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The first-year students are solving series circuits and explaining what’s happening. Most are able to connect their answers and thoughts to evidence we’ve gathered this semester. But most are struggling with the questions about causality.
For each effect they describe mathematically, I ask them to explain what is physically capable of causing that effect. Or, they can choose to explain why the result seems like it can’t be happening. It doesn’t have to be cannonical, but it must be internally consistent, not circular, and supported by our evidence. They are struggling most with explaining Kirchhoff’s Voltage Law. This is understandable — I don’t think I could explain it heuristically either. However, only one student took the opportunity to say why it doesn’t make sense.
We’ve done lots of practise writing cause statements. They know what “begging the question” means. I’ve modelled, and we’ve practised, the importance of saying “I don’t know” when that’s the most accurate thing we can say. Examples of student thinking are below.
I’m tempted to propose a taxonomy of acausal strategies. Which examples of student thinking do you think fit where? Would you add or remove categories? Could you propose some pithy names for them?
- It does that because it’s designed to do that
- It does that because if it didn’t, this other important thing wouldn’t happen
- It does that because there’s a law that says it has to do that
- It does that because it does that (begging the question)
- It does that just because
My questions are:
- What do the students know?
- Why do so few students say “I don’t know” or “it doesn’t make sense”?
- Are they freer from preconceptions about the space-time continuum than I am?
- What’s my next move?
“An electron has to use up all its energy that it gets from the battery. This is caused because if all of the energy wasn’t used, the circuit wouldn’t give accurate results, or work properly.”
“When electrons pass through a component, that causes them to lose energy. The electrons would have to be able to flow through the circuit in order to keep the current and battery functioning.”
“An electron has to use up all the energy it gets from the battery. This is caused because if the voltage from the power source is 5V, the electrons have to use up all of their energy, in this case they use up all of it in the resistor (except for the little energy used in the switch).”
“The electrons always use up exactly the energy they gain in the battery because of conservation of energy.”
“It doesn’t make sense that if there’s only one component in the circuit, it always uses up exactly the battery’s voltage. A higher resistor should be like a steeper hill — harder for the electrons to get past, and requiring more energy.”
My last post was about encouraging my students to re-evaluate what they think is certain. I’m trying to help them break the habit of arguing from authority, of stepping in with swift shame and punishment of classmates who are “wrong,” and encourage them to notice their own thinking… and even to go so far as exposing that thinking to the class! Even when they’re unsure!! And in fact to become unsure. To seek out uncertainty and celebrate it as a form of intellectual courage. That’s going to be scary, and it depends on creating a supportive climate.
I responded to a comment on that post, in part: “I do realize that I’m pulling the rug out from under their trust in their own perception of reality, and that’s an unpleasant experience no matter what. Sometimes I think this is actually a spiritual crisis rather than a scientific one.” To be fair, I’m careful not to suggest that their perception of certainty is invalid; only that it is important to notice the evidence that underlies it. But that means considering the possibility that the evidence could once in a while not be strong enough. That new knowledge might complicate old knowledge. In the conversations that follow, the students talk about wondering whether certainty exists at all, and whether anything exists at all, and what knowing means in the first place. That leads to what it means to “be right”… and then what it means to “do right.”
Because… if you can’t know things for sure, you can’t be a good person? I think? Because there is a single correct answer and deviating from that is not only to “be wrong” — it is to “do wrong.” And if you “sin” in this way privately in your own head, that’s bad enough to inspire fear of meaninglessness. But if you do it in front of others, it’s shameful and inspires fear of punishment.
My best guess is that they have tangled up “right and wrong test answers” with “right and wrong moral behaviour” — being a “good person” means being a good student… usually a compliant one.
And since our definition of “moral good” is so narrow (especially in school systems), you don’t have to be “wrong” to be “bad.” Even failing to be sure is failing to be “good”.
