showing equations is not teaching

October 3rd, 2008

I'm going to describe something that you know very well, and that you do all the time. I'll describe it algebraically, so that we can keep it somewhat rigorous, like good teaching prescribes. Once I'm done, you'll know exactly what I'm talking about.

  1. c <= C
  2. w = (0 <= c < V)
  3. 0 < d < v
  4. p = {p1, p2, ..., pn}
  5. t = px

Got it? It has a colloquial name: doing laundry. Here's the same thing in words.

  1. grab a subset of the clothes in the laundry basket/hamper
  2. contents of washing machine equal to said clothes, but greater than zero, lesser than washing machine's volume
  3. contents of detergent compartment greater than zero, lesser than its volume
  4. machine has a set of programs
  5. duration of wash determined by chosen program

Here's the thing. If you understand laundry, and you knew that's what the equations were supposed to describe, you could probably figure out what's what. At the very least, you could come up with your own set of equations, and they might be similar enough to infer the original meaning.

But what if you had never heard about laundry, and all you got were these equations. Could you figure it out? No. You're just not that clever.

Now put yourself in the shoes of someone who's teaching laundry. You know laundry inside out, you can derive the equations at will. Laundry is the most obvious and trivial subject as far as you're concerned. Students come to your class, today's topic is laundry. You spend a couple sentences describing laundry. You explain it in words that your students don't understand. Then you present the equations. Then you go to lunch feeling good about yourself, passing on the knowledge and all that.

As it happens, not all the students latched onto the theory of laundry. Some are turning up, asking dumb questions. What is wrong with these people? How can you fail to understand laundry? You'd have to be dense. Geez, the quality of our freshmen really is plummeting. There's no way my generation was so thick.

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