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Series circuits are one of the foundational concepts in electrical work, and one of the first things students build/think about/get assessed on in their first months at school.  My definition of two series components:

  • Two components are in series if all the current in one flows into the second, and all the current in the second comes from the first

Things I have heard about series components:

  1. Components are in series if they’re in a square shape
  2. Components are in series if all the current in one flows into the second
  3. Components are in series if they’re both connected to the power supply
  4. Components are in series if they’re aligned in a straight line

In the first year of the program, we spend a lot of time refining our ideas about which circuits have which behaviours.  We refine and revise and throw out ideas.  By the end of December we should have something fairly strong.

Last week, I had a second-year student tell me he knew that two components were in series because of reason #3 above.  I’m struggling to make sense of this, and the accountability of teaching in a trade school hangs over my head like the razor-edged pendulum in the pit.  In May, some of these students will be working on large-scale industrial robots.  These things weigh tons, carry blades and torches, and can maim or kill people in an instant.  Electronics is not an apprenticeable trade. Grads will not carry tools for a journeyman for three years — they get put right to work.  Also, electronics is not a construction trade — it is a repair trade.  That means that work is almost always done under pressure of short timelines and lost money — the electronics tech doesn’t get called out until something is broken.

I have two years to make sure they are ready to at least begin their industry-specific training.  It’s not good enough for them to sometimes make sense of things — they need nail these foundational concepts every time in order to to use the training the employer provides and make good judgement calls on the job.  Please, no comments about how education is about broadening the mind and this student is learning lots of other valuable skills.  While that’s true, it’s not currently the point. When that electronics tech does some repairs on the heart-rate monitor keeping tabs on your unborn child, you are not going to be any more interested in the tech’s broad mind than I am.

What does it mean if a student can spend 4 months in DC circuits, not fully integrate the concept of series components, pass the course, and 8 months later still have an unstable concept?

Here are all the ideas I can think of at the moment.  Don’t panic — I don’t think these are all equally likely.

  1. Their experience in DC circuits is not doing enough to help them make sense of this idea
  2. The assessments in DC circuits are not rigourous enough to catch students who are still unsure about this
  3. This student is incapable of consistently making sense of this idea, and should not have been accepted into the program in the first place
  4. It’s normal for students to form, unform, and reform their ideas about new concepts.  It’s inevitable, and sometimes students will revert to previous ways of thinking even after the fantastic course and the rigourous assessments.

If it’s #1, I’m not sure what to do.  I’ve already given over my courses to sense-making, critical thinking, and inquiring.  Do they need more class hours, more time outside class hours, or just different kinds of practice?  Maybe the practice problems are too consistent, failing to address students’ misconceptions.

If it’s #2, I’m not sure what to do.  I feel pretty confident that I’m assessing their reasoning rather than their regurgitating.  More assessments might help — not sure where to get the time.  A final exam might help.  I can’t see my way clear to passing or failing someone on the strength of a final exam, but I’d at least know a bit more about which concepts are still shaky.  I’ve sometimes given a review paper in January on the concepts learned in the previous semester, and worked through multiple drafts — I could start doing that again.

If it’s #3, I’m definitely not sure what to do.

If it’s #4, how do I reconcile this with my sense of personal responsibility to not send them out to get injured or injure someone else?  I realize I’ve framed this in a fairly dramatic way, and not every student who’s unsure of what a series circuit is will end up harming someone.  It’s much more likely that they’ll end up on the job and start to consolidate their knowledge and clear up their misconceptions.  However, it’s also likely that they’ll end up on a job where they suddenly realize that they don’t understand the basic things they’re being asked to do.  This bodes poorly for the grad’s confidence and enjoyment of their career, the employer’s willingness to hire future grads, and of course the quality of our biomedical equipment, manufacturing equipment, navigational equipment, power generation instrumentation, … .  It also bodes poorly for my ability to believe that I am doing a reasonable job.

Thoughts?

 

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:

Topic: Voltage

Cause

Definition

Characteristics

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.

This morning, my students are reading about negative feedback and assessing the information provided using our standard rubric, which asks them to summarize and write their questions.  They’re finding it difficult to understand, almost too confusing to summarize.  I remind them that that’s ok — to summarize what they can, if they can.  I also tell them to write questions as they read, not to wait until the end of the passage to write them down.

