Gas station without pumps

2013 August 27

Impedance matching as instructional metaphor

Filed under: Uncategorized — gasstationwithoutpumps @ 05:38
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Joe Redish, in his blog The Unabashed Academic, wrote a post  (What should we tell a colleague about DBER?) about getting colleagues to listen to advice from education researchers.  He recounts incidents which help explain why so many teachers are reluctant to listen to education researchers, then summarizes the message that he would like to get across:

1. Think carefully about what your real goals are for the particular population of students you are teaching.

2. Find ways to get sufficient feedback from the students that you can figure out, not just whether they have learned what you have taught, but how they have interpreted it and what knowledge and perspectives they bring to your class.

3. Respect both the knowledge they are bringing and them as learners. “Impedance match” your instruction to where they are and what they have to work with.

4. Repeat. That is, go back and re-think your goals now that you know more about your students.

I rather like the metaphor of impedance matching for teaching students.  It explains quite clearly (at least to those with any electrical engineering) the problem that is being addressed, in trying to adjust the signal provided to the load to get as much of the signal absorbed by the load as possible.

Of course, there are several problems that this metaphor brings up.  One, we are rarely teaching a single student at a time, but we can only match one impedance.  The metaphor suggests that we have to pick one student as our “typical” student and match them.  While that is probably better than what some teachers do, it is far from adequate to teach the wide range of students we usually get even in tiny classes.  We need to provide a range of different instruction, so that everyone in the class is learning, though not necessarily all learning the same thing.

There is also the problem that impedance matching is a metaphor that assumes we are the source and the students passive receivers of information, which doesn’t work that well with his point 2, about getting sufficient feedback from the students.  When trying to match an unknown impedance, we usually adjust things so that we get no reflection from the load—exactly the opposite of what we want from students!

Impedance matching is done to minimize the power needed in the source to get sufficient signal in the load—often to maximize the signal-to-noise ratio at the receiver.  That seems like a worthy goal, either minimizing our effort to get a desired outcome, or maximizing what the students learn for a given level of effort.

But the real goal is maximizing the signal-to-noise ratio, and impedance matching is often not the most important part of that task.  Reducing the noise is often more important than increasing the signal, and if the noise is introduced early in the process, it can be difficult or impossible to remove later.  This comes back to his point 1: figuring out what your real goals are, and shaping your instruction to meet those goals.  If you add a bunch of extraneous stuff that does not help students toward the goals, it not only wastes time but may actively oppose their learning what is needed.

The signal-to-noise metaphor brings up another approach: active noise cancellation.  It is now fairly easy to get headphones that not only provide good reproduction of music, but also actively cancel the sounds from the environment, so that one can listen even on airplanes and in other noisy environments.  For active noise cancellation to work, you need to have microphones or other sensors to detect the noise, and processing to precisely counter act it.  This is the idea behind his point 2: finding out what misunderstandings the students are mixing with the ideas you are trying to get them to understand, and actively cancelling those misunderstandings.

Again, it is not an easy task for large-group instruction.  Even noise-cancelling headphones need separate microphones and processing for each ear, because the noise at one ear is not the same as the noise at the other.  If you try to cancel the wrong noise, you may add  up adding more noise than you remove, creating a misunderstanding where there wan none previously.

I was hoping to use a different metaphor for handling  varying, unknown noise—the spread-spectrum technique, where the signal is not concentrated in a single frequency, but spread over many and less susceptible to accidental or deliberate interference.  Unfortunately, the spread-spectrum technique requires close cooperation between the transmitter and receiver, with the receiver knowing the spreading code or the frequency hopping pattern.  I don’t think that students understand the codes we use nor that hopping around all over the place and expecting our students to know precisely where we will go next is likely to be a good teaching metaphor!

What about you, readers? Can you come up with useful metaphors about teaching from electrical engineering, physics, or computer science?  (By “useful”, I mean ones that will help a teacher understand a pedagogic technique better.)

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