So, I’m provoking a moral, or maybe a spiritual, crisis — or maybe exposing an underlying crisis that was there all along. What do I do about it? How do I help students enter into uncertainty without being immobilized or injured by it? They don’t know what to do when the rigid rules are removed, and I don’t know what to do when they get scared. What do we do when we don’t know what to do?
Our classroom conversations range over ontology, epistemology, ethics, and, yes, faith. I realize I’m treading on thin ice here; if you think opening a conversation about faith and spirituality in my classroom (or on this blog) is a mistake, I hope you’ll tell me. But I don’t know how to talk about science without also talking about why it’s not faith, to talk about truth and integrity without talking about what it means to do what’s “right”, why all of these might contribute to your life but one can’t be treated as the other. And it’s a line of conversation that the students dig into avidly, almost desperately. Putting this stuff on the table seems to offer the best possibilities for building trust, resilience, and critical thinking.
So when the students open up about their fear and anger around what “right and wrong” have meant in their lives, and why so many possibilities of what they could mean have been hidden from them, I go there (with care and some trepidation). I’m careful not to talk about particular sects or creeds — but to invite them to think about what they think of as morally right and wrong, what fits into that structure, and why models of atomic structure don’t need to be shoehorned into that framework.
There is occasionally some overlap though.
A historical figure I’ve learned a lot from wrote in her journal about re-evaluating an especially weighty authority…
And then he went on … “Christ saith this, and the apostles say this;’ but what canst thou say?” … This opened me so, that it cut me to the heart; and then I saw clearly we were all wrong. So I sat down … and cried bitterly… “We are all thieves; we are all thieves; we have taken the [ideas] in words, and know nothing of them in ourselves.“
Since this belongs to a particular faith community, I don’t bring it into the classroom. I think about it a lot though; and it’s the spirit I hope students will bring to their re-evaluation of the high school physics they defend so dearly.
If I expect them to respect and honour the thinking of their classmates when they think it’s wrong (Bad? EVIL?), it’s crucially important that they feel respected. If I want them to stop arguing from authority, I have to be meticulous about how I use mine. One technique I’m going to try tomorrow is sharing with the class some of the “cool moves” I noticed on the most recent quiz.
New Plan
Despite my angst about this issue, I’m actually thrilled by the curious, authentic, and humble thinking that’s happening all over the place. So tomorrow I’ll show some of these (anonymous) examples of non-canonical ideas and explain what I think is good about them.
As for the students who argue from authority and squash all other ideas, I seem to be failing at understanding their needs and changing their minds. I’ll keep working on it. But I’m also going to try something new. I will make sure to seek out their assistance in dreaming up praise for their classmates.
My definition of “inquiry” as an educational method: it’s the students’ job to inquire into the material, and while they do that, it’s my job to inquire into their thinking.
So yes, the goal is really “inquiry-based learning”. I’ve written lots before about what the students do. But this post is about what I do. I have to inquire at least as much as the students do.
I’ve written that before, more than once… but do you think I can find it on my own blog? Nope. Also, I stole it originally, probably from Brian Frank. Do you think I can find it on his blog? *sigh* If anyone finds it, in either place, let me know, would ya?
What’s new about my ability to inquire into my students’ thinking is that I’m treating it more like a qualitative research project. Someday I’ll go take a qualitative methods course and actually know what I’m talking about (I’m taking suggestions for methods texts, courses you liked, or profs you respect)… but until then, I’m muddling through better than usual.
Activities That Help Me Inquire Into Student Thinking
This year I added a day before light bulbs where they made circuits out of playdough. It was silly, messy, and fun. It also yielded lots of new info about their thinking about electrons, voltage, current, charge, etc., which I asked them to record on this handout.
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Record-Keeping
Whatever they write down ends up in a spreadsheet that looks like this:
| 2015 Intake ideas so far | Name | Date | Context | V | R | I | P | C | Energy | Potential |
| voltage is potential difference amount of potential energy between points | XXXXXX | 09-Sep-15 | Squishy Circuits | x | x | x | ||||
| Insulators stop energy from passing through | XXXXXX | 09-Sep-15 | Squishy Circuits | x | ||||||
| Conductors allow the transfer of energy | XXXXXX | 09-Sep-15 | Squishy Circuits | x |
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I just keep adding tags on the right to keep track of whatever topic I need to keep track of. That way I can sort by topic, by date, or by student. It also helps me see which activities yielded what kind of curiosity.
