"Junk" Science LO21650

John Paul Fullerton (jpf@myriad.net)
Mon, 17 May 1999 14:08:44 -0500

Replying to LO21623 --

> T.J. Elliott says, in part:

> > I was reminded of the writing of Robert Kegan in 'Over Our Heads' who
> > maintains that there are different orders of thinking requiring the
> > ability -- as they rise -- to see things progressively more
> > abstractly, as alternatively related and unrelated (I am grossly
> > oversimplifying). Your observation was to me echoic. But Kegan is
> > not so sanguine about the
> > ability to 'teach' this higher order; he finds it missing in
> > about half the adult population. He also sees it as developmental and
> > only naturally occurring in small increments. Thought you'd enjoy the
> > parallel theme.

John Zavacki responded

> Proponents of W.E. Deming (a group in which I claim membership) would
> smile at the fifty percent figure. Dr. Deming believed that in all
> systems, including education and government, fifty percent of behaviors
> are below the mean and fifty percent above.

I haven't been following the thread, other than seeing the title; however,
today the title brought to mind the untaught element in schoolwork. I've
just taken the introductory course on differential equations in college at
age 37 and find that the emphasis is much toward learning a set of math
techniques and learning when to apply those techniques. The question of
what a differential equation is and why it appears in scientific
investigations is accounted for early in the textbook and from then on
it's techniques and applications.

I can't say anything against education or my experience of it or my
participation in it; that's a restraint that I believe in, so my comment
is not intended as dismissing or thinking less of any of it. Yet I find
that my search for answers to "why" questions is more easily addressed
through guessing! Why do differential equations appear in scientific
investigations? Because those mathematical descriptions (differential
equations) can more easily be stated than their solution. Why may
differential equations be more easily stated? Because they're more easily
observed? Why more easily observed? Because they involve change and it is
easier to perceive change as an event. (For example, we could see a model
of a Star Wars spaceship; when its gun turrets begin to turn and so forth,
we more easily identify the parts of the spaceship.) In any case, I looked
for such an explanation and did not find it, and through thinking about it
made up my own. I don't know whether it's right, and it's not expected
that my score will rise because of thinking about that.

I've wondered whether mathematics is taught the way that people who like
math (and people whose work we study now) practice or practiced it. Two
figures in the history of vectors, Hamilton and Grassman, went about their
projects philosophizing about time and space. How different is the use of
vectors now. More than one book introduces vector products as definitions
that will be found to be useful later. Where did they come from? Why do
they help us? What do they do? Probably the answer is sitting before us in
the mathematical steps that vector products involve; however, that doesn't
mean that the understanding of their benefit in math work is the same for
every student.

Back to "teaching higher order". Acknowledging the guideline of 7 plus or
minus 2 ideas in mind at a time (not saying simultaneously thought) the
many more than 5 or 10 ideas that get taught will have to be put into
successive packages. Though I may know why items 1-5 go into package A1,
it may benefit another who works with me to be told why. It seems like the
assumption in math is that good students will sort through the elements
and make optimized use of them, or that the sorting and optimization is
actually being taught though not being repeated every day. I'm not sure
and don't remember being told these things.

Have a nice day
John Paul Fullerton


"John Paul Fullerton" <jpf@myriad.net>

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