You are currently browsing the category archive for the ‘Student thinking about thinking’ category.

diagram of axon terminal and dendrite

It’s that time of year again — the incoming first-year students worked through How Your Brain Learns and Remembers.  Some student comments I don’t want to lose track of:

“Of course you can grow your intelligence.  How else am I not still at the mental capacity of a newborn?”

“Where do dendrites grow to?  Why?  How do they know where to grow to?”

“I think I can grow my intelligence with lots of practice and a calm open mind!”

“Though I feel intelligence can grow, I feel it can’t grow by much.  Intelligence is your ability to learn, and you can’t just change it on the spot.”

“I think I can grow my intelligence because the older I get the smarter I get and I learn from mistakes.”

“I can definitely become more intelligent or more knowledgeable, otherwise no point in trying to learn. However, everyone is different, so each person could take more time to grow the dendrites and form the proper memories.”

“I think you can grow your intelligence through practice.”

“Do some people’s dendrites build quicker/slower and stronger/weaker than others?  Do some people’s break down quicker or slower than others?”

“You should be keeping up through the week but you probably can do homework only on weekends if you really focus.”

“People as a whole are always able to learn.  That’s what makes us the dominant species. It’s never too late to teach an old dog a new trick.”

Did you know robots can help us develop growth mindset?  It’s true.  Machine learning means that not only can robots learn, they can teach us too.  To see how, check out this post on Byrdseed.  I have no idea why watching videos of robots making mistakes is so funny, but my students and I were all in helpless hysterics after the first minute of this one…

After a quick discussion to refresh our memories about growth mindset and fixed mindset (which I introduced in the fall using this activity), I followed Ian’s suggestion to have the students write letters to the robot.  One from each mindset.  I collated them into two letters (shown below), which I will bring back to the students tomorrow.  All of this feeds into a major activity about writing good quality feedback, and the regular weekly practise of students writing feedback to themselves on their quizzes.

I didn’t show the second minute of the video until after everyone had turned in their letters.  But I like Ian’s suggestion of doing that later in the week and writing two new letters… where the fixed mindset has to take it all back.

Fixed Mindset

Growth Mindset

Dear robot, try not flipping pancakes.  Just stop, you suck.  Why don’t you find a better robot to do it for you? You are getting worse.  There is no chance for improvement.  Give up, just reprogram yourself, you’ll hurt someone. Perhaps you weren’t mean to flip pancakes. Try something else.  Maybe discus throwing. Dear robot, please keep trying to flip the pancake. At least it left the pan on attempt 20.  Go take a nap and try again tomorrow.  Practise more. Don’t feel bad, I can’t flip pancakes.  Keep working, and think of what can help.  I see that you’re trying different new techniques and that’s making you get closer. Maybe try another approach.  Would having another example help? Is there someone who could give you some constructive feedback? Or maybe have a way to see the pancake, like a motion capture system. That would help you keep track of the pancake as it moves through the air. Keep going, I believe in you!




I did my first round of interim feedback last week.  I asked students to comment on their DC Circuits course:

  • What do you like?
  • What do you dislike?
  • How are we doing with respecting our class norms?


Overall, students seem to appreciate the critical thinking approach.  They are warming to the idea that the purpose of a question is not necessarily to catch someone out, and they are noticing the difference in how it feels to think quickly vs. slowly, even if they don’t always love it.

Here’s a sample of the responses.  I’m especially excited about the ones in bold, because they represent things I’ve struggled with in the past.

I Like

“Shop work — If I’m confused about something in class, it really helps to understand better if I do it myself.”

“Being treated as thinkers. I ask a question and we discuss it.”

“Being challenged to think instead of just repeating what is taught like a robot.”

“When you work in a factory you get in a cycle of just doing and not thinking.”

“I like how it’s about science”

“Making things work and learning how it works”

“Everyone’s theories”

“Positive learning atmostphere”

“Makes me realize how much I like electronics”

“Friday assessments are not stressful.”

“Methodical, worksheets are precise.”

“Gets more interesting every day”

“I like that I am now better at asking questions about things that I don’t understand.”

I Dislike


“A lot of questions go unanswered.  I understand we will learn for ourselves a lot but others are nice to have answered when brought up.”

“Pace is a bit fast. Need more time to understand theories.”

“Pace is a bit slow.  But I do realize we all have to be on the same level and learn the basics first.”

“I dislike feedback sheets, but I really don’t care how I learn,”

“Methodical, work sheets can sometimes slow down what should be a simple task.  Am willing to take good with the bad in this case.”

“In the beginning I was frustrated about the research we had to do on electrons, atoms, and charge.  I understand why you had us do that though.  I just found it hard and tedious.”

What’s Going Well With our Rights and Responsibilities?

“Respectful / Positive / Relaxed / Professional / No one makes fun of anyone else”

“Following directions”

“Work ethic”

“Everyone gets along”

“Giving everyone a say in discussions”

“Helping others”

“Answering questions”

“Every one is here to learn”

“Asking questions and being open about concerns”

“You are definitely challenging us and making us think.”

“I think we’re learning to say ‘I don’t know’ and allow for knowledge gaps.”

