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Re: [Phys-l] ivory windmills



It has been pointed out, off-list and on, that my previous
post was somewhat unbalanced. Let me try to restore some
balance.

IMHO the goal of the educational system as a whole is to
prepare students to do well in real life.

So ... suppose at the end of the chapter X there are 40
exercises. Suppose exercises 1 through 32 are cut-and-dried
building blocks that deal with concepts covered in chapter
X, one concept at a time ... while exercises 33 through 40
are more open-ended and integrative, including stuff from
previous chapters and (!) maybe even stuff from real life.

That's all fine. Building-blocks are necessary.

However, my point is that the building blocks are not
the goal; they are necessary _but not sufficient_ in
order to reach the goal.

Therefore much depends on which exercises the students
actually do. In particular, suppose you assign ten of
the exercises, namely 4, 8, 12, 16, 20, 24, 28, 32, 36,
and 40 ... and the student actually finishes all but
the last two ... IMHO that doesn't count as 80% success
but rather as no success at all, because the whole point
of the assignment, and the whole point of the educational
system as a whole, is for the students to learn to handle
real-world problems.

By way of analogy: Suppose a certain flying student
has learned to use the rudder (in isolation), use the
ailerons (in isolation), use the throttle (in isolation),
et cetera. Alas, the student cannot integrate those
things well enough to land the plane. You don't really
want me to sign that person off as qualified to be a
pilot, do you?

Building blocks are fine. They are necessary. I spend
a *lot* of my time racking my brain trying to find ways
to break complex ideas into explainable chunks ... but
all that counts for nothing if we just move "towards"
the goal without actually achieving the goal.

On 04/11/2012 12:12 PM, Aburr@aol.com wrote:
As one who has and is writing homework problems, it is hard enough to
write correct, clear, and relevant restricted concept ones.

I agree. I never said any of this is easy. Teaching is
hard. Good teaching is really, really hard.

I've spent unreasonable amounts of time (recently and
otherwise) trying to come up with good pedagogical examples
that involve numbers that are significant in the Nth
digit but uncertain in the first or second digit, e.g.

⎛ 1.497925297894696 ... ⎞
X = ⎜ ± 0.1 ⎟
⎝ ⎠

The problem is not a lack of real-world examples. The
problem is that most of the real-world examples are so
complicated that the roundoff issue gets lost. There's
not much point in talking about "big eigenvalues" and
"small eigenvalues" to a high-school student who has
never heard of matrices.

I'm reasonably happy with the signal-averaging example,
http://www.av8n.com/physics/uncertainty.htm#sec-extracting
which is a rather mild example, insofar as only a couple
of "extra" digits are needed to solve the problem:

I'm also reasonably happy with the pH example,
http://www.av8n.com/physics/uncertainty.htm#sec-ph-quadratic
since
-- It requires lots and lots of "extra" digits,
-- It is a 100% unadulterated real-world application,
-- It is IMHO an /interesting/ application.
-- The term that is in danger of being wiped out by roundoff
is not some minor correction term; it is the entire answer.
-- It requires nothing more than high-school math.
-- There are multiple ways of getting the answer, each of
which illustrates a technique that is portable to other
real-world applications.

I am verrry aware that examples like this are not easy to
come up with. But still, it needs to be done. Anything
less defeats the purpose of the educational system.

Those types of
more general and inclusive problems are more appropriate (indeed necessary)
on final exams and employment interviews.

I 100% agree that comprehensive, real-world problems are
appropriate and necessary on final exams and job interviews
... but my point remains: We want to arrange the training
so that everybody knows /in advance/ that the students will
do well on the job interview, and (!) on the job thereafter.

That means they need lots of practice with open-ended,
integrative exercises all through the year ... indeed
all through the years, plural.

Also, a point about metacognition: The students need to
be told what is going on. They need to be told what the
actual goal is, and then told how the various building
blocks contribute to that goal.
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