## Sunday, March 20, 2011

### Misconceptions Misconceived: The example of current

If you've ever been in a physics classroom or read a paper in physics education research, you probably have heard students saying that current is "used up" in a circuit.

For example, in a one-bulb-one-battery circuit, a student might think that current is provided from the battery and transported to the bulb, where some of it is used up. Students often say that some of that current is returned to the battery to repeat the cycle, which is evidenced by the fact that you need a return wire. In thinking more specifically about measures of current, a student might say that there is more current before the bulb and less current after, because some of the current was used up. Based on this idea, once all the current is used up, the battery is dead, which explains why batteries die.

• The current in a single-bulb-single-battery circuit is the same everywhere, not different. There are different ways to make sense of this, but a physicist often thinks of this in terms of the continuity equation– if charge isn't building up anywhere, the flow must be steady.
• The battery is also not a source of current. It provides the conditions for maintaining a difference in voltage, which provide further conditions for current to flow. For that reasons, batteries don't die when they run out of current; they die when they can no longer maintain a voltage difference. This voltage difference cannot maintained once the battery disassociates all of the ionic compounds inside (which is where the energy in the battery is stored as chemical-potential energy)
• Bulbs also don't use current, and current is not lost there. Current isn't "stuff" you can lose, because it's a process (the flow of stuff). But energy does "leave" the circuit system here in the form or radiated light and heat.

In order to talk about what's so great about this misconception, I want to engage you with this gem. The excerpt below is from a student enrolled my science teaching and learning seminar. This particular student has never taken any physics. They were asked to read a paper about children's mental models of electricity and pick one of the mental models to write about:
"I want to talk about Model C (the current consumed model) , since that is the model I am currently stuck on. I really have no knowledge of how a circuit works and what the circuit does to provide or result in electricity. But to me, it would seem that “energy” would be coming into the light made from the light bulb, and thus the energy leaving the bulb in the form of light would result in less energy leaving the bulb in the wire going back to the battery. Also, batteries die, so one would think that its ability to provide current to the system is lost in that process. It must have gone somewhere, right?

"So Model C (which I suppose must be wrong) is reinforced by the simple ideas that we deal with regularly concerning electricity. We are told to unplug unused electronics to reduce the use of electricity… (but is that really what we are doing?) And how does this make sense: If current travels through a circuit and none is “used up”, why are our electricity bills so high? If we don’t actually use it up, why do we have to keep buying more? Model C just makes the most sense."
OK. What has this student done:
• First he identifies a puzzle: If energy is being lost at the bulb, shouldn't less of something being going in than going out?
• Second he identifies a bad solution to that puzzle: Asserting that the current must be the same doesn't resolve the puzzle.
• Third he identifies questions: Why do batteries die? Why do we pay for electricity?
• Fourth he is committed to sensibility (not authority): Despite knowing he is wrong, he is for all for Model C.
You should be impressed. Because this student owns his thinking. He is aware of his ideas, his questions, and his puzzles. He is articulate about why Model C makes sense to him.

His misconception makes more sense than most students' acceptance of the right answer.

I have seen (to good effect) instructors and curriculum use some combination of these approaches toward "fixing" this current-used up misconception:
• Engaging students with thinking about empirical evidence that support the idea the current is the same on both sides of bulb.
• Engaging students with arguments for why current cannot be different. (e.g., if it were different, you'd get a traffic jam or build up of charge; or by appealing to the of matter, charge, etc.)
• Engaging students with what current "is" - it is not a "thing" or substance that is used up, it is a flow of charge (a process);
• Engage student in learning about and applying Kirchoff's Laws.
These approaches can be done together in a variety of ways that are effective, and they each embody something important about science and science learning:
1. Empirical evidence - what data could I collect to help address this question?
2. Argumentation - In light of evidence, what claims can I support?
3. Ontology - what is the nature of this concept or quantity?
4. Scientific Knowledge - how do scientists represent, talk about, and use these concepts?
For that reason, Kudos to us for engaging students with important aspects of science as they learn something that is hard to learn.

But where do these strategies miss the mark?

They are all built around the idea that students' thinking has more to do with current, than the questions, puzzles, and the desires for explanation from which those ideas emerged.

From my experience, the students I encounter are not really trying to explain anything about current. They are trying to make sense of how bulbs and batteries work: They have ideas about what aspects of the situation are in need of explanation. They also have questions about how it works. They are capable of recognizing puzzles and inconsistencies. And they have some ideas about how they might explain and address those questions. The above excerpt has more ideas about "energy" than about current, and I'm impressed.