What Could We Improve About our Rights and Responsibilities?


“Talking while others are talking.  ”

“Give more help time for those who are a little slower”

“More deeper explanation”


I’ve written before about using Diana Hestwood’s slide deck on growth mindset.  It’s called “How Your Brain Learns and Remembers,” and it uses an explanation of neuron biology to promote a growth mindset.  I found the slide deck pretty self-sufficient — it was complete enough not to require a presenter.  In the spirit of “Presentation Zen,” I converted it into a handout and asked students to complete the questions embedded in it.

Note: my students needed a full 20 minutes to complete this thoughtfully without feeling rushed.  This year I didn’t give them quite enough time and their responses are less personal than they have been in the past.


Comments From Students

“It takes more than insight of studying for dendrites to grow, it will take practice.”

“Good exercise, I recommend it for future students.”

“Neurons are amazing!”


On Exploring RC Circuits and trying to figure out why the capacitor charges faster than it discharges

Student 1: “Is the charge time always the same as the discharge time?”

Me: “According to this model, it is, if the resistance and capacitance haven’t changed.”

Student 2: “I’ve got data where the charge time was short and the discharge time was long.”

Me: “Why would a reasonable teacher say something that contradicts your data?”

Student 3, excitedly: “What circuit was it?  Was there anything else in the circuit?”

Student 1: “I can’t remember what it was called — it had a resistor, a capacitor, and a diode.”

Student 2: “That’s it then!  The diode — it’s changing its resistance!”

Student 1: “Yes — it goes from acting like a short to acting like an open.  Thanks for bringing that up [Classmate’s Name] — I just answered a HUGE question from that lab!”

Student services counsellor who sat in for a day

“You’re challenging my whole idea about science.”

While exploring why capacitors act like more and more resistance as they charge

“Maybe the negative side of the cap is filling up with electrons, which means less capacitance.  According to the ‘tau model’, charge time = 5 * R * C.  So if the charge time never changes, and the capacitance is going down, then the resistance must be going up.”

[I’m excited about this because, although it shows a misunderstanding of the definition of capacitance, the student is tying together a lot of new ideas.  They are also using proportional reasoning and making sense of the story behind a formula. I need a better way to help students feel proud of things like this…]

Student critique of a Wikipedia page

“There’s some great begging the question, right there!”

Student analyzing the mistake in their thinking about a resistor-diode circuit

“I didn’t think of current not flowing at all during the negative alternation of the source.  This would mean that the direction of current through the resistor does not technically change.  I thought that if current was flowing through the resistor, it would change direction even if there is a very small amount of current flowing.  I did do a good job about thinking of the electrons already in the wires.”

One student’s feedback on another student’s paper

“I understand fully what you are trying to explain!”

On figuring out why a diode works

“If you make the connection to a wire, it’s like how copper atoms…”

“If it wasn’t doped, wouldn’t current flow in both directions?”

Students discussing a shake-to-charge flashlight they are designing

“In our rechargeable flashlight, if you put the switch in parallel with the diode, when it’s closed it will just short it out…”

Student who gave a recruiting presentation at a high school

“The day was a great step up for me that I never ever thought possible.  To be able to go back to the high school where I am pretty sure most had given up hope on me and see and hear them tell me how proud they are of me for where I am today is a feeling I will never forget.”

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.”

On graphical waveform addition

“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.”

My students have recently discovered the convention of describing silicon diodes as having a forward voltage of 0.7 V.  They know that this is not always true — or even usually true, in their experience.  The way they reconciled the difference made for an interesting conversation about abstraction — the verb, not the noun.

After some constructive class discussion about possible approaches, they decided to use the diode’s “turn-on voltage” in predictions.  That’s the smallest voltage at which measurable current will flow — for a rectifier diode using our meters, it’s about 400 mV.  It’s also the voltage that, subtracted from the supply, gives the highest estimate for voltage across the other components and therefore the highest estimate of current.  They thought a high current was the “worst-case scenario” in terms of protecting the diode from damage.  When it turned out in the lab that this made their percent differences unusually high, they were willing to sacrifice accuracy for safety.

So why do authoritative sources say that all silicon diodes have a forward voltage of 0.7 V?  Except for the ones that say it is definitely always 0.6 V?

The students shared their confusion and no small amount of anger.  The problem wasn’t with having chosen some constant value; they got that you had to pick a value to work with when making predictions.  The problem wasn’t the need to abstract information out of the picture; they discussed several reasonable approaches to that problem and chosen one based on their evidence and judgement. Their problem was with sources that never mentioned that a choice had been made at all.

They were irritated, considering this at best a “mistake” and at worst a “lie.”  As I often do, I asked the students “why would a reasonable textbook author do this?”  Here are their answers:

It could be a typo.

It could be a shortcut for the author’s convenience.

Maybe they learned it that was so they put it in their textbook that way.

Maybe the authors are so experienced that they forgot that they made an assumption.

When the students ran out of ideas, I contributed mine: that the author had done this deliberately to make things simpler for students.  They were stunned.  How could anyone think it would be easier to have a “fact” printed in the textbook that was clearly contradicted by their measurements?  How could anyone not realize that it made them doubt their skill, even their perception of reality?  They were describing feeling “gaslit.”