My Favourite Ideas So Far
What holds matter together?
Are electrons what power actually is?
Batteries in a row must connect to each other like how magnets connect together to attract each other (2 negatives connected doesn’t work)
Closing the switch should double the power supply, but there was no noticeable difference. Why?
When negative side of battery reaches positive side of other battery, shouldn’t it be a complete circuit?
Put the switch on the other side of the bulb. Does it matter?
Why did the 2 dim lights light at all, when the path of least resistance was through the 1 light bulb path? In my “double the wires” circuit, they didn’t light at all.
Why don’t any of the bulbs turn on? I would have thought that at least the first bulb would faintly glow.
Resistance is how much current is lost in the current
What separates Watts from Volts?
If I Inqire Into My Own Thinking…
What’s the pattern here about which ideas are exciting to me? Well, quite a few of them are challenges to common misconceptions. Despite my resistance, it seems I’ve still got a bit of a case of misconception listening.
The other pattern is that they all point either to questioning cause, or improving precision. Those are discipline-specific skills, part of the “implicit curriculum” that people in my field often think of as unlearnable “aptitudes” instead of skills. So there’s a practise of inclusion underlying my choices — making these skills explicit benefits everyone but especially the people with little previous exposure to technical fields. Cause and precision are also things that I personally find satisfying and beautiful. No coincidence about the overlap — I chose my field for a reason. I’ll have to be careful to encourage curiosity wherever I find it, not just in the students who ask the kinds of questions I like best.
Here are some conversations that come up every year.
1. Zero Current
Student: “I tried to measure current, but I couldn’t get a reading.”
Me: “So the display was blank?”
Student: “No, it just didn’t show anything.”
(Note: Display showed 0.00)
2. Zero Resistance
Student: “We can’t solve this problem, because an insulator has no resistance.”
Me: “So it has zero ohms?”
Student: “No, it’s too high to measure.”
3. Zero Resistance, In a Different Way
Student: “In this circuit, X = 10, but we write R = 0 because the real ohms are unknown.”
(Note: The real ohms are not unknown. The students made capacitors out of household materials last week, so they have previously explored that the plates have approx. 0 and the dielectric is considered open)
4. Zero Resistance Yet Another Way
Student: “I wrote zero ohms in my table for the resistance of the battery since there’s no way to measure it.”
What I Wonder
- Are students thinking about zero as indicator that means “error” or “you’re using the measuring tool wrong?” A bathroom scale might show zero if you weren’t standing on it. A gas gauge shows zero when the car isn’t running.
- When students say “it has none” like in example 2, what is it that there is none of? They might mean “it has no known value”, which might be true, as a opposed to “it has no resistance.”
- Is this related to a need for more concreteness? For example, would it help if we looked up the actual resistance of common types of insulation, or measured it with a megger? That way we’d have a number to refer to.
- #3 really stumps me. Is this a way of using “unknown” because they’re thinking of the dielectric as an insulator that is considered “open”, so that #3 is just a special case of #2? Or is it unknown because the plates are considered to have 0 resistance and the dielectric is considered open, so we “don’t know” the resistance because it’s both at the same time? The particular student who said that one finds it especially hard to express his reasoning and so couldn’t elaborate when I tried to find out where he was coming from.
- Why does this come up so often for resistance, and sometimes for current, but I can’t think of a single example for voltage? I suspect it’s because both resistance and current feel concrete and like real phenomena that they could visualize, so they’re more able to experiment with its meaning. I think they’re avoiding voltage altogether (first off, it’s about energy, which is weird in the first place, and then it’s a difference of energies, which makes it even less concrete because it’s not really the amount of anything — just the difference between two amounts, and then on top of that we never get to find out what the actual energies are, only the difference between them — which makes it even more abstract and hard to think about).
