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Calculators in Teaching Mathematics  David Galernter
Posted:
Sep 29, 1998 7:39 PM


[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.]
Subject: NEW YORK POST: COMMENTARY STORY
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.
************************************************************* http://www.nypostonline.com/com mentary/2735.htm
COMMENTARY
PUT DOWN THAT CALCULATOR, STUPID!
By DAVID GELERNTER
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 acofounder 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; theadvanced stuff you'll really learn." Which is clearly upsidedown. 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 oncall 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 timetested 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; teacherstobe, 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 edschool 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, knowitall crib sheet, you undermine learning  obviously. So let's get rid of the damned things. Professional educators are leading us fullspeed 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.
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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 3! = REFUSE 10! = 3628800
All we need is an algorithm for estimating human computation time.
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THIS IS THE SINGLE GREATEST IDEA I HAVE EVER SEEN IN THIS AREA!
I doubled over with laughter and am telling everyone at _____ about it.
You should (seriously) write an oped type article on this; it is INCREDIBLY funny, worthy of publication, and could make you rich and famous.
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Long ago at some meeting, ________ suggested calculators 'without' decimal point display...
(Who will contact the manufacturers? )
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Jerry P. Becker Dept. of Curriculum & Instruction Southern Illinois University Carbondale, IL 629014610 USA Fax: (618)4534244 Phone: (618)4534241 (office) Email: JBECKER@SIU.EDU



