Student Thinking About Abstracting

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

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

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

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

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

It could be a typo.

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

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

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

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

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

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

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

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

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

9 comments

  1. It may be neither a simplification nor a lie, but a different definition of “threshold” than they are using. It may be worthwhile to have them plot current vs. voltage for the diodes. Even better, have them plot sqrt(current) vs. voltage. If the diodes behave in the way the classical models for them suggest, then there is a change in behavior at the threshold voltage.

    • The problem here is the omission of the notion that it is a model. There is, obviously, nothing wrong with the model itself.

      Characterizing diodes is exactly where we started — a much more generative starting point than simply proclaiming, as our textbook does, that Vf = 0.7V, with no explanation of why that threshold was chosen, or even that it’s a threshold. Noticing the need for that choice, and evaluating why someone would choose the various options, is infinitely more useful than memorizing a magic number.

      0.7V is, of course, a better threshold than the one the students chose, in some respects (although the change in behaviour occurs between roughly 500mV and 900mV — not “at” 0.7V). The point is how often curriculum materials do not do the very thing you (and I) suggest: start by characterizing diodes.

      • Do the straight line fits for sqrt(I) vs V below 500mV and above 900mV intersect at 0.7V? (Like the corner frequency of RC filters, the behavior near the threshold is messy, but away from the threshold can be quite simple.)

      • I’m familiar with the usefulness of and justifications for that model. I tried to communicate that in the original post without dwelling on it, because I am hoping to focus on a point of pedagogy, not physics.

        What frustrates me and disorients my students is that those justifications are never discussed, and even the fact that this is a model is omitted. To further “simplify” (obscure) the situation, most discussions of the matter don’t distinguish between two ideas: “the model has a change in behavior at 0.7V,” vs. “they physical system has a change in behavior at 0.7V.” Finally, the chapter starts with the most abstracted model (1st diode approximation) and ends with the less abstracted (3rd diode approximation).

        I’m interested in these judgement calls — why, when, and how we make them, whether we make them carefully or carelessly, the criteria we use.

        In this post, I’m trying to investigate the questions about educational design, not physics, but it seems not to have come across — let me know if there’s a way I could present that more clearly.

  2. I hear what you’re saying, I think. Recent experiences in class indicate a marked preference for the easy answer, the guessable v anything requiring thought. Still gobsmacked by a student’s statement that learning something was “…fun in theory. However it is difficult to care…I don’t want to learn how to… The {program name} is a lower level..than some people realise.” Sad commentary on past school experience and/or societal expectation.

    • Interestingly, my students were saying the opposite: that encountering the “messy” reality helped them think and understand, and that they resented a textbook author presenting something “guessable.”

      That was exciting to me: helping students encounter the “mess” FIRST, before discussing the official models, improved their content knowledge and also shifted their attitude so that “easy” answers started to seem unsatisfying.

      Here’s what was frustrating: textbook authors consistently start from the most abstracted model (in our case, the first diode approximation) and move toward slightly less abstracted models (the third diode approximation). I think the authors are assuming that highly abstracted models are “easier,” and therefore a more accessible place to start — especially if we anticipate that that’s what students prefer. These authors never put students in contact with the “messy behavior” at all. Both the sequence (more to less abstracted) and the omission of the messy reality seem wrong to me.

      Here’s what was sad: that my students come to me thinking that science is about “facts” rather than models, and that they are not in the habit of wondering how the “official” models got chosen. I’m also saddened that if students experience the distinction between messy reality and models, it feels like some kind of awful trick that’s being played on them. Maybe this is caused by them never having to create or evaluate models, or by climbing the “ladder of abstraction” in the wrong direction. Finally, I’m saddened that many students seem never to encounter the messy reality at all — assuming that the model is not a human judgement but a natural law.

    • Wow — that’s an interesting comment from the student. Surprisingly honest, which is refreshing. I wish I could convince all my students to be that direct with me about what they really think…

  3. When a real diode is reverse biased a minuscule leakage current flows through the device. This current can be effectively ignored as long as the reverse breakdown voltage of the diode is not exceeded At potentials greater than the reverse breakdown voltage, charge is pulled through the p-n junction by the strong electric fields in the device and a large reverse current flows. This usually destroys the device, hence no model is required for this phenomenon. An exception to this is diodes of the breakdown, or zener, type.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s