Date: May 4, 2000 11:27 AM Author: Anne Wheelock Subject: Op-Ed by W.Schmid in Harvard Crimson FYI -

This op-ed may be of interest. It's posted at

http://www.thecrimson.harvard.edu/opinion/article.asp?ref=7818

Published on Thursday, May 04, 2000

New Battles in the Math

Wars

By WILFRIED SCHMID

What is 256 times 98? Can you do the multiplication

without using a calculator? Two thirds of Massachusetts

fourth-graders could not when they were asked this

question on the statewide MCAS assessment test last year.

Math education reformers have a prescription for raising

the mathematical knowledge of schoolchildren. Do not

teach the standard algorithms of arithmetic, such as long

addition and multiplication, they say; let the children find

their own methods for adding and multiplying two-digit

numbers, and for larger numbers, let them use calculators.

One determined reformer puts it decisively: "It's time to

acknowledge that continuing to teach these skills (i.e.,

pencil-and-paper computational algorithms) to our

students is not only unnecessary, but counterproductive

and downright dangerous."

Mathematicians are perplexed, and the proverbial man on

the street, when hearing the argument, appears to be

perplexed as well: improve mathematical literacy by

downgrading computational skills?

Yes, precisely, say the reformers. The old ways of teaching

mathematics have failed. Too many children are scared of

mathematics for life. Let's teach them mathematical

thinking, not routine skills. Understanding is the key, not

computations.

Mathematicians are not convinced. By all means, liven up

the textbooks, make the subject engaging and include

interesting problems. But don't give up on basic skills!

Conceptual understanding can and must coexist with

computational facility--we do not need to choose between

them.

The disagreement extends over the entire mathematics

curriculum, kindergarten through high school. It runs right

through the National Council of Teachers of Mathematics

(NCTM), the professional organization of mathematics

teachers. The new NCTM curriculum guidelines,

presented with great fanfare on April 12, represent an

earnest effort at finding common ground, but barely

manage to paper-over the differences.

Among teachers and mathematics educators, the

avant-garde reformers are the most energetic, and their

voices drown out those skeptical of extreme reforms. On

the other side, among academic mathematicians and

scientists who have reflected on these questions, a clear

majority oppose the new trends in math education. The

academics, mostly unfamiliar with education issues, have

been reluctant to join the debate. But finally, some of them

are speaking up.

Parents, for the most part, have also been silent, trusting

the experts--the teachers' organizations and math

educators. Several reform curricula do not provide

textbooks in the usual sense, and this deprives parents of

one important source of information. Yet, also among

parents, attitudes may be changing. A recent front-page

headline in the New York Times declares that "The New,

Flexible Math Meets Parental Rebellion."

The stakes are high in this argument. State curriculum

frameworks need to be written, and these serve as basis for

assessment tests; some of the reformers receive substantial

educational research grants, consulting fees or textbook

royalties. For now, the reformers have lost the battle in

California. They are redoubling their efforts in

Massachusetts, where the curriculum framework is being

revised. The struggle is fierce, by academic standards.

Both sides cite statistical studies and anecdotal evidence

to

support their case. Unfortunately, statistical studies in

education are notoriously unreliable--blind studies, for

example, are difficult to construct. And for every

charismatic teacher who succeeds with a "progressive"

approach in the classroom, there are other teachers who

manage to raise test scores dramatically by "going back to

basics."

The current fight echoes an earlier argument, over the

"New Math" of the '60s and '70s. Then, as now, the old

ways were thought to have failed. A small band of

mathematicians proposed shifting the emphasis towards a

deeper understanding of mathematical concepts, though on

a much more abstract level than today's reformers. Math

educators took up the cause, but over time, most

mathematicians and parents became unhappy with the

results. What had gone wrong? Preoccupied with

"understanding," the "New Math" reformers had neglected

computational skills. Mathematical understanding, it

turned out, did not develop well without sufficient

computational practice. Understanding and skills grow

best in tandem, each supporting the other. In most areas of

human endeavor, mastery cannot be attained without

technique. Why should mathematics be different?

American schoolchildren rank near the bottom in

international comparisons of mathematical knowledge.

Our reformers see this as an argument for their ideas. But

look at Singapore, the undisputed leader in these

comparisons: their math textbooks try hard to engage the

students and to stimulate their interest. In early grades,

they present mathematical problems playfully, often in the

guise of puzzles. Yet the textbooks are coherent,

systematic, efficient, and cover all the basics--worlds

apart from the reform curricula in this country. How I

wish Singapore's approach were adopted in my daughter's

school!

The curriculum, of course, is not the only reason for

Singapore's success, nor is it even the most important

reason. The teachers' grasp and feeling for mathematics:

that is the crucial issue, already for teachers in the early

grades. Here, it turns out, many of the reformers agree

with the critics. Teacher training in America has

traditionally and grossly stressed pedagogy over content.

The implicit message to the teachers is: If you know how

to teach, you can teach anything! It will take a heroic

effort--by mathematicians and math educators--to change

the entrenched culture of teacher training.

Mathematicians do not want to invade the educators' turf.

We are not qualified to do their work. Yet we are

qualified as critics of reforms in math education. We

should call attention to reforms we see as well meaning,

but hectic and harmful. Most music critics would not do

well as orchestra musicians. They do have acute hearing

for shrill sounds from the orchestra.

Wilfried Schmid is Dwight Parker Robinson Professor of

Mathematics. Earlier this year, he served as a

mathematics advisor to the Massachusetts Department of

Education.