Re: [Phys-L] other problems with what is (or isn't) on the test

[John Denker <jsd@av8n.com>]

On 06/18/2012 02:47 PM, Peter Schoch wrote:
> Yes, in NJ to be a HS teacher of Science or Math you need to have a
> degree in the subject first and then add-on the teaching courses.

That's good.  Definitely a step in the right direction.

> Since I teach Physics and ODE, I get to see them all at my community
> college.  It is amazing how much of a fight they put up -- "Why do we
> need to learn this if we'll never teach more than Calculus?" etc.

If they don't know the right answer to that question, it's good
that they are asking the question out loud ... as opposed to just 
guessing the wrong answer, i.e. just assuming the course is a
meaningless hoop they have to jump through.  They need to hear
the right answer, loud and clear.

> Once I have them in class, I do my best to not only show them the
> course content but how it all fits together.  Once they see all the
> interconnectedness of it, they appreciate it more; and anecdotally,
> they report doing much better at their 4-yr. schools and in the
> classrooms than their peers (the schools also report this to us).

1) Good. Thanks. That's the right answer, or at least a big
piece of the right answer.

This is exactly on-topic for this thread.  Being able to see
and appreciate the connections between ideas is high on the
list of things that should be on the test but aren't ... and
the list of things that should be part of the official course
description but aren't.

It's a scandal that "connectedness" is not a big part of the
syllabus at every level from kindergarten on up.  It's a scandal
that so many students have to wait until they're in college before 
somebody clues them in about this.  Better late than never ... 
but in a sane world we wouldn't be forced to choose between late 
and never.

2) Here is a slightly more detailed answer (but still only a
partial answer) to the students' question:

These folks, when they become teachers, will soon discover that
they can't teach everything at once ... but they have to start
somewhere, which means that they will need to introduce lots
of approximations, lots of pedagogical simplifications.  At
almost any minute of the day, they will face a 17-way choice.
There will be faced with 17 different approximations, all of
which are a_priori plausible, all of which work equally well
_in the short term_ ... but 16 of them are losers that will
have to be unlearned sooner or later, whereas only one of
them is a keeper that serves as a foundation and a springboard
for further developments.  Anybody who hasn't been down the
road far enough won't understand where the road is leading,
and will make the wrong choice every time.

As perhaps the most spectacular example, somebody who hasn't
taken college physics has no business teaching calculus at
the high-school level (or any other level).  Calculus was
invented for a reason!  It was invented for solving physics
problems.  (Calculus has expanded a bit since then, but even
so, physics is still its home turf.)

As a more prosaic but still important example:  When I was
in high school geometry, a substitute teacher quietly admitted
that he didn't see what any of it was good for.  I kid you
not.  He said:  "The area of a parallelogram?  Who cares? 
When was the last time I needed to buy the right amount of 
paint for parallelogram-shaped wall?"  Somebody needed to 
tell the guy that parallelogramshave applications other 
than paint, such as:
  *) Torque is a bivector, and is subject to the parallelogram 
   rule.  Examples include:
   -- torque as applied to lug nuts when changing a tire
   -- torque as applied to cylinder-head bolts, which is
    a rather critical application
   -- torque aka moment as applied to putting passengers
    and luggage in the right places in an airplane, which
    affects stability and controllability, not to mention
    structural integrity.
   -- bending moments in architecture and civil engineering
   -- torque that makes your ski binding release, or breaks
    your leg if it doesn't release.
   -- torque that swings a baseball bat or a golf club, in
    somewhat non-obvious ways.
  *) angular momentum
  *) the magnetic field
  *) the electric field (if you do it right, in spacetime)
  *) et cetera

I'm not saying that the geometry teacher needs to go into that
level of detail, but he needs to internalize the headline,
namely that parallelograms have *lots* of applications other
than painting.  He needs to say -- with conviction -- that
the applications run the gamut from auto mechanics to zoology,
including lots of stuff in between.  He needs to be able to 
trot out examples if/when needed.

He *also* needs to be able to put on his mathematician hat and
say that Euclidean geometry is elegant and beautiful and logical,
and would be interesting even if it didn't have any applications.
That story doesn't work for all students, but it works for some,
and it needs to be said.  See also
  http://www.maa.org/devlin/devlin_03_08.html

In a sane world the geometry text would support both of these
points by discussing the applications and discussing the elegant
and creative aspects of mathematics ... but I'm not holding my
breath waiting to see that.