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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Posted: May 22, 1998 11:27 AM
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New York Post, Thursday, May 21, 1998

[Note: David Gelernter is a professor of computer science at Yale
University and author
of "Drawing Life," among other books. He is The Post's new Thursday columnist.
Look for his commentary every week in this space. ]



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 a
co-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 was.

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;
the advanced 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

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.
Copyright (c) 1998, N.Y.P. Holdings, Inc. All rights reserved.
Topic No. 11

Date: Fri, 22 May 1998 06:53:03 -0700
From: (Ruth Parker)
Subject: Re: K-16: Yale Prof on Calculators and Ed Profs (fwd)
Message-ID: <v01540b00b18b309d028a@[]>

In his New York Post diatribe against mathematics education, Dr. Gelernter
states, "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... We're told (in
effect) 'you
can leave the easy problems to your calculator; the advanced stuff you'll
really learn.'"

I would like to know Dr. Gelernter's sources. I know of no mathematics
educator who would make such a claim. It is certainly not a position that
I've ever heard from the National Council of Teachers of Mathematics
(NCTM). If he's going to be a regular columnist who comments on education,
I hope Dr. Gelernter will soon do his homework. If he looks at any of the
elementary mathematics programs recently developed to support NCTM-based
reform efforts, he will clearly see that work with number facts still plays
a predominant role at the primary level. To suggest otherwise is simply
irresponsible. Many mathematics educators, who have thought deeply about
this issue, would agree that the ready availability of calculators and
computers makes number sense and facility with numbers (large and small)
even more important, not less so.

As for having memorized his multiplication facts in the 2nd grade, I'm
curious to know when and where Dr. Gelernter went to school. I clearly
remember memorizing my multiplication facts. Mrs. LeMaster taught them to
me and she was my 4th grade teacher. And I'm to old to have experienced
the 1960's "new math" movement.

I hope Dr. Gelernter will read the National Council of Supervisors of
Mathematics' latest monograph titled "Future Basics: Developing Numerical
Power." It is a far more accurate representation of the position taken by
many within the mathematics education community than are many of Dr.
Gelernter's inflammatory accusations. I'm sure he can locate the document
at NCSM's web site:

Ruth Parker

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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