- Since this comes up over and over about measurement, is it related to seeing the meter as an opaque, incomprehensible device that might just lie to you sometimes? If so, this might be a kind of intellectual humility, acknowledging that they don’t fully understand how the meter works. That’s still frustrating to me though, because we spend time at the beginning of the year exploring how the meter works — so they actually do have the information to explain what inside the meter could show a 0A reading. Maybe those initial explanations about meters aren’t concrete enough — perhaps we should build one. Sometimes students assume explanations are metaphors when actually they’re literal causes.
- Is it related to treating automated devices in general as “too complicated for normal people to understand”? If that what I’m reading into the situation, it explains why I have weirdly disproportionate irritation and frustration — I’m angry about this as a social phenomenon of elitism and disempowerment, and I assess the success of my teaching partly on the degree to which I succeed in subverting it… both of which are obviously not my students’ fault.
Other Thoughts
One possibility is that they’re actually proposing an idea similar to the database meaning of “null” — something like unknown, or undefined, or “we haven’t checked yet.”
I keep suspecting that this is about a need for more symbols. Do we need a symbol for “we don’t know”? It should definitely not be phi, and not the null symbol — it needs to look really different from zero. Question mark maybe?
If students are not used to school-world tasks where the best answer is “that’s not known yet” or “that’s not measurable with our equipment”, they may be in the habit of filling in the blank. If that’s the case, having a place-holder symbol might help.
This year, I’ve really started emphasizing the idea that zero, in a measurement, really means “too low to measure”. I’ve also experimented with guiding them to decipher the precision of their meters by asking them to record “0.00 mA” as “< 5uA”, or whatever is appropriate for their particular meter. It helps them extend their conceptual fluency with rounding (since I am basically asking them to “unround”); it helps us talk about resolution, and it can help in our conversation about accuracy and error bars. Similarly, “open” really means “resistance is too high to measure” (or relatedly, too high to matter) — so we find out what their particular meter can measure and record it as “>X MOhms”.
The downfall there is they start to want to use those numbers for something. They have many ways of thinking about the “unequal” signs and one of them is to simply make up a number that corresponds to their idea of “significantly bigger”. For example, when solving a problem, if they’re curious about whether electrons are actually flowing through air, they may use Ohm’s law and plug in 2.5 MOhms for the resistance of air. At first I rolled with it, because it was part of a relevant, significant, and causal line of thinking. The trouble was that I then didn’t know how to respond when they started assuming that 2.5MOhms was the actual resistance of air (any amount of air, incidentally…), and my suggestion that air might also be 2.0001 MOhms was met with resistance. (Sorry, couldn’t resist). (Ok, I’ll stop…)
I’m afraid that this is making it hard for them to troubleshoot. Zero current, in particular, is an extremely informative number — it means the circuit is open somewhere. That piece of information can solve your problem, if you trust that your meter is telling you a true and useful thing. But if you throw away that piece of information as nonsense, it both reduces your confidence in your measurements, and prevents you from solving the problem.
Some Responses I Have Used
“Yes, your meter is showing 0.00 because there is 0.00 A of current flowing through it.”
“Don’t discriminate against zero — it isn’t nothing, it’s something important. You’ll hurt its feelings!”
Not helpful, I admit! If inquiry-based learning means that “students inquire into the discipline while I inquire into their thinking”*, neither of those is happening here.
Some Ideas For Next Year
- Everyone takes apart their meter and measures the current, voltage, and resistance of things like the current-sense resistor, the fuse, the leads…
- Insist on more consistent use of “less than 5 uA” or “greater than 2MOhms” so that we can practise reasoning with inequalities
- “Is it possible that there is actually 0 current flowing? Why or why not?”
- Other ideas?
*I stole this definition of inquiry-based learning from Brian Frank, on a blog post that I have never found again… point me to the link, someone!