Especially, I remind them that common cause of “getting stuck” is waiting until they understand the paragraph before writing down a question.  The problem, of course, is that you might not be able to understand the passage until after the question is answered.  Waiting for understanding before asking questions is like waiting to be fit before going to the gym.

I have this conversation with one student:

Student: “What I’m afraid of is, if I get partway through the paragraph and write a question, then I get later in the paragraph and write down another question, I’ll get to the end and realize, Oh, that’s what it meant, and I won’t need to ask that question any more.”

Me, joking: “So what happens then?  What horrible consequence ensues?”

Student: “I have to kill an eraser!”

Me: “No need to erase it.  Just write a note that says, ‘oh, now I get that… [whatever you just understood].  Have you ever noticed how often I do that on your quizzes and papers?  I write questions as I’m reading, then I cross them out when I get to the end and write a note that says “never mind, I see that you’ve answered the questions down here.”

Student: [noncommittal shrug, smiling, seems willing to try this]

I think that’s an ok way to get the point across.  I sit back down.  Then I need to be a smart ass.  I go back to chat with the same student.  “You know, from our conversation earlier, it sounded like you were saying, ‘I’m afraid that if I ask questions, I’ll get it.’ ”

My point, of course, is that asking questions, thinking through our questions, and clarifying to ourselves what question we mean to ask can be an important part of sense-making, and can even help us answer our own questions.  But that’s not how it comes across to the student.  Now he’s been backed into a corner, shown the absurdity of something he just said.  He scrambles to defend his statement.  “No, what I meant was that if I ask questions while I’m reading, I might get to the end and not understand my… [pause] I can’t put it into words.”

Notes to self

  • Students sometimes think they should delay asking questions until after they have understood something.  This causes deadlock and frustration.  Strategize about this with students.
  • Pointing out someone’s misconception, especially in the middle of class, does not usually result in a graceful acknowledge of “oh, yeah, that doesn’t really make sense, does it?”  It usually results in backpedaling and attempts to salvage the idea by re-interpreting, suggesting that I didn’t understand them, or saying “I understand it, I just can’t put it into words.”
  • The phrase “I understand it but I just can’t put it into words” is highly correlated with “You just pointed out a misconception to me and now I must save face by avoiding your point at all costs.”  Use this clue to improve.
  • Dear Mylène, you think you’re too highly evolved to use “elicit-confront-resolve” to address student misconceptions, but you’re mistaken.  It’s causing students to avoid their misconceptions instead of facing them. Find a way to do something else.

Today we were brainstorming ideas about electricity, practicing clarifying, and creating questions that start “What causes…”.  Some students are anxious about this, seem to fear that if they ask those questions, they will have to answer them.  My goal is for us to draw the boundaries of what we do and don’t know — not to get lost in some metaphysical endless loop.  Facing the giant pile of what we don’t know is hard sometimes.

I say “If it seems like we’ll never run out of questions, don’t worry.  We don’t have to answer those questions — we’re just keeping track of what we have and haven’t answered.  And anyway, if we ran out of questions, wouldn’t that be awful and boring?”

The answer from the back of the room is, “No, that would be great.  And then I’d be smart.”

What’s my next move?

In my ongoing struggle to help my students make sense of their own mistakes, I sometimes hear them say that the reason they misapplied a skill is that they were “overthinking.”  I’ve always had a hard time responding to this.  I’m not even sure I know exactly what they mean by it, and when I try to have the conversation, I get the impression that there are so many hidden assumptions that we’re not communicating well.

I want them to focus on the quality of their thinking, not the amount, so I find the conversation frustrating.  If I were to try to put myself in their place, here are some possible translations:

  • Is their meaning of “overthinking” similar to my meaning of “close reading”?
  • “Over”-thinking… too much thinking?
  • Thinking carefully might bring up new possibilities that you can neither support nor contradict.  If we’re in class when it happens, it probably causes perplexity.  If the student is in a test when it happens, their inability to either test the new possibilities or ask questions about them is probably really frustrating — a frustration that they blame on the thinking itself
  • Thinking carefully (or a lot?) makes you start noticing complexity and nuance.  If you are noticing them for the first time, they may distract your mind away from the things you used to think about, making a familiar landscape seem unfamiliar.
  • Is this related to the level of abstraction?  If students are used to reasoning within an abstraction that they accepted but did not build (in other words, they did not choose to simplify or remove information — the model was given to them that way), then thinking closely might cause them to notice one of the other “rungs” of the abstraction ladder, which could change the pattern of their reasoning.

