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?