Re: teaching and understanding

[palmer@sfu.ca (Leigh Palmer)]

> On 12/28/96 Donald E. Simanek, with whom I agree so often, wrote:
>
> > Many exams reward mere memorization, cramming of definitions and slogans,
> > slavishly carrying out procedures and recipes and pattern-following.
> > These do not measure understanding.
>
> True. But that does not mean that "knowing without understanding" should
> not be rewarded. Levels of understanding are hard to quantify; most often
> understanding is the last step in the process of learning. We begin by
> emitating and we end, hopefully, by being emitated. Yes, textbooks and
> classroom activities should promote understanding, gradually. Expecting
> too much may have negative effects on our mental health, expecting too
> little may kill our self-respect. Probing for understanding during an
> exam, taken under pressure, may be counter-productive.
>
>         Ludwik Kowalski           KowalskiL@alpha.montclair.edu

I agree with Ludwik, perhaps even more strongly. There is value to rote
memorization even; it keeps items which may be understood later close to
the consciousness and embeds them deeply in the subconscious mind. As an
example I will cite one item: "Entropy is a function of the state of a
system." I'm sure that was drilled into me successfully as a factoid
by Mr. Nash when I was a freshman at Sacramento Junior College. I'm sure
that sometime in my junior year at Cal I learned *how* to calculate the
entropy *change* from the thermodynamic coordinates of state. I think
that sometime in grad school I began to get some inkling of what that
meant and why it was marvelous, and only after I began teaching here at
SFU did I achieve an enlightened state where I could visualize entropy
geometrically in phase space and understand the dynamical evolution of
systems in that space. It would be very hard for me to dismiss the value
of what Mr. Nash told me way back in my freshman year. He understood the
entropy in just the way I do now, I now know, and he did not expect me
to achieve that level of understanding instantly!

I know a lot of high school teachers. Unlike many of my colleagues who
dismiss high school physics teaching as valuless because we have to
start teaching from first principles in college, I recognize that there
is considerable value in learning something, even if imperfectly, from a
sympathetic and knowledgeable teacher. Most of the high school science
teachers I know are such people, I'm pleased to be able to report.

Leigh