I’ve done a better job of launching our inquiry into electricity than I did last year. The key was talking about atoms (which leads to thoughts of electrons), not electricity (which leads to thoughts of how to give someone else an electric shock from an electric fence, lightning, and stories students have heard about death by electrocution).
The task was simple: “Go learn something about electrons, about atoms, and about electrical charge. For each topic, use at least one quote from the textbook, one online source, and one of your choice. Record them on our standard evidence sheets — you’ll need 9 in total. You have two hours. Go.”
I’ve used the results of that 2-hour period to generate all kinds of activities, including
- group discussions
- whiteboarding sessions
- skills for note-taking
- what to do when your evidence conflicts
- how to decide whether to accept a new idea
We practiced all the basic critical thinking skills I hope to use throughout the semester:
- summarizing
- asking questions about something even before you fully understand it
- identifying cause and effect
- getting used to saying “I don’t know”
- connecting in-school-knowledge to outside-school experiences
- distinguishing one’s own ideas from a teacher’s or an author’s
I’m really excited about the things the students have gotten curious about so far.
“When an electron jumps from one atom to the next, why does that cause an electric current instead of a chemical reaction?”
“When an electron becomes a free electron, where does it go? Does it always attach to another atom? Does it hang out in space? Can it just stay free forever?”
“What makes electrons negative? Could we change them to positive?”
“Are protons the same in iron as they are in oxygen? How is it possible that protons, if they are all the same, just by having more or fewer of them, make the difference between iron and oxygen?”
“If we run out of an element, say lithium, is there a way to make more?”
“Why does the light come on right away if it takes so long for electrons to move down the wire?”
“What’s happening when you turn off the lights? Where do the electrons go? Why do they stop moving?”
“What’s happening when you turn on the light? Something has to happen to push that electron. Is there a new electron in the system?”
“With protons repelling each other and being attracted to electrons, what keeps the nucleus from falling apart?”
“What happens if you somehow hold protons and electrons apart?”
“Would there be no gravity in that empty space in the atom? I like how physics are the same when comparing a tiny atom and a giant universe.”
How are these students thinking about causality?
What should I ask next?
“Electrical charge is caused due to the movement of electrons from atom to atom.”
“The appearance and properties of atoms are changed cause protons are added or removed from it.”
“Atoms are the basic building block of matter because all matter contains atoms.”
“Atoms are electrons, protons, and neutrons and are bound together by magnetic forces.”
“Electrons excess makes charge negative, while protons excess makes charge positive. Why are these the charges?”
“Electrons cancel out protons because of the protons’ positive charge.”
“Electrons likely move so slow due to the difficulty of exerting force on them.”
“Electrons in motion cause excess energy called tails.”
“When electrons are further away it causes them to have higher energy levels.”
“The positive parts ‘want’ electrons because they are oppositely charged and so they are attracted to each other.”
“A photon absorbed by an electron causes it to escape from the atom.”
“What causes charge to never be created or destroyed?”
I wrote recently about creating a rubric to help students analyze their mistakes. Here are some examples of what students wrote — a big improvement over “I get it now” and “It was just a stupid mistake.”
The challenge now will be helping them get in the habit of doing this consistently. I’m thinking of requiring this on reassessment applications. The downside would be a lot more applications being returned for a second draft, since most students don’t seem able to do this kind of analysis in a single draft.
Understand What’s Strong
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“I thought it was a parallel circuit, and my answer would have been right if that was true.”
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“I got this question wrong but I used the idea from the model that more resistance causes less current and less current causes less power to be dissipated by the light bulbs.”
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“The process of elimination was a good choice to eliminate circuits that didn’t work.”
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“A good thing about my answer is that I was thinking if the circuit was in series, the current would be the same throughout the circuit.”
Diagnose What’s Wrong
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“The line between two components makes this circuit look like a parallel circuit.”
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“What I don’t know is, why don’t electrons take the shorter way to the most positive side of the circuit?”
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“I made the mistake that removing parallel branches would increase the remaining branches’ voltage.”
