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Topic: Calculators in Teaching Mathematics -- David Galernter
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Jerry P. Becker

Posts: 13,020
Registered: 12/3/04
Calculators in Teaching Mathematics -- David Galernter
Posted: Sep 29, 1998 7:39 PM
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[Note: Received from a colleague on the West Coast. One person gives an
opinion of the article, followed by the article, and then there are four
reactions, following the article.]


The following article, reprinted in the latest Readers Digest, is a clear
example of the direction that I as a school board advocate. This position
is completely in opposition of the NCTM advocation. The NCTM philosophy is
the one that the State of Alaska has advocated throughout the Math
Standards for Alaska.

NCTM has some very fine and worthy efforts in the field of mathematics;
however, this position on calculators is dead wrong.

This article clearly points out the situation of using calculators in the
early elementary class room creates too much opportunity for poor learning
habits, developing into a crutch not a tool.

Proof and evidence to demonstrate ability to do basic math by rote just has
to be a requirement prior to letting calculators be used. All other
reasons for their use before that demonstration are bogus.





CALCULATORS should be banned from American elementary schools. We have
deeper educational problems, but calculators are interesting because they
pose a concrete policy choice. We could kick them out tomorrow if we wanted
to; the cost would be zero, and the education establishment couldn't stop
us if we'd made up our minds. We won't do it, but we ought to. The
practical gain would be large, the symbolic value even greater.

If you hand a child a calculator, you must take care that it is used
judiciously or the result is catastrophic: an adult who can't do basic
arithmetic. Such a person is condemned to stumble through life's numeric
moments in a haze.

The National Council of Teachers of Mathematics has a position paper
recommending "the integration of the calculator into the school
mathematics program at all grade levels in class work, homework and
evaluation." Most schools reject this bad advice and use calculators only
occasionally: students
work some problems by hand and use calculators for the rest.

From its perch on the sidelines, the calculator subtly undermines the whole
math curriculum. (Walking to school isn't bad if you do it every day - but
if you sometimes ride, walking can start to seem like a pain.) And "once
the calculator goes on," says Mike McKeown, a geneticist at the Salk
Institute in San Diego, "the brain goes off, no matter what we hope."
McKeown is aco-founder of "Mathematically Correct," a group that lobbies
for common sense in math education.

My generation of schoolchildren mostly learned the times tables in second
grade. (Japanese children still do.) You can't proceed to long
multiplication and division, and fractions and decimals, without knowing
the times tables. But at the school my kids attend, which seems fairly
typical for Connecticut, students don't master the times tables until
fourth grade. These children burn
lots of class hours in second and third grades learning something other
than basic arithmetic; have they mastered some marvelous new kind of
mathematics? Not so you'd notice.

It appears that, mostly, they've spent the extra time learning how to mouth
off, which they were pretty good at already. Along the way they've cranked
out the occasional essay about the larger role of mathematics in society,
but they'd have more to say on this topic if they knew what mathematics

Teachers and principals who defend calculators make this argument:
Calculators are cheap, handy and accurate. To the extent we allow children
to rely on them, teachers needn't waste time on basic arithmetic - and can
proceed faster and deeper into more advanced terrain.

As most parents realize, this is complete nonsense.

If you haven't mastered basic arithmetic by hand, you can't do arithmetic
at all - with or without calculators. Calculators are reliable but people
aren't; they hit wrong keys. You can't solve a problem unless you start
with a general idea of the right answer. Otherwise you don't catch your
errors, and
you and your calculator are a menace.

But suppose you're perfect; you never hit wrong keys. Even so, if you
can't do arithmetic manually you can't do it mentally; and you will need to
do rough mental arithmetic all the time. Is there time to do this before
that? What year was he born, how long ago did that happen, when will I
arrive, how
much cash will that leave me, what do I tip, is this a bargain or an
outrage? You encounter such problems shopping, strolling, driving, lying on
the beach, waiting at McDonald's, paying the cab driver - yes you could
whip out your calculator on such occasions, and you could skip learning how
to drive and simply consult the owner's manual each time you needed to make
a right turn; but is that what we want for our children?

We're told (in effect) "you can leave the easy problems to your calculator;
theadvanced stuff you'll really learn." Which is clearly upside-down.
Common sense suggests that you master the basic material and look up the
advanced stuff. Most people have no use for "mathematical concepts" anyway
- arithmetic yes, group theory no. For the others, the theory that "real
math" has
nothing to do with arithmetic is wrong - engineeers and hard scientists are
invariably intimate with numbers. They have to be. So if you don't go on in
math, basic arithmetic is crucial. Whereas if you do go on in math, basic
arithmetic is crucial.

It comes down to this: Knowledge you can "look up" is knowledge you don't
have. To be educated is to master a body of facts and skills and have them
on-call 24 hours a day, as you talk and walk and read and work and garden
and scheme and think. You can't master everything, but after many
centuries of mulling we are agreed on a time-tested basic agenda - reading
and writing and history; basic arithmetic.

Our education establishment is deeply confused. Recently, Carol Innerst of
the Washington Times investigated teacher training in today's ed schools;
teachers-to-be, she discovered, are taught how to "think like children."
Back in real life, adults don't need to think like children; children need
to think like adults. That's what education is for.

The yawning chasm between ed-school doctrine and common sense has already
swallowed up (to our national shame) a whole generation of American kids.
Big reforms are needed, but the electronic calculator perfectly captures
what the struggle is about. When you hand children an automatic,
know-it-all crib sheet, you undermine learning - obviously. So let's get
rid of the damned things.
Professional educators are leading us full-speed towards a world of smart
machines and stupid people.
David Gelernter, professor of computer science at Yale University and
author of "Drawing Life," among other books, is The Post's new Thursday
columnist. Look for his commentary every week in this space.

I'm in complete agreement.

My basic position, stated approximately 3 zillion times (a number not
accessible even on the most powerful calculator) is that students should be
given calculator licenses the same way that we give driver's licenses.
Only students demonstrably competent in arithmetic should be allowed to
have them.

Yes, I know this is unrealistic, but the idea of producing smart
machines and stupid people is abhorrent to me, too.


Instead of licenses, we need to have "smart calculators" that will only
answer difficult questions for students. If a student asks something
they should be able to do by hand or in their mind (in reasonable time)
the calculator should refuse -- e.g.,

5 + 13 = REFUSE
cos(77) = 0.22495
sin(5) = 0.08715
tan(45) = REFUSE
log(1) = REFUSE
sq.root (88) = 9.3808
sq.root (400) = REFUSE
10! = 3628800

All we need is an algorithm for estimating human computation time.



I doubled over with laughter and am telling everyone at _____ about it.

You should (seriously) write an op-ed type article on this; it is
INCREDIBLY funny, worthy of publication, and could make you rich and famous.


Long ago at some meeting, ________ suggested calculators 'without'
decimal point display...

(Who will contact the manufacturers? )


Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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