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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
I promised, months ago, to write about
an example of a measurement cycle, including how I chose the questions, why they arose in the first place, and how students investigated them
I’ve tried all summer to write this blog post and failed, mostly because I’m discovering the weaknesses in my record-keeping. I’m going to answer as much of the question as I can, then make a few resolutions for improving my documentation.
Last year in DC Circuits (then in AC Circuits, and in Semiconductors 1 and 2), our days revolved around building and refining a shared model of how electricity works. There were two main ways we built the model:
- measuring things, then evaluating our measurements (aka “The Measurement Cycle”)
- researching things, then evaluating the research (aka “The Research Cycle”)
The measurement cycle
- In the process of evaluating some research or measurements, new questions come up. I track them on a mind-map (shown above).
- When I’m prepping our shop day, I pull out the list of questions and find the ones that are measurable using our lab equipment.
- I choose 4-6 questions. I’m ideally looking for questions that have obvious connections to what we’ve done before, that generate new questions, and that are significant in the electronics-technician world (mostly trouble-shooting and electrical sense-making).
- Things I think about: What are some typical ways of testing these questions? Do the students know how to use the equipment they will need? Is it important to have a single experimental design, or can I let each lab group design their own? Is there a lab in the lab-book with a good test circuit? Is there a skill on the skill sheet that will get completed in the course of this measurement? The answers to these questions will become my lesson plan.
- At the beginning of the shop period, I post the questions I expect them to answer and skills I expect them to demonstrate. We have a brief discussion about experimental design. Sometimes I propose a design, then take suggestions from the class about how to clarify it or improve it. Sometimes I ask the lab groups to tell me how they plan to test the question. Sometimes, I just ask for a “thumbs up/down/sideways” on their confidence that they can come up with a design and, if they’re confident, I turn them loose.
- If they will need a new tool to test the questions, we develop and document a “Hazard ID and Best Practice” for that tool. (More on this soon…)
- The students collect data — one data point for each question. When they finish (and/or, if they have questions), they put their names up on the white board.
- When a group finishes, they have to walk me through their data. I check their lab record against our “best practices for shop notebooks” (an evolving collection of standards generated by the class), and point out where they need to clarify/make changes. If their measurement process has demonstrated a skill that’s on the skill sheet, I sign it off. Then I take pictures of their lab notes, and they are done for the day. I run the pics through a document scanning app and generate a single PDF.
- On our next class day, everyone gets a copy of the PDF. I break them into 4-6 groups, one for every question they tested. No lab partners together in a group. Each group analyzes everyone’s data for a single question, makes a claim, and presents it to the class. The class helps the presenters reconcile any contradictions, then they vote on whether to accept the idea to the model. This process generates lots of new questions, some of which can’t be answered. They go on the list for next week.
- Repeat for 15 weeks.
Example from September
Students were evaluating their measurements to figure out “What happens to resistance when you hook multiple wires together?” Here’s the whiteboard they presented to the class. Lots of good stuff going on here: they’re taking note of the effect meter settings have on measurement, noticing that wires have resistance (even though they’re called “conductors,” not “resistors”), and they’re able to realize that the meter measures the resistance of the leads, as well as what’s connected to the leads. In case you can’t read their claim, it says “Longer or more leads we connect and measure the resistance, more resistance we get.”
Questions students were curious about
Here’s where this inquiry-style stuff pays me dividends: I’m anticipating the path of future questions, and I’m thinking maybe it will be “what happens when you hook things up in parallel or in other arrangements.” I am so wrong. The next question is, “is it exactly proportional?” Whoa. I love that they’re attending to the fact that things aren’t always proportional.
The next question surprises me even more. It’s “If this works for test leads, does it work for light bulbs/hookup wires/resistors too?“
I was kind of stunned by that. At this point, the model includes the idea that resistance varies with length, cross-sectional area, and material. This should lead us to expect different amounts of resistance from different materials, but not entirely different patterns of variance. Especially between test leads and hookup wires!
On one hand, I’m afraid this means they think that light bulbs and hookup wire somehow obey fundamentally different physical laws than test leads. Their willingness to imagine the universe as disconnected and patternless offends against my sense of symmetry, I guess. I get over myself and realize that it’s awesome that they want their own sense of symmetry to be based on their own observations. So, I add it to the list of questions for the following week. I mentally curse the lab books of the world, which would have hustled the students past this moment without giving them a chance to notice their own uncertainty, which would then end up buried in their heads, a loose brick in the foundation of their knowledge, practically impossible to excavate.
How they investigated
The following week, we investigate “Is the change in resistance exactly proportional” and “do other materials do the same thing.” In our beginning-of-class strategy session, I tease out what exactly they want to know. Are they asking if the change in resistance is exactly proportional to … length? number of leads? What? They want to know about length, so that’s settled. There are lots of other questions on the docket that day, including
- Is there resistance in a terminal block?
- Can electrons get left behind in something and stay there? [I think this is a much more interesting way to ask it than the textbook-standard "Is current the same everywhere in a series circuit"]
- If electrons can get stuck, would it be a noticeable amount? Is that why a light dims when you turn it off? Are they getting lost or are they slowed down?
- Can more electrons pass through a terminal block than a wire?
- If you connect light bulbs end-to-end, we expect the total resistance to go up, but what will happen to the current? Is it the same as with one bulb? Will there be less electrons in bulb 3 than in bulb 1? Will the bulbs be dimmer as you go along?
They’re confident using the tools and materials, so I let them design their experiments however they want.
Some very cool experiments resulted. To check if total resistance in series was additive, one group used light bulbs, one used resistors, and (my favourite) one group removed two entire spools of hookup wire from the storage cabinet and measured the resistance of the spools separately, then connected in series (as shown).
This generated some odd data and some experimental design difficulties: there was no easy way to figure out the length of the spool. They could still tell that their data was odd, though, because the spools appeared visually to be about the same length, so whatever that length was, they should have roughly twice as much of it (short pause to appreciate that the students, not the teacher or textbook, made this judgement call about abstraction). Or, at least, the resistance should be more than that of one spool.
And that’s not what happened. If you look closely at the diagram, each spool appears to have 3 ends… Note that the sentence at the bottom shows that they distrust their meter. However, they did not fudge the data, despite not believing it was right. I believe that this is my reward for not grading lab books. Wait — not grading lab books is my reward for not grading lab books!
In the following class, this experiment generated no additions to the model but a mother lode of perplexity. It also resulted in demands for a standardized way of recording diagrams [Oh OK, since you insist...], and questions about what happens when you hook up components “side-by-side” instead of “one after the other.” And we’re off to the races again.
Speaking of standards for record-keeping…
It was really difficult to find the info for this blog post, because my record-keeping system last year was not designed to answer the question “how did questions arise.” It was intended to answer the question, “Oh God, what the heck am I doing?”
Some changes that will help:
- Using Jason Buell’s framework to keep whiteboards organized in Claim/Evidence/Reasoning style
- In the PDF record of students’ measurements, including a shot of the front-of-class whiteboard where I recorded the agenda
- Giving meaningful names to those PDF files. “20110928 lab data” is not cutting it.
- During class discussion, recording new questions next to the idea we were discussing when the question came up. Similarly, on the mind-map, attaching new questions to the ideas/discussions that generated them..
- Keeping electronic records of the analysis whiteboards (step 9 above), not just the raw data. Maybe distribute these to students as well, to have a record for their notes when we inevitably have to revisit old ideas and re-evaluate them in light of new evidence.