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“What I didn’t realize was that in circuit 2, C is the only element in the circuit so the voltage across the light bulb will be the battery voltage, just like light bulb A.”
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“I looked at the current in the circuit as if the resistor would decrease the current from that point on.”
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“I think I was thinking of the A bulb as being able to move along the wire and then it would be in parallel too.”
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“What I missed was that this circuit is a series-parallel with the B bulb in parallel with a wire, effectively shorting it out.”
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“What I did not realize at first about Circuit C was that it was a complete circuit because the base of the light bulb is in fact metal.”
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“I thought there would need to be a wire from the centre of the bulb to be a complete circuit.”
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“I wasn’t recognizing that in Branch 2, each electron only goes through one resistor or the other. In Branch 1, electrons must flow through each resistor.”
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“I was comparing the resistance of the wire and not realizing the amount of distance electrons flowed doesn’t matter because wire has such low resistance either way.”
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“My problem was I wasn’t seeing myself as the electrons passing through the circuit from negative to positive.”
Improve
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“In this circuit, lightbulb B is shorted so now all the voltage is across light bulb A.”
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“When there is an increase in resistance, and as long as the voltage stays constant, the current flowing through the entire circuit decreases.”
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“After looking into the answer, I can see that the electrons can make their way from the bottom of the battery to the middle of the bulb, then through the filament, and back to the battery, because of metal conducting electrons.”
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“To improve my answer, I could explain why they are in parallel, and also why the other circuits are not parallel.”
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“I can generalize this by saying in series circuits, the current will stay the same, but in parallel circuits, the current may differ.”
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“From our model, less resistance causes more current to flow. This is a general idea that will work for all circuits.”
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:
- Components are in series if they’re in a square shape
- Components are in series if all the current in one flows into the second
- Components are in series if they’re both connected to the power supply
- 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.
- Their experience in DC circuits is not doing enough to help them make sense of this idea
- The assessments in DC circuits are not rigourous enough to catch students who are still unsure about this
- This student is incapable of consistently making sense of this idea, and should not have been accepted into the program in the first place
- 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.
In the same vein as the last post, here’s a breakdown of how we used published sources to build our model of how electricity works.
- I record questions that come up during class. I track them on a mind-map.
- I pull out the list of questions and find the ones that are not measurable using our lab equipment, and relate to the unit we’re working on.
- I post the list at the front of the room and let students write their names next to something that interests them. If I’m feeling stressed out about making sure they’re ready for their impending next courses/entry into the work world, I restrict the pool of questions to the ones I think are most significant. If I’m not feeling stressed out, or the pool of questions aligns closely with our course outcomes, I let them pick whatever they want.
- The students prepare a first draft of a report answering the question. They use a standard template (embedded below). They must use at least two sources, and at least one source must be a professional-quality reference book or textbook.
- I collect the reports, write feedback about their clarity, consistency and causality, then hand back my comments so they can prepare a second draft.
- Students turn in a second draft. If they have blatantly not addressed my concerns, back it goes for another draft. They learn quickly not to do this. I make a packet containing all the second drafts and photocopy the whole thing for each student. (I am so ready for 1:1 computers, it’s not funny.)
- I hand out the packets and the Rubric for Assessing Reasoning that we’ve been using/developing. During that class, each student must write feedback to every other student. (Note to self — this worked with 12 students. Will it work with 18?)
- I collect the feedback. I assess it for clarity, consistency, and usefulness — does it give specific information about what the reviewee is doing well/should improve. If the feedback meets my criteria, I update my gradebook — giving well-reasoned feedback is one of the skills on the skill sheet.
- If the feedback needs work, it goes back to the reviewer, who must write a second draft. If the feedback meets the criteria (which it mostly did), then the original goes back to the reviewer, and a photocopy goes forward to the reviewee. (Did I mention I’m ready for 1:1 computers?)
- Everyone now works on a new draft of their presentation, taking into account the feedback they got from their classmates.
