Re: Teaching methods (was "Homework...")

["John S. Denker" <jsd@MONMOUTH.COM>]

Hi Folks --

This discussion has gotten off to a good start.  Many good
questions have been raised and some good points have been
made.

However, some of the arguments have been unduly polarized.
To make progress, we need a more nuanced discussion.
 -- Few of us believe homework is 100% good or 100% bad.
 -- Few of us believe lecturing is 100% good or 100% bad.
 -- Few of us believe having students "discover" things on
    their own is 100% good or 100% bad.
 -- Few of us believe that standardized testing is 100%
    good or 100% bad.
 -- Most of us believe that skillful individual tutoring is
    helpful if you can afford it, but under current budget
    conditions we can't afford very much of it.

We need to stay away from no-fat no-salt no-carbohydrate fad
diets.  And we shouldn't argue in favor of one extreme by
ridiculing the opposite extreme.  (I'm arguing for a balanced
diet by scorning _all_ the extremes.)

Also, it doesn't do much good to measure the effect of one
variable, while umpteen other variables are uncontrolled,
especially if there's not much consensus as to what objective
we're trying to optimize.  (Optimal effectiveness?  Optimal
cost-effectiveness?  Short-term gain on some test?  Lifetime
happiness and productivity?)

At present, pedagogy is an art with some inchoate pretensions
of becoming a science some day.  The scientific approach would
be to set it up as a multivariate optimization problem.  But
it's not 100% obvious how to quantify the dependent variable
(the objective function), and it's not 100% obvious how to
quantify the independent variables:
 -- how much lecturing, and what kind of lecturing?
 -- how much homework, and what kind of homework?
 -- how much play, self-directed experimentation, etc.???
 -- etc.

In the absence of ways to quantify such things, the discussion
tends to degenerate to the coarsest quantization, namely all
versus nothing.  We know the solution-set doesn't include the
extremes, so until we start using less-extreme descriptions, we
have no hope of finding the solution set, or even describing
whatever solutions (or near-solutions) have been found.

Also.... Tucker Hiatt asked:
> Isn't most of physics so counterintuitive to most people that
> "discovery" is highly problematic?

That's a good point.  As the saying goes, "education is the process
of cultivating your intuition."  Things that are counterintuitive at
the beginning of the course should be intuitive afterwards.  If
everything were _a priori_ intuitive, we wouldn't need educational
institutions at all.

Similar remarks apply to homework (the topic that started this
thread).  Practice makes perfect IF AND ONLY IF students are
practicing the right things.

I tell my students:  right now you think I've got all the answers.
But in the long run, 90% of what you know you will have taught
yourself.  My job is to get you to the place where you can teach
yourself, by reading and thinking and practicing.  (etc. etc. etc.)