I’m going to try to pay closer attention to this in the coming year.  In the meantime, it came up in class today and I was finally pleased with how I responded.

We had just finished doing the bicycle experiment inspired by Rebecca Lawson’s research.  Students look at  stick-drawing bicycles and have to pick the one that most resembles an actual bike.  Lots of people were surprised at how difficult it was.  One brave students shared “I don’t know why, but I thought the chain ran from wheel to wheel.”  We talked a bit about how easy it is to feel familiar with things, and genuinely know a lot about them, while not noticing what we don’t know.  I then moved on to the next topic — the importance of double-checking what we read, hear, and remember.

I was talking about how memory can be misleading.  I used the example of the feeling you have when you walk into a test feeling confident, then sit down and realize you can’t solve the question.   The same student fell back on what seemed to be a tried-and-true way of thinking, commenting, “Isn’t it true that a lot of times you overthink things, and you should just stick with your first instinct?”

My reply was to ask gently, “How did it work out with the bicycle?”

I went on to say that what I expected from them was not more thinking nor less thinking, but technician thinking.  Too much food can make you sick and so can too little.  The wrong kind of food for your situation can also be bad.  Similarly, our goal is not certain quantity of thought, but a certain kind — particular habits of mind based on particular specialized skills and ideas.  We’ll see how this supports our conversations in the future.

How do you learn to use a new piece of software (or web service or smart phone)?  I notice that some people press all the buttons, others prefer step-by-step instructions in the form of “press this button, then press that button.”  Some want to watch an experienced user, then experiment on their own (and I’m sure there are lots of other in-between approaches). 

I got to thinking about this because my partner (who is quite uneasy about computers) was trying to email me an address from an electronic address book, but wrote it out on paper then typed it in.  When I suggested copying and pasting, the response was “I don’t know how to copy in this program.”  It’s an interesting point.  Not everyone knows that there are software conventions determined by the operating system.  But in the absence of that knowledge, I think some users would try the “copy” routine that worked for them in other programs, just to see if it worked.  Others would not trust themselves to try something in which they haven’t been directly instructed.

Does anxiety about new technology cause people to not experiment?  Or does the lack of habit/experience with experimenting cause the anxiety?  Or both?

I discussed this with a friend over dinner.  She was describing her attempts to encourage broader use of the electronic media available at her workplace, and is definitely a “press all the buttons” kind of user.  She is not a tech professional, and she is not 22, so the stereotypical answers are clearly inadequate.  I asked her where she learned to engage with unfamiliar technology that way.  Her answer was, “from my long-standing distrust of humans.”  We shared a laugh, but it gradually seemed less funny. 

I don’t think she doesn’t trust people to be honest.  I take it to mean that she doesn’t trust people to be right.  At least not all the time, and not comprehensively.  It connects to a very interesting exchange that happened at Casting Out Nines and Gas Station Without Pumps.  Does trusting our teachers make it easier to learn?  Or harder?

I think a better question is “trust them to do what?”

When I am learning from someone (I include the authors of books), I need to trust that they will respect me.  I also need to trust that they are qualified and experienced with the material. For the sake of my learning, I also need to not trust them to be right.  It’s possible there’s a typo or that the teacher misspoke (or truly misunderstands).  It’s much more possible that what I understood is not what the author/teacher meant.  If I “trust” my teacher to “tell me the truth,” what I am really trusting is my own perception of what they meant — which is highly fallible even if the source material is accurate.  Besides the problem of miscommunication, there’s a deeper problem: trusting a source to be right means reasoning from authority — and that’s faith, not science.  If students are engaged in an un-scientific reasoning process, it undermines whatever scientific content we are reasoning about.

Where it falls apart in my classroom: it’s hard for my students to distinguish between not assuming their teachers are right, vs assuming their teachers are wrong. 

Homework: figure out how to convince students that they shouldn’t trust me to be right even though a lot of their schooling tells them that’s blasphemous; also, convince students that they should trust me to respect them even though a lot of their schooling tells them I won’t.

