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Re: [Phys-l] "Unlearning"



On 09/09/2010 03:45 PM, Ann Reagan wrote:
You mean, why teach things we all KNOW are wrong, like F = ma or P =
mv? Or why teach that thermal expansion is linear , or that air obeys
the ideal gas law? Perhaps because in a wide range of important
cases, it gives a useful working approximation that describes the
world in which we live.

There are two sides to this coin:
a) everybody uses approximations every day ... in the
classroom, in the research lab, and in everyday life.
b) approximations, are, by definition, inexact.

The point is that fact (b) does not mean that you should
avoid all approximations ... and just as importantly,
fact (a) does not give you a license to use whatever
approximation comes to mind. This is because some
approximations are very much better than others.

The task we all face is to distinguish good approximations
from bad approximations. This requires judgment and skill.

Similar words apply to teaching and learning: It is impossible
to teach (or learn) everything at once, so you have to start
/somewhere/ and work your way up. This does not, however,
give you a license to start "anywhere" that comes to mind.
This is because some starting-places are very much better
than others.

In particular, it is worth pointing out that just because
this-or-that technique is not very powerful does /not/
make it a good starting point. For example, you can eat
vichyssoise with a fork, but it's not a good idea. Using
a spoon is both easier and better. Spoons are readily
available. You might as well do it right the first time.

If you would like a less-fanciful metaphor, learning to
type with two fingers, hunt-and-peck, is /not/ any kind
of foundation; it is not any kind of stepping stone along
the path to proficient touch-typing.

The quality of approximations covers a whole continuum.
There are many shades of gray, including
-- perfection
-- near perfection
-- good approximation
-- rough approximation
-- travesty
-- perversion

We can also talk about crutches.
*) An ordinary person doesn't need a crutch at all.
*) A handicapped person may or may not benefit from
using a crutch.
*) Crutches are dangerous if improperly used. They
can cause short-term problems and can even cause
serious, irreversible injury.

I suspect that what BC was referring to, in his ever-
so-cryptic style, was not ideas that are very slightly
imperfect. Step-by-step refinement of a good idea is
not what we usually call "unlearning" ... and it's not
a problem.

The problem involves unlearning ideas that are useless
or worse, ideas that should never have been learned in
the first place.

The example he cited -- the idea "significant figures --
comes up every year at this time. Unlike F=ma, it is a
prominent member of the list of things that should never
have been taught in the first place. The alternatives
are easier /and/ better.

An even worse problem starts from the fact that students
can -- and do -- figure out that what's being taught
doesn't make sense. The more the teacher defends the
nonsensical ideas, the more the loss of trust. This
is a Bad Thing.

And IMHO the worst part doesn't involve any particular
bad idea; I don't really care very much about sig figs
in particular. The worst part is that when nonsensical
ideas are being taught, it reinforces the students'
belief that rote-only learning is the key to success,
and that thinking about the subject doesn't pay. I
don't scare easily, but this scares me.

There's a lot more I could say about this, but I'll
stop here for now.