But I shouldn't be that impressed. Why? Because the excerpt above is fairly characteristic of the students I encounter in the real world when I talk to them about bulbs and batteries. Of course, if I hand them a multiple choice pretest about current, they look like they have a misconception about current. But when I talk to them away from worksheets and multiple-choice instruments–when they know that I care about what they think and that they will have to put some care and effort into expressing their ideas to me– they talk about evidence, and ideas, and inconsistencies, and questions. And sometimes they bring up ideas like energy, current, voltage, and sometimes they use those words in ways that I wouldn't. But is that a misconception? I'm not so sure.

The questions and ideas that arise in those conversations are way more interesting to me than this question:

Is the current at point C greater than, less than, or equal to the current at point D?

--> Who asks these questions anyway? No one in the real world asks questions like that. My students are way more interesting and critical with their own questions.
So here's the problem:

The four strategies to eradicate students' misconceptions do not address any of the questions or issues that perplex students.

By focusing on immediately on current, we are simply trying to correct a detail of their thinking that we are unhappy about. In doing so, we stamp "current must be the same" over the students' interesting questions and insights. And, sure, maybe we even do this in an intellectually honest way so that they really understand deeply why current must be the same. But I fear that along the way we've lost their interest, curiosity, and sense of access to the phenomena. Or we've replaced with a false sense of interest–an interest in superficial understandings.

How I Reconcieve Misconceptions

I will say, in most classes I have experienced, I see instructors spending way too much time trying to eradicate misconceptions. I, instead, try to choose to pursue and explore the questions and puzzles students identify. Along the way, misconceptions seem to corrects themselves through the honest pursuit of students' ideas and questions, because we've been exploring and refining those ideas along the way. And while I may want to monitor misconceptions, I shouldn't be fixated on them or apply too much press on them. The truth is, the more pressure I apply to this misconception, the quicker students learn that I am there to correct them. Once that happens, game over.

So when my students say that current must be different, I don't hear a misconception. I hear an ingenious way of trying to answer the question, "Why do batteries eventually die?" and a good explanation for how bulbs can be a sink for energy.

When a student balks at the idea that "current is conserved", I think, "Great, it doesn't make sense, does it?" When students don't want to accept that answer, I see them as being committed to sensibility (not to authority).

I'm MORE worried about the students who quickly accept the "right" answers. I really am.

And then end of the day, I'm not interested in stamping out misconceptions and replacing them with impoverished ideas, nor am I interested in having students ignore perplexity in the world.

1. This is a great post! How do we take our physics courses and frame them in terms of students' own ideas and questions? Is there enough to reframe an entire year of intro physics?

2. I'm not trying to dog you here, but I didn't really read past this paragraph:
" The current in a single-bulb-single-battery circuit is the same everywhere, not different. There are different ways to make sense of this, but a physicist often thinks of this in terms of the continuity equation– if charge isn't building up anywhere, the flow must be steady."

I worked with many great physicists, including a couple with a really, really big prize and I've never seen one of them think of anything in terms of "the continuity *equation.*" The really good ones are always thinking in terms of a physical model, and that might lead to a convenient way to express that model using an equation, but never, not once can I imagine a great teacher going to an equation when dealing with high school students or even 90% of undergraduates. Always begin with a physical model. (Unless you can't of course, eg quantum physics etc, but even then, make mention of that caveat.)
Perhaps you did that but you really did cause my loss of interest when you went directly to an equation.

3. @ Rick. Thanks for your journalistic critique.

4. @Frank... this might answer your question about possibility of filling a course with students' own question. In one hour, with the right question and facilitation, we were excited about a lot of awesome questions, which could be explored forever.

5. @Brian - ok, message received. Always being helpful, I suggest you not try out for American Idol.

6. @ Rick. ;) It's been a loooong week.

7. Been there, didn't mean to rub you. Just have scarce time to make comments and that can cause a few shortcuts. I do assume people post to create discussion. It's hard to tell when that is not the case. Hope your weekend is good.

8. This post is making me think hard... about teaching AND about electricity. I don't feel like I know much about electricity, but I don't think I ever had this misconception about current, in large part because I was taught about electricity with a skit in which kids playing electrons holding flashlights got shoved out of a "battery," along a path, into a "lightbulb" (where they turned on their flashlights"), and along a path back to the battery. So the voltage differential was a mystery (not in my model) but current seemed pretty obvious.