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.

Next

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.

Is school like a grocery store of ideas?  Learning should result in understanding and action, but we’re not always clear about what kind.  There’s a big difference between understanding the organization of the grocery store layout, and understanding how to grow food yourself.

Photo of farm country landscape

I live in farm country.  Changes to zoning bylaws can draw protests of hundreds of people.  People know where and how and by whom their food is produced.  We also know how we affect the system — even if it’s only through our consumer choices and by-election votes.  We’re engaged with the production narrative of our food.

I recently finished reading Shop Class as Soul Craft (thanks, John).  I hope you’ll overlook the silly title because, though the book has its flaws, it’s also full of useful and refreshingly unusual ideas.  One of the less surprising ones is that we have a responsibility to know the production narrative of our stuff, as well as our food.  Knowing who makes what, and why, can take us past catchphrases (buy local) and teach us about class, agency, and democracy, if we let it. (Update: my review is on Goodreads)

I’ve been thinking about these because of a recent post on Educating Grace about what “sense-making” is, and why it sometimes diverges from understanding.  I don’t know the answer, but the question is becoming urgent in my classroom.  Brian Frank weighs in with a comment, and Grace responds with an even more perplexing post.

Here’s an excerpt from Brian’s comment:

Without knowing how to participate in the creation, telling, and changing of stories, learning science stories is no different than learning myths… The more we make our disciplines exclusionary, the more myth-making we do.

I haven’t fully wrapped my head around this.  It’s starting to sound as though what my classroom needs more of is the production narrative of our ideas.

The game field of infinite moves

Frank Noschese just posed some questions about “just trying something” in problem-solving, and why students seem to do it intuitively with video games but experience “problem-solving paralysis” in physics.  When I started writing my second long-ish comment I realized I’m preoccupied with this, and decided to post it here.

What if part of the difference is students’ reliance on brute force approaches?

In a game, which is a human-designed environment, there are a finite number of possible moves.  And if you think of typical gameplay mechanics, that number is often 3-4.  Run left, run right, jump.  Run right, jump, shoot.   Even if there are 10, they’re finite and predictable: if you run from here and jump from exactly this point, you will always end up at exactly that point.  They’re also largely repetitive from game to game.  No matter how weird the situation in which you find yourself, you know the solution is some permutation of run, jump, shoot.  If you keep trying you will eventually exhaust all the approaches.  It is possible to explore every point on the game field and try every move at every point — the brute force approach (whether this is necessary or even desirable is immaterial to my point).

In nature, being as it is a non-human-designed environment, there is an arbitrarily large number of possible moves.  If students surmise that “just trying things until something works” could take years and still might not exhaust all the approaches, well, they’re right.  In fact, this is an insight into science that we probably don’t give them enough credit for.

Now, realistically, they also know that their teacher is not demanding something impossible.  But being asked to choose from among infinite options, and not knowing how long you’re going to be expected to keep doing that, must make you feel pretty powerless.  I suspect that some students experience a physics experiment as an infinite playing field with infinite moves, of which every point must be explored.  Concluding that that’s pointless or impossible is, frankly, valid.  The problem here isn’t that they’re not applying their game-playing strategies to science; the problem is that they are. Other conclusions that would follow:

  • If there are infinite equally likely options, then whether you “win” depends on luck.  There is no point trying to get better at this since it is uncontrollable.
  • People who regularly win at an uncontrollable game must have some kind of  magic power (“smartness”) that is not available to others.

And yet, those of us on the other side of the lesson plan do walk into those kinds of situations.  We find them fun and challenging.   When I think about why I do, it’s because I’m sure of two things:

  • any failure at all will generate more information than I have
  • any new information will allow me to make better quality inferences about what to do next

I don’t experience the game space as an infinite playing field of which each point must be explored.  I experience it as an infinite playing field where it’s (almost) always possible to play “warmer-colder.”  I mine my failures for information about whether I’m getting closer to or farther away from the solution.  I’m comfortable with the idea that I will spend my time getting less wrong.  Since all failures contain this information, the process of attempting an experiment generally allows me to constrain it down to a manageable level.

My willingness to engage with these types of problems depends on a skill (extracting constraint info from failures), a belief (it is almost always possible to do this), and an attitude (“less wrong” is an honourable process that is worth being proud of, not an indictment of my intelligence) that I think my students don’t have.

