happen.”  Most recently, I wrote about how using a biological model of the growing brain might help develop the skills needed to talk about a physical model of atomic particles.

Sweng1948 commented that cause and definition become easy to distinguish when we talk about pregnancy, and seemed a little concerned that it would come off as flippant.  To me, it doesn’t — especially because I use that example all the time. Specifically, I talk about the difference between “who/what you are” (the definition of you) and “what caused you” (a meeting of sperm and egg).  In the systems of belief that my students tend to have, people are not thought to “just happen” or “cause themselves.”  It can help open the conversation.  However, even when I do this, they are surprisingly unlikely to transfer that concept to atomic particles.

Biology Vs. Physics

My students seem to regard cause differently in biology vs. physics.  They are likely to say that eating poorly causes malnutrition and eating well contributes to causing good health; they are less likely to say that the negative charge of electrons causes them to move apart, and more likely to say that electrons move apart because they’re electrons, and that’s what electrons do.

Further, once they conclude that moving two electrons apart causes their repulsion to weaken, they are unable to decide whether moving them closer together strengthens it (I have no idea what to do about this).  It’s also often opaque to students whether one electron is repelling the other, or the second one is repelling the first. This happens in various contexts: the other day, a student presented the idea that cooling a battery would lower its voltage.  Several students were frustrated because they had asked what would raise a battery’s voltage, not what would lower it, and were a bit aggressive in telling the presenting student that he had not answered their question.

That’s one of the reasons I was interested in using this “brain” model as a way to open the conversation about causality and models in general; they do cause better with biology.  I’ll have to figure out next year how to build a bridge between cells and atoms…

I’m not sure why it’s so difficult.  Here are a few stabs at it:

1. Is it because they see causality as connected to intention — in other words, you are only causing things if you do them on purpose?
2. Does their experience of their own conscious agency helps them see how their choices are causes that have demonstrable effects — such that things that don’t have choices also seem not to cause things?
3. Is it because living things are easier to see and relate to than electrons?
4. Is it because they see cause as inextricably linked to desire?   Something like, “What caused me to buy a bag of candy is that I wanted it. So, electrons must move because they want to.”

I sometimes fool myself into thinking that my students have understood some underlying principle when they anthropomorphize particles and forces: “The electron wants to move toward the proton.” “Voltage is when an electron is ready to move to another atom.”  I assume that they are constructing a metaphor to symbolize what’s going on, or using a verbal shorthand.  Then I realize, many students don’t think of the electron’s “desire” as a metaphor, and can’t connect this to ideas about energy, charge, etc. Consider this my plea to K-12 teachers not to say that stuff, and when students bring it up, to engage with them about what exactly that means.  Desires are things we can use willpower to sublimate.  Forces, not so much.  That’s why it’s called force.

Something about cause leads to students treating particles (and, for that matter, compilers and microprocessors) as if they, like people, might act the way we expect, but they also might not.  I can’t tell whether it’s because there could be an opposing force, or “just because.”  If it’s the former, then there’s a kernel of intellectual humility here that I respect: a sort of submission to the possibility that there are forces we don’t understand, and our model will only work if there are no opposing forces we haven’t accounted for.  However, I often can’t find out whether they’re talking/thinking about science or faith, because the responses to my questions are often defensive, along the lines of “My physics teacher said it’s complicated.  The reason they didn’t teach it to us in high school is that it’s just too hard for anyone to learn, unless they’re a theoretical physicist.” (*sigh*. Hoping the growth-mindset ideas will help with this).

We Can’t Understand It Fully, So There’s No Point

Also, the “we don’t understand it fully” shrug seems to be anti-generative: it leads to an intellectual abdication.  It’s a defence against the idea that we should just go ahead and use our model to make predictions, then test the predictions to find the holes in the model.  Or maybe I’ve got it backwards — maybe the intellectual abdication causes the shrug.  I’m back to growth mindset again, but not about growing ourselves — growth mindset for the model too!  Fixed mindset says there’s no point making a prediction that might be wrong.  Only a growth mindset sees the value in testing a prediction with the intention of helping the model (and ourselves) get stronger.

I expect that the word “potential” is part of the problem here (as in, potential difference and potential energy) — to my students, “potential” means something that you need to make a decision about. They say that they will “potentially” go to the movies that night, which means they haven’t chosen yet.  By that logic, if you have a “potential difference”, that means there might be a difference, but there might not, too. Depending on what the electron decides.  Potential energy?  Maybe you’ve got (or will later have) energy, maybe you don’t.  What’s strong about this thinking is that they’re right that there’s something that “might or might not” happen (current, acceleration, etc.).  What’s frustrating is that I don’t know how to help them unpack the difference between a “force” and a “decision” in a way that actually helps.

(And no, the connections to the uncertainty principle, the observer effect, the unpredictability of chaotic systems, and the challenges to causality posed by modern physics are not lost on me… but I’d rather my students work through “wrong” conclusions via confidence in reasoning, than come to some shadow of the “right” conclusions via an assumption of their own intellectual inadequacy.)