Pedagogically, what I'm wondering is, don't most conceptions/misconceptions have a scenario that makes them worth wondering about? So... lightbulbs and batteries and wall sockets make us wonder, "just what gets used up when I 'use' electricity? How do I 'conserve' that? Why is the 2nd bulb on a circuit dimmer than the first?" etc." The answers to those questions have to do with something else... energy and voltage I guess. For what scenario is the current being constant the answer? What experiences led physicists to quantify and measure current?

I guess I'm wondering whether we need to be wary of misconceptions, or if we need to be wary of using the wrong experiences to address misconceptions. Playing with electricity, natural questions emerge, and we build models to answer those questions. When the models have "bugs" that are unrelated to the interesting questions, teachers shouldn't lecture or give seemingly unrelated tasks to address those misconceptions. Instead they should say, "great, this is a functional model for the experiences we've had and questions we've asked! Does it apply to this next experience?" And engage kids in asking those questions, too.

9. OK. So to address your concern. It is probably a bad idea for me to put "physics" upfront, when I want to talk about students. That's bad journalism to make my audience wait.

But,I think I was trying present an argument ("no build up of charge implies constant flow"). This is a physical argument (based on a conceptualization of a flow model). In many physicists' minds, my argument is strongly associated with a more abstract principle often named by reference to the equation of continuity. Notice that I didn't write down that equation, I presented the argument and also named that argument by referring to a "culturally agreed upon" name for that argument.

10. Max, I think you hit the nail on the head. I'm concerned that we obsess over misconceptions, instead of the honest pursuits to understand the world from which those misconceptions arise. I'm for helping students to continue pursuing that understanding of the world, and patiently letting students' ideas change through that pursuit.

11. Very thought-provoking, and leaves me with a lot of questions :) Let me try to articulate at least one of them, although my own misconceptions about current may be getting in the way of my being able to fully understand this!

It sounds like your students are asking "why does the battery die" rather than the more artificial "what is current," and you'd like to address the former question rather than the latter, because while there's value in both, there's more value in the former since it's more authentic, fosters a better learning environment, etc.

If I'm interpreting this post correctly, then I totally agree. My question, however, is whether the two are exclusive-- and this is where my shaky physics understanding comes into play-- to what extent will students address the question "what is current" through addressing "why does a battery die"? If the answer is "not very much," would we then need another student-generated authentic question that leads us to a more thorough exploration of current, or could we step in and explain current and explain how it's related?

Not sure if I'm making sense here :)

12. So we get to chatting about this on Twitter, and I say, "in a series circuit, the 2nd bulb is dimmer than the 1st," proving that I too have misconceptions about current! And, providing me with a scenario that makes me wonder and for which the constant-ness of current comes to the rescue, I think. I hope it does anyway...

13. @ Grace. I think you are soooo right that the two are not necessarily mutually exclusive. I'm not advocating for one over the other. And I think you are right to say we should be mindful to engage students with phenomena and curiosities that will touch upon important disciplinary knowledge. Just because students are curious about something, doesn't mean it will be productive for science learning.

14. @Max

Thanks for sharing this. I think it's awesome. And I wouldn't say you have a misconception. I'd say you are coming to view your own understanding as possibly problematic, and it seem to me that you are interested enough in your own ideas (and the ideas of others) to pursue that understanding further. I think that's where I want my students to be.

Good luck with your own inquiry. Let me know where you land.

15. This post sent me down a rabbit hole-- and I dragged several colleagues & a former roommate (now physics PhD student) into it, but two hours later, the figurative (and in this case appropriate) light bulb finally went off.

I think I finally understand the relationship between current, voltage, resistance, power, batteries and light bulbs at a conceptual level rather than as a series of equations to be endlessly and mindlessly manipulated.

Thanks for a highly entertaining Friday afternoon (although I should probably now go and reflect on what skills I've acquired to allow me to be a self-driven learner in this way such that I can think about better preparing students to do so)!

16. @Grace. I got a chance this morning to follow along for a bit of your rabbit hole chase, at least the part that made it to twittering among you, max, and Frank.

You are quite welcome for the entertaining Friday afternoon. I've been going to down that rabbit hole for sometime. I'm not sure where the bottom is, if there even is one?

And recently, I've lost too many hours to following question, "How does a refrigerator work?" There are some many puzzles to sort out, and every time you solve one, a new one emerges.

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