Richard Louv makes a related point in Last Child in the Woods: Saving Our Children From Nature-Deficit Disorder (my review and some quotes here).  He suggests that there are specific advantages to unstructured outdoor play that are not available otherwise — distinct from the advantages that are available from design-y play structures or in highly-interpreted walks on groomed trails.  Unstructured play brings us face to face with infinite possibility.  Maybe it builds some comfort and helps us develop mental and emotional strategies for not being immobilized by it?

I’m not sure how to check, and if I could, I’m not sure I’d know what to do about it.  I guess I’ll just try something, figure out a way to tell if it made things better or worse, then use that information to improve…

As part of the course evaluation for High-Reliability Soldering, I asked these questions.

Are there different kinds of confusion?  If so, do you learn more from certain kinds?  Why?

There is confusion that happens when you get too much information at the same time.  And confusion that happens when you think you know the answer but it’s the next best thing.  I learn more when getting it wrong and learning from my mistakes.

I think their 2 different kinds of confusion, 1st being “something you are just starting to learn” and 2nd being “something that you can’t understand.”  You can learn from both because the more you learn, the more new things you will discover.

Yes.  New confusion, I learn by practicing and stuff I thought I knew confusion, makes me get frustrated because it makes me think that my whole theory is wrong even tho parts might be right.

No, all confusion is the same, the attitude I have can be different in different circumstances.

What would help you get the most learning out of confusing ideas?  Why?

Someone that knows what they’re talking about explaining it in a way I can understand.  Or just a lot of practice, I find experience a key way to understand something.

Trying not to get frustrated, making sure I understand the idea first

Having time to take my time and look over what I was confused about.  Going over it as a class if more than one person is confused about the same thing.  You wouldn’t feel alone, like you were the only one who didn’t understand.

Just sitting down with someone who understands, and knows what they are doing.  Because I know I can ask questions that they can answer properly and with knowledge and not just kinda guess at the answer.

My thoughts

In our previous conversation about confusion, I got the impression that “I’m confused” could mean “I can’t tell these ideas apart/I’ve come to contradictory conclusions” (the dictionary definition of confusion), or it could mean “I don’t know” (i.e. a word, a procedure, or how to approach a problem).  They are very hard on themselves when they encounter things they don’t know.  I’m guessing that the thought process goes something like “Schools are set up to only give you information you already know.  So if I don’t know something, it must mean that I did something wrong or I’m stupid.”  I’m guessing here, I’ll have to come back to this.

From the responses above, it seems that my students use “confusion” even more broadly to include overwhelm, fatigue, and “when you thought you knew the answer.”

A number of students distinguished between the confusion of not knowing and the confusion of thinking you knew something.  I’m going to pay closer attention to which reactions go with which conditions.  My gut feeling is that “not knowing” usually results in frustration and requests for answers, but “when you thought you knew” results in anger and accusations of unfairness.

I might further distinguish the “when you thought you knew” confusion into two types: things you thought you knew based on previous experience, and things you thought you knew caused by pseudoteaching by yours truly…

You can see the tension between what students see as “guessing” and what I see as “gathering evidence and figuring it out.”  A related point is throwing out an entire model or train of thought because of finding one mistake.  Obviously, I need to approach this differently.  Maybe help students take more control of finding evidence, linking evidence to inferences, so that if they find contradictory evidence, it’s more clear which inferences it affects, or which evidence they need to double-check.

Finally, the responses show a pattern of responding to confusion by seeking an authority to hand over the right answer.  That’s not always a bad idea, of course.  But there are a lot of other approaches missing from the list.  I get the feeling this is going to be one of those long-term headaches that’s going to make me reorganize the inside of my brain.

Is confusion useful?

Confusion as my students see it incorporates a lot of things, some of which are not useful for learning (fatigue, self-flagellation).  My definition of confusion barely overlaps with theirs — including things like perplexity, conflict, and curiosity.  Gotta sleep on this one before I can figure out what on earth to do about this.

However, asking my students about confusion was extremely useful.  It definitely created perplexity for me, which means it’s driving my learning.  I feel like I have a permanent reservation at the all-you-can-eat food-for-thought buffet.

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