- I collect the new drafts. If I’m not confident that the class will be able to have a decent conversation about them, I might write feedback and ask for another draft. (Honest, this does not go on forever. The maximum was 4, and that only happened once.) I make yet another packet of photocopies.
- Next class, we will push the desks into a “boardroom” shape, and some brave soul will volunteer to go first. Everyone takes out two documents: the speaker’s latest draft, and the feedback they wrote to that speaker.
The speaker summarizes how they responded to people’s feedback, and tells us what they believe we can add to the model. We evaluate each claim for clarity, consistency, causality. We check the feedback we wrote to make sure the new draft addressed our questions. We try to make it more precise by asking “where,” “when,” “how much,” etc. We try to pull out as many connections to the model as we can. The better we do this, the more ammo the class will have for answering questions on the next quiz.
Lots of questions come up that we can’t answer based on the model and the presenter’s sources. Sometimes another student will pipe up with “I think I can answer that one with my presentation.” Other times the question remains unanswered, waiting for the next round (or becoming a level-5 question). As long as something gets added to the model, the presenter is marked complete for the skill called “Contribute an idea about [unit] to the model.”
We do this 4-5 times during the semester (once for each unit).
Example of a student’s first draft
I was pretty haphazard in keeping electronic records last semester. I’ve got examples of each stage of the game, but they’re from different units — sorry for the lack of narrative flow.
This is not the strongest first draft I’ve seen; it illustrates a lot of common difficulties (on which, more below). I do want to point out that I’m not concerned with the spelling. I’ve talked with the technical writing instructor about possible collaborations; in the future, students might do something like submit their paper to both instructors, for different kinds of feedback. I’m also not concerned with the informal tone. In fact, I encourage it. Getting the students to the point where they believe that “someone like them” can contribute to a scientific conversation, must contribute to that conversation, or indeed that science is a conversation, is a lot of ground to cover. There is a place for formal lab reports and the conventions of intellectual discourse, but at this point in the game we hadn’t developed a need for them.
Feedback I would write to this student
Source #1: Thanks for including the description of what the letters mean. It improves the clarity of the formula.”
Source #2: It looks like you’ve used the same source both times. Make sure to include a second source — see me if you could use some help finding a good one.
Clarity: In source #1, the author mentions “lowercase italic letters v and i…” but I don’t see any lower case v in the formula. Also, source #1 refers to If, but I don’t see that in the formula either. Can you clarify?
Cause: Please find at least one statement of cause and effect that you can make about this formula. It can be something the source said or something you inferred using the model. What is causing the effect that the formula describes?
Questions that need to be answered: That’s an interesting question. Are you referring to the primary and secondary side of a transformer? If so, does the source give you any information about this? If you can’t find it, bring the source with you and let’s meet to discuss.
Common trouble spots
It was typical for students to have trouble writing causal statements. I’m looking for any cause and effect pair that connect to the topic at hand. I think the breadth of the question is what makes it hard for students to answer. They don’t necessarily have to tell me “what causes the voltage of a DC inductor to be described by this formula” (which would be way out of our league). I’d be happy with “the inductor’s voltage is caused by the current changing suddenly when the circuit is turned on,” or something to that effect. I’m not sure what to do about this, except to demonstrate that kind of thinking explicitly, and continue giving feedback.
It was also common for students to have trouble connecting ideas to the model. If the question was about something new, they would often say “nothing in the model yet about inductors…” when they could have included any number of connections to ideas about voltage, current, resistance, atoms, etc. I go back and forth about this.
In the example above, I could write feedback telling the student I found 5 connections to the model in my first three minutes of looking, and I expect them to find at least that many. I could explicitly ask them to find something in the model that seemed to contradict the new idea (I actually had a separate section for contradictions in my first draft of the template). That helped, but students too often wrote “no contradictions” without really looking. Sometimes I just wait for the class discussion, and ask the class to come up with more connections, or ask specific questions about how this connects to X or Y. This usually works well, because that’s the point at which they’re highly motivated to prevent poorly reasoned ideas from getting in to the model. Still thinking about this.
