An Essay about Teaching and Learning
Stephen C. Ehrmann
In 1967, when I was first-year student in
engineering, I took physics. To derive a mathematical
equation to describe how a pendulum sways back and forth,
the professor began with Newton's Laws. Then he write line
of line of
algebra, crawling down the blackboard, each line
representing a step in the reasoning. The climax at the
bottom of the board: a surprisingly
short equation which, the professor told us, was called the
Equation of Simple Harmonic Motion. T is the time it
takes the pendulum to swing, L is the length of the
pendulum, and g represents the strength of gravity.
One implication: the time it takes a pendulum to swing
doesn't depend on how hard you push it, just on how long the
pendulum is.
The professor then pointed out that this
equation doesn't just describe the swinging of a pendulum.
The same equation, he said, also describes the vibration of
a weight suspended between two springs. And it also
describes the flow of electricity in a simple electrical
circuit that consists of a battery and three elementary
components (a resistor, a capacitor, and an inductance, as I
recall) linked together with wire. Then the professor
leaned forward over the lectern and asked with some passion,
"Isn't that beautiful?" I was in the second row and I wrote
it all down, concluding my notes with the word 'beautiful,'
just in case "beautiful" turned up on the next
quiz. Then I left for my
next class.
Several months later I learned the same
equation again, this time in a calculus course, and the
lecturer said the same thing. And "beautiful!" I wrote once
again in my notes. And I heard "beautiful" down a third
time, two years later, in an introduction to electrical
engineering.
Two years later, I had become a doctoral
student in management at that same university. I shared an
office with Lew Erwin, a doctoral student in mechanical
engineering. We had been undergraduates together and were
good friends.
"So why did you leave engineering?" Lew asked
me one day. I was already enough of a manager to answer a
question with a question, so I retorted, "Why did you stay
in engineering?"
He thought for a moment and then responded,
"Well, take something like the Equation of Simple Harmonic
Motion. It describes the motion of a pendulum, and a mass
vibrating between two springs, and electricity flowing
through a simple RLC circuit, and I think that's
beautiful!" What happened to me at that moment has happened
again every time I've told the story. And it's happening as
I write these words. My eyes teared up, my jaw dropped, and
I said in awe, "My god, it is beautiful."
Almost twenty years later, I was listening to
a couple of physicists, Joe Redish and Jack Wilson, talk
with one another. By this time I was a program officer with
responsibilities to find and then support innovative work in
higher education. I'm afraid my attention wandered after
awhile as they talked with one another. One of them said
something like, "Yahda yahda yahda equation of simple
harmonic motion." And suddenly all of those things that
happened in college came up back to me and for the first
time I wondered, "Why was it that three excellent
instructors worked so hard to teach me something, and failed
completely, when a couple years later a simple remark did
the trick?"
So I wrote a little paper for myself,
comparing two quite different notions about why this might
be so.
-
Maybe I'd matured, in
the way that William Perry once described college students
maturing. Perry's research suggested that younger
students tend to see the world in black and white terms,
with the professors the sources of truth and knowledge.
After a couple of years of development, they can
conceive that there might be more than one truth but, at
this point, they have only themselves as a point of
reference. "Everyone has a right to his own opinion," is
a comment that's a hall of this stage. Only later,
often not until after graduation, can students use
evidence and their own values to choose among several
'truths,' using evidence reason to take a stand and to
act.
-
Or perhaps I'd seen the beauty so easily
because, by this time, I'd done research myself and had
learned how hard it is to describing something complicated
and real in a simple, useful way, and how much harder it is
to come up with such a simple, useful conceptual description
that would 'work' for three different situations that, on
the surface, looked completely different. (By that argument,
the way to help freshmen see the beauty is to make sure they
do this kind of research when in high school).
I finished
the paper unsure of which explanation was more persuasive.
It seemed a good agenda for future research.
I sent a copy to Lew Erwin, by now a
professor himself at our old university. Next time I saw
him, I asked "So which of these two theories is right?"
"You're wrong," he replied. "Both
your theories are wrong. You
learned about the beauty of the equation from me because it was me who told
you. I'm your friend. That's certainly how I learned it. At
nights sometimes, I would sit on the roof of our fraternity
with my friend Phil Abbot, looking at the stars and talking
about things like this."
Lew went on, "I've been teaching for a while
now and I've figured out that a teacher may be able to teach
what to think. But only a friend can teach you how to feel
about it."
I think there's some truth in all three
explanations. College does help some students develop
through a very complex process of reorganizing the ways they
understand the world. And research -- research that
encourages students to develop explanations and then test
those explanations -- can help. But Lew was right, too.
Our relations and conversations with friends, often
outside classrooms, can change how we feel about things
Lew died young. It was the most horrible of
ironies: late one night, as he lay sleeping with his wife,
his wonderful heart just stopped beating. I told this
story at his memorial service and, ever since, I've told it
to others, to let them know what he taught me. Please pass
it on.
PS. Want to learn about the
Equation of Simple Harmonic Motion? Here's
one of many sources on the Web.
PPS. What does all this have to do
with educational uses of technology? We know that technology, whether that technology is a
computer or a piece of chalk, doesn't cause learning.
However, technology can serve the cause of learning by enabling
people to learn in ways that
might otherwise be difficult or impossible.
So, if you
believe the Perry explanation, technology can give students
more choices in how to learn, choices that stretch but don't
go beyond the student's stage of understanding. That's a
strategy that Perry scholars have recommended.
If you think
that research experience was the key, computers and the
Internet have vastly widened the scope of meaningful
research open to undergraduates and students in K-12
schools.
And if you think that being with friends is key,
consider how to use modern technology to increase the ways
in which people can bump into one another, and commune.
To repeat, none of these uses of technology
would compel all students to learn the beauty of that equation.
But aren't they three interesting ways to water the seeds we
plant?
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