[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. http://www.nypostonline.com/commentary/2735.htm ]
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 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 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. ************* Copyright (c) 1998, N.Y.P. Holdings, Inc. All rights reserved. ************************************************************ ************************************************************ Topic No. 11
Date: Fri, 22 May 1998 06:53:03 -0700 From: email@example.com (Ruth Parker) To: firstname.lastname@example.org Subject: Re: K-16: Yale Prof on Calculators and Ed Profs (fwd) Message-ID: <email@example.com>
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: forum.swarthmore.edu/mcsm.