Example Student Feedback
(click through to see full size)
I don’t have a copy of the original paper on “Does the thickness of wire affect resistance,” but here is some feedback a classmate wrote back.
Again, you can see that this student answered “What is the chain of cause and effect” with “No.” Part of the problem is that this early draft of the feedback rubric asks, in the same box, if there are gaps in the chain. In the latest draft, I have combined some of the boxes and simplified the questions.
What’s strong about this feedback: this student is noticing the relationship between cross-sectional area of a wire (gauge), and cross-sectional area of a resistor. I think this is a strong inference, well-supported by the model. The student has also taken care to note their own experience with different “sizes” of resistor (in other words, resistors of the same value that are cross-sectionally larger/smaller). Finally, they propose to test that inference. The proposed test will contradict the inference, which will lead to some great questions about power dissipation. Here the model is working well: supporting our thinking about connections, and leading us to fruitful tests and questions.
Example of my first draft
Sometimes I wrote papers myself. This happened if we needed 12 questions answered on a topic, but there were only 11 students. It also happened when we did a round of class discussions only to realize that everyone’s paper depended on some foundational question being answered, but no one had chosen that question. Finally, I sometimes used it if I needed the students to learn a particular thing at a particular time (usually because they needed the info to make sense of a measurement technique or new equipment). This gave me a chance to model strong writing, and how to draw conclusions based on the accepted model. It was good practice for me to draw only the conclusions that could be supported by my sources — not the conclusions that I “knew” to be true.
I tried to keep the tone conversational — similar to how I would talk if I was lecturing — and to expose my sense-making strategies, including the thoughts and questions I had as I read.
In class, I would distribute my paper and the rubrics. Students would spend the class reading and writing me some feedback. I would circulate, answering questions or helping with reading comprehension. I would collect the feedback and use it to prepare a second draft, exactly as they did. If nothing else, it really sold the value of good technical writing. The students often commented on writing techniques I had used, such as cutting out sections of a quote with ellipses or using square brackets to clarify a quote.
Reading student feedback on my presentations was really interesting. I would collect their rubrics and use it to prepare a second draft. The next day, I would discuss with them my answers and clarifications, and they would vote on whether to accept my ideas to the model. At the beginning of the year they accepted them pretty uncritically, but by the end of the year I was getting really useful feedback and suggestions about how to make my model additions clearer or more precise.
I wish I had some student feedback to show you, but unfortunately I didn’t keep copies for myself. Definitely something I will do this year.
How It’s Going
I’m pretty satisfied with this. It might seem like writing all that feedback would be impossible, but it actually goes pretty quickly.
Plan for improvement: Insist on electronic copies. Last year I gave the students the choice of emailing their file to me or making hard copies for everyone and bringing to class. Because bringing hard copies bought them an extra 12 hours to work on it, many did that. But being able to copy and paste my comments would help. Just being able to type my comments is a huge time-saver (especially considering the state of my hand-writing).
The students benefit tremendously from the writing practice, the thinking practice and, nothing to sneeze at, the “using a word-processor correctly” practice. They also benefit from the practice at “giving critical feedback in a respectful way,” including to the teacher (!), and “telling someone what is strong about their work, not just what is weak.” If their writing is pretentious, precious, or unnecessarily long, their classmates will have their heads. And, reading other students’ writing makes them much more aware of their own writing habits and choices.
I’m not grading the presentation, so I don’t have to waste time deliberating about the grade, or whether it’s “good enough.” I just read it and respond, in a fairly conversational way. It’s a window into my students’ thinking that puts zero pressure on me, and very little pressure on the students — it’s intellectually stimulating, I don’t have to get to every single student between 9:25 and 10:20, and I can do it over an iced coffee on a patio somewhere. I won’t lie — it’s a lot of work. But not as much work as grading long problem sets (like I did in my first year), way more interesting, and with much higher dividends.
Resources
MS Word template students used for their papers
Rubric students used for writing feedback. Practically identical but formatted for hand-written comments
