NetNews Usenet Archive 1992 #26/NN_1992_26.iso/spool/sci/math/14612

Internet Message Format | 1992-11-08 | 8.9 KB

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From: [e-mail] (J.D. Baldwin)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: What can we have for an educational system?
Message-ID: <[e-mail]>
Date: 8 Nov 92 21:27:29 GMT
References: <[e-mail]> <[e-mail]>
    <[e-mail]>
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Organization: Comp. Sci. Dep't., U.S. Naval Academy, Annapolis, MD
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In-reply-to: [e-mail]'s message of 08 Nov 92 14:20:00 -0400

In article <[e-mail]>
[e-mail] (Herman Rubin) writes (quoting
[e-mail] ([Andrew Hackard]):
>>It ill behooves me to comment on the first half of this, since I'm going
>>to be a teacher next year (ideally, a competent one, though I'm loathe
>>to make that claim myself).  However, I'm curious, Mr. Rubin: what
>>alternative school system do you propose?
>
>It is barely possible to have a fair public educational system.  But such
>a system must not operate on the basis of adjusting the education of some
>children to that of others.  Such a system must not operate on the basis
>of merely teaching "what the children can learn well," with little idea of
>curricular organization.  But it must also consider that there are many
>ways of acquiring understanding; I see no possibility even of avoiding a
>lot of experimentation, as we do not really know how to teach other than
>rote memorization and "plug-and-chug" computation. [. . .]  If I may
>be so bold as to state the purpose of education, as opposed to
>training,
>
>    Education is preparation for the totally unforeseen situation.

And if *I* may be so bold as to quote my own favorite definition,
attributed by James Stockdale (in a 1981 essay) to Mark van Doren:
"Before proclaiming a man educated, we must ask this question:  'Could
he re-found his civilization?'"

It is my belief that this definition includes yours and a host of
others besides.  It also has the advantage of being utterly
unattainable, which implies the correct view that education is a
lifelong process which can never be "completed" in a real sense.

[The usual Herman Rubin intelligent, forceful statement of the problem
deleted.]

>But there is a major problem in a public system, and that is that different
>people have vastly different ideas of what and how children should be taught.
>There is no reason why your neighbors should be allowed to decide how your
>children should be taught.  There should be input from the scholars, but the
>final decision must be in the hands of the parents.  This would have been
>very difficult to do in the past, but is much easier now.

All very true, but lacking in specific political action suggestions
that I think the original poster was asking for.  Mr. Rubin probably
doesn't agree with all of the suggestions below, but I know our
philosophies are compatible:

1.  Abolish the education major, or at least its role in the teacher
    certification process.  Math should be taught by people who have
    studied math.  More about this below.

2.  Mr. Rubin's comments about experimentation, trial and error, etc.
    are very cogent.  This isn't a perfect world.  Some teachers are
    just going to have to try things that don't work, then go back and
    try again another way.  It will also require more individual
    attention to students.  This ties in somewhat with #1:  a person
    who is well-grounded in a subject will be much better equipped
    to try new techniques effectively than one who is "teaching" from
    a detailed, rote-memorization, lesson plan.
       In any case, a system full of teachers competent in their
    fields, even if they are blindly groping their way toward the
    correct way to teach their material, is bound to be better than
    what we have now, which is a system replete with idiots, with
    a solid grasp on the current WRONG way to teach it.
       (Also, note the high quality, in general, of teaching as
    practiced at the University level in the U.S.  Ask yourself how
    much "education" training the typical college professor has.)

3.  Local control by parents (and other school-district taxpayers and
    citizens) over the process.  The more local the control, the
    better.  Again, it's not an ideal solution (the ideal solution
    would have *individual* parents dictating specifics for their
    *individual* children).  However, this approach maximizes the
    impact a parent may have on his own children's education, while
    recognizing the realities of a system that just can't accommodate
    radical, total individualization of every aspect of its
    curriculum.

>And we must have teachers who understand the subjects they are teaching.
>This means that the first grade arithmetic teacher must understand the
>structure of the number system and the use of symbols.  The first grade
>teacher of reading must have a good grasp of grammar.  An elementary
>school teacher of science must understand the fundamentals of physics,
>chemistry, and biology.  A teacher of history should be aware of world
>history, and the interrelations between the various political, geographical,
>economic, and cultural forces throughout the ages.

Amen!  I believe that most of these requirements are satisfied by a
good, solid undergraduate major in the subject in question.  To err on
the conservative side, I'd probably require a master's or a bachelor's
with "demonstrated competence" in the field.  (I leave the question of
how such competence is to be "demonstrated" open.)

Two anecdotal data that illustrate this idea:

Richard Feynman related a story (in "Surely You're Joking," also
related in James Gleick's recent biography) about the way his father
answered a question when he was a child.  He (Richard) had asked why,
when he put a ball in a wagon and pulled the wagon, the ball rolls to
the back of the wagon.

His father replied that no one knows *why*, but he went on to give a
very simple explanation of inertia: that it is a property all things
have and that it makes things "resist" a force that is "trying" to
move them.  The important thing here is that Feynman's father had a
*fundamental* (no accident that Mr. Rubin chose that word)
understanding of the issues involved, but his explanation was NOT a
*difficult* one.  Imagine an educational system in which things are
explained, in such terms, to children at a very early stage in their
education.

The second anecdote is a personal one.  I recall vividly asking my
high school math teacher (who was an OK teacher, in general) why we
weren't allowed to say that "one over infinity is zero" when it
clearly *was* zero and when I had read somewhere that "lim (x->inf)
[1/x] = 0."  He simply kept replying that that isn't the way it works.
In retrospect, I realize that he didn't *know* what I learned as a
sophomore math major: that "lim" is a *notation* for the idea that if
x is allowed to grow arbitrarily large, we may make the expression 1/x
arbitrarily close to zero.  Again, not a *difficult* concept, merely a
*fundamental* one.  As a high school student, I was more than capable
of making the distinction (and so, probably, were nearly all of my
classmates).  A simple undergraduate math education on the teacher's
part would have gone a long way here.

People who oppose basic competency in science for science teachers
(though they'd never admit opposing it when the question is framed
that way) often complain that advocates of this idea are demanding too
much of the students--that we somehow wish graduate-level math forced
onto third-graders and tensor calculus onto high school physics
students.  This is incorrect.  We merely wish non-falsehoods to be
taught, so that there is less to unlearn at later stages.  How many of
us were mislead in school by being told that astronauts float
"weightless" in space because the earth doesn't exert a gravitational
force on them?  (In fact, the earth's gravitational pull on shuttle
astronauts, for example, is very very slightly less than it is on you
right now.)  What kind of school system would we have if every teacher
had a level of competence that enabled him to explain away, simply and
clearly, such misconceptions every time they came up?

(And all of this is quite aside from the fact that the truly
outstanding student would have the needed expertise at hand when he
began to outstrip the curriculum and pursue independent study.  But
that's another post.)
--
 From the catapult of:              |+| "If anyone disagrees with anything I
   _,_  J. D. Baldwin, Comp Sci Dept|+| say, I am quite prepared not only to
 _|70|___:::)=}-  U.S. Naval Academy|+| retract it, but also to deny under
 \      /   [e-mail]   |+| oath that I ever said it." --T. Lehrer
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