I confess that I was delighted.  It marks a shift in their thinking about science: away from judging reality according to how well it fits their predictions, toward judging predictions according to how well they model reality.  And yes, I called it the “second diode approximation,” and warned them that they would encounter the first and third approximations as well.

But mostly, I was sad about how consistently teaching materials do this. The fact that an abstraction has an official name is not a justification for introducing it first in a curriculum.  I am more and more sure that my students understand more when we start from complexity as we experience it, then move toward idealized concepts only if they help us get closer to a goal.

Brian Frank gives a bunch of examples and helpful exercises for (current or) aspiring teachers, including this quote:

The shortcuts, omissions, and ‘simplifications’, which are meant to reduce complexity are not conducive to understanding; they are specious, and they make genuine understanding extremely difficult. (Arons, “Teaching Introductory Physics”, pg. 24)

Will this always be true?  If not, how could I distinguish  contexts in which it would help to go the other way?  What else can I do to “inoculate” students against these approaches when they inevitably encounter them?

My students use the same assessment rubric for practically every new source of information we encounter, whether it’s something they read in a book, data they collected, or information I present directly.  It asks them to summarize, relate to their experience, ask questions, explain what the author claims is the cause, and give support using existing ideas from the model.  The current version looks like this (click through to zoom or download):

Assessment for Learning

There are two goals:

  • to assess the author’s reasoning, and help us decide whether to accept their proposal
  • to assess one’s own understanding

If you can’t fill it in, you probably didn’t understand it.  Maybe you weren’t reading carefully, maybe it’s so poorly reasoned or written that it’s not actually understandable, or maybe you don’t have the background knowledge to digest it.  All of these conditions are important to flag, and this tool helps us do that.

The title says “Rubric for Assessing Reasoning,” but we just call them “feedbacks.”

Recently, there have been a spate of feedbacks turned in with the cause and/or the “support from the model” section left blank or filled with vague truisms (“this is supported by lots of ideas about atoms,” or “I’m looking forward to learning more about what causes this.”)

I knew the students could do better — all of them have written strong statements about cause in the past (in chains of cause and effect 2-5 steps long).  I also allow students to write a question about cause, instead of a statement, if they can’t tell what the cause is, or if they think the author hasn’t included it.

So today, after I presented my second draft of some information about RMS measurements, I showed some typical examples of causal statements and supporting ideas.  I asked students to rate them according to their significance to the question at hand, then had some small group discussions.  I was interested (and occasionally surprised) by their criteria for what makes a good statement of cause, and what makes a good supporting idea.  Here’s the handout I used to scaffold the discussions.

The students’ results:

A statement of cause should …

  • Be relevant to the question
  • Help us understand the question or the answer
  • Not leave questions unanswered
  • Give lots of info
  • Relate to the model
  • Explain what physically makes something happen or asks a question that would help you understand the physical cause
  • Help you distinguish between similar things (like the difference between Vpk, Vpp, Vrms)
  • Not beg the question (not state the same thing twice using different words)
  • Be concrete
  • Make the new ideas easier to accept
  • Use definitions

Well, I was looking for an excuse to talk about definitions — I think this is it!

Supporting ideas from the model should…

  • Help clarify how the electrons work
  • Help answer or clarify the question
  • Directly involve information to help relate ideas
  • Help us see what is going on
  • Give us reasoning so we can in turn have an explanation
  • Clarify misunderstandings
  • Allow you to generalize
  • Support the cause, specifically.
  • Be specific to the topic, not broad (like, “atoms are made of protons, electrons, and neutrons.”)
  • Not use a formula
  • It helps if you understand what’s going on, it makes it easier to find connections

The Last World

Which ones would you emphasize? What would you add?

Dan Goldner inspired me to start keeping track of these moments of hope and change.

Jan 18, from struggling student:

“I’ve never thought about things so intently before.  You’re changing the way we think.  It’s really different from what I’m used to.  You really have to understand why you think what you do.  I talk to everyone about it — I’ve been talking to my parents about it.”

Jan 18, from philosophical student;

“Someone at work the other day said ‘I can’t believe I did something so stupid!’ and I said, ‘Don’t disrespect your past self.’ “

Jan 24, From usually-overwhelmed right-answer-seeking student:

“I was all excited, I thought ‘I’m going to be the first person to break Ohm’s Law!’  And then I checked, and Ohm’s Law works fine, but wouldn’t that be awesome?”

Jan 25, from struggling student:

“It’s so different from high school!  In high school it seemed like you always had to know something, you could  never say ‘I don’t know.’ “ME: “Oh.  Was it bad if you didn’t know something?”

Stoic, Silent Student joins in: “Yeah!  That was not OK.”

ME: “I never take that into account enough.  The way I see it, of course we want to talk about what you don’t know.  What would be the point of talking about the things you already know?”

SS: “I think it’s getting better.  People are getting more comfortable just throwing things out there.”

Jan 28:

“Practice makes better!” (Me and student, simultaneously)

Jan 30 (click through for photo):

An offering

The way to a teacher’s heart is through safely, strategically destroyed components