🚀 go-pugleaf

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This article is from weemba@brahms.berkeley.edu (Matthew P. Wiener)
 and was received on Tue Jul  1 12:58:41 1986
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Seems we just had this debate concerning word processing!

In article <383@hplabsc.UUCP> gmp@rayssd (Gregory M. Paris) writes:
>
>Discourages understanding?  How does memorizing the multiplication tables
>from 1 to 13 encourage understanding of multiplication?  How does doing
>endless addition of 4 digit numbers encourage understanding of addition?
>These are things that children are forced to do in elementary school, and
>I contend that these things are counter to understanding.  I fail to see
>how adding tedium to a child's education, or to any task in general, can
>aid understanding.  This is seems even more apparent when dealing with
>complex engineering or scientific matters, where complex mathematical
>tasks are carried out by computers, leaving humans to do the interpretation
>and understanding of the results.  Computers and calculators have *freed*
>people to concentrate their mental abilities on understanding the problem
>at hand.   In the vernacular above, this is a good thing.

You've touched a nerve here.

First off, there's a lot of bad teaching out there, and you are kidding
yourself if you are blaming it on the material.  Using calculators does
not change this.  Indeed, I believe they encourage bad teachers to do
worse.

I do not believe understanding of anything difficult can come cheap and
easy.  I do not believe that having a computer changes that.  I believe
having a computer allows for greater realism in designing curricula.
And nothing more.

I am not happy with the standard curricula, by the way.  But that has
nothing to do with my beliefs concerning calculators and computers in
the classroom.

These machines come with an aura of perfection.  Why?  I have no idea.
But this aura is very damaging to students.  Most of them have no sense
of magnitude anymore.  They assume they entered the data in perfectly.
They can't do back-of-the-envelope calculations.  They are unable to
estimate.  They turn in pages of output called results. They give ans-
wers with meaningless precision.  (Even the ones who know better will
reflexively quote their digital watches if asked for the time.  Aargh!)

[Jon Bentley (`Programming Pearls') has an amusing anecdote about the
 precision of answers - he asked a student once how long a program took
 to run.  The student answered "about 150" "150 what?" "Umm..either micro-
 seconds or milliseconds, I'm not sure".   Needless to say, there is a BIG
 difference between the two!    -- Dave]

Do the students learn to think now that the computer has "freed" them?
No.  They learn how to run someone else's program.  They learn how to
specify options on a command line.

Do they learn how to understand what they are doing?  No.  They become
industrial strength bean counters.

When the task gets complicated, do they first approach the easy cases?
No.  They have learned to jump right into the hardest messes, because
of the unlimited power the computer gives them.

They will go for the three hundred parameter model when a mere five will
do, enamored of their numeric power, hypnotized by the formal simplicity,
and blissfully unaware of the ludicrousness of their enterprise.

They have no failsafe instincts.

They have no way of checking anything.

They are the vanguard of the new innumeracy.

They will wander in foggy Numberland forever if permitted.
------------------------------------------------------------------------
The above article refers to students, and is based on what I've seen far
too often, even among "A" students.  Who "they" are is not really spelled
out, of course.  And once "they" get out into the real world, some common
sense returns.  But a lot of damage is done first, and I believe the way
computers are used is a major contributor to this process.
------------------------------------------------------------------------
I'd like to quote Forman S Acton _Numerical Methods that Work_, pp245-6,
with a parallel attitude to a slightly different concern:
	
	Although we have no desire to blunt the enthusiam of the
	neophyte computor, many of whose excesses must be charged
	to the educational process, we would be remiss if we did
	not raise the spectre of uncritical wastage of computa-
	tional resourses by persons who are old enough to know
	better.  We grudgingly concede that there are times when
	it is better to use the computer inefficiently than to
	saddle a professor with a laborious search for a better
	algorithm; nevertheless enough identifiable nonsense goes
	on in th computer room to justify a brief but hopefully
	cautionary exhibit.  We begin with a personal experience.

	[1949 2 day inversion of a 16x16 matrix of 10-digit num-
	bers.  Turned out the matrix was orthogonal, which could
	have been verified in 10 minutes from the original formu-
	lae for the matrix entries.]  We were less than overjoyed,
	although--philosophically speaking--it was a good test of
	our inversion routine.

	In this day of electronic computation one might argue for
	the uncritical inversion of such a matrix on the grounds
	that it only takes fractions of a second while the proof
	of orthogonality would require minutes and might not then
	succeed--indeed, the matrix might not even be orthogonal.
	Why not invert and be done with it?  But in 1949 we who
	had striven mightily for two days had no such perspec-
	tive.  We were angry and with reason.  Somebody had not
	done his proper homework and we had to suffer for it.
	Your author, in 1970, still opposes this kind of uncrit-
	ical, shoot-from-the-hip computation.  It is an outward
	and visible sign of an inward and intellectual deficiency.
	It epitomized the "Why think? Let the computer do it" re-
	action that, unchecked, quickly undermines any critical
	review of either the direction or the value of an inves-
	tigation.  The computer is a precision tool.  It should
	not be used as a bludgeon or a substitute for thought.

As the S Harris cartoon punchline goes (roughly): "Yu meen Iv bin using
a defektiv speling program?"

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720