Re: Physics teaching reform was "acceleration due to gravity"

[John Denker <jsd@MONMOUTH.COM>]

At 12:34 PM 1/27/01 -0600, John M. Clement wrote:
> most of the major reformed curricula use g=9.8N/kg.

I have no objection to using N/kg when convenient;  see below for more on this.

> In addition they sesibly refer to the force due to gravity as F_g, and the
> acceleration due to gravity as a_g (neglecting other forces).  The
> notation would be to use a for all accelerations, and F for all forces
> with appropriate subscripts.

This is clearly a good idea.

> Each of these steps alone does not solve all problems,

Indeed not.

> This obviously does not solve the basic problem of low thinking skills.

Indeed not.

> Low thinking skills are attacked mainly by appropriate elicit, confront, and
> resolve strategies.

The topic of "thinking" covers a lot of ground.  Redefining the topic so
narrowly that it can be "mainly" attacked by such a narrow set of
strategies seems ill-advised.  A serious discussion of the topic would need
to account for the skill-set each student has at the start of the course,
the level of physics facts and/or thinking skills one is trying to teach,
and many other factors.

> The equivalence of units is extremely dense to non formal thinkers, and
> causes problems even when initially encountered by formal thinkers. Also the
> common assumption that teaching formal logic fixes these problems, is false.
> Informal logic and opportunities to think logically can be beneficial.

a) I agree that some young students can't handle formal logic.
b) I agree that students who can't handle logic can profitably
   study other topics.
c) We should not imagine that while they are studying these
   other topics, they will discover logic on their own,
   in a flash of inspiration.

I think would be silly to drop logic from the curriculum just because
"some" students at "some" stage can't handle it.

I don't know what "extremely dense" means in this context.  I've seen
classes of 10th-graders (15-year-olds) learn the sort of dimensional
analysis we are talking about here, and they didn't think it was a
particularly big deal.  They didn't learn it overnight;  it took a number
of hours spread over a number of weeks.

I am not asking that students discover on their own the relationship
between Newtons and kg*m/s^2 -- just that they be able to deal with it
after it has been appropriately explained to them.

Also recall that what set me off on my most recent tirade was "a certain
number" of high-school students who finished the year not knowing the
difference between "some accelerations" and "all accelerations".  The last
time I checked, that distinction was literally kindergarten stuff:
 a) all toys are in the toy-chest
 b) some toys are in the toy-chest
 c) no toys are in the toy-chest.



At the other extreme, I think that it is OK to expose students to topics
that not everyone (or perhaps not anyone) in the class can master.  A lot
of young kids are aware that fastball and curveball pitches exist, even if
they have no idea how to throw one.  They can play the game at the
little-league level, and watch big-league games, even if they haven't
mastered the fine points.

Some experience throwing ill-controlled non-curvy pitches is a prerequisite
for throwing well-controlled curvy ones later.  The ability to throw
well-controlled curves is not a prerequisite for getting experience with
the game.

We should keep in mind that there is a huge spread in logical ability out
there.  There are some nine-year-olds who can solve intricate logic puzzles
such as "Hermione's Potion Puzzle" (page 285 of Harry Potter volume
1).  And they solve it using less information than Hermione herself used
(i.e. they can't see the sizes of the various bottles).  Meanwhile, of
course, there are plenty of adults who don't have the skill to solve such
problems.
  http://www.trig.net/~dave/harrypotter/harrypuzzle.html


> This is similar to the problem
> students have with math.  They fail to master the thinking needed to
> comprehend simple problems, and then they are taught matrix algebra in
> algebra II among other advanced topics.  Needless to say they find it
> confusing, and matrix algebra does not address the lower level problems.

I'm sure this scenario is common enough, but it's not what anybody is
intending and certainly not what anybody is advocating.  It's not even
typical; otherwise people would have stopped doing it eons ago.  All too
commonly, it's what happens to a subset of students who have fallen behind
(perhaps because of their innately different developmental sequencing, or
because of illness, or relocation, or previous inept teaching, or whatever)
and their educational system is too inflexible to deal with the situation.

This is every instructor's every-day nightmare:  students who are trying to
learn advanced topics but are suffering from weaknesses in the prerequisite
fundamental areas.  I see this in my students all the time.  It takes every
trick in the book, and a few more tricks than that, to get them
straightened out before they get hopelessly frustrated.

The other day I was amused to see what this looks like in reverse, when
after a goodly amount of experience as a self-taught skier, I took a skiing
lesson.  The poor instructor was dying of frustration.  I didn't know the
terminology, so it was hard for him to communicate.  I had a huge number of
small bad habits, all interconnected so that fixing any one of them was
going to make things worse, and he didn't know where to begin.  We sorted
it out eventually.

> Now there are many teachers who will not acknowledge this problem.
> ....  Eventially the paradigm is changed, not by converting the old, but
> rather by converting the young. .... Do we have to wait for a full
> generation to have major improvement in physics teaching?

I'm not sure there's a consensus on what "The Problem" is, let alone how to
fix it.  If "The Problem" is that some students are left behind while
others are bored beyond tears, it will take more than currently-envisioned
"reformed curricula" to fix that.