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From the Washington Post, Tuesday, December 21, 2004; Page A10. See

https://www.washingtonpost.com/wp-dyn/articles/A15026-2004Dec20.html

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Math Educators Find Common DenominatorsBy Valerie Strauss

Confused by the latest "good news-bad news" headlines about how U.S.

students compare in math with their peers in foreign lands? Wondering

whether the math program at your child's school is teaching addition

better than another program might?

You aren't alone. Many parents are asking these questions and finding

that, when it comes to math, the educational landscape in the United

States can be maddeningly complicated.

Math programs that give students different ways to answer basic

problems are beloved by some teachers, while others scoff and label

the programs "fuzzy math." Research reports are issued, then debunked

by critics. And the long-running "math wars," pitting traditionalists

against reformers, are at high pitch.

Any large-scale meeting of the minds about the best way to teach the

subject, educators and mathematicians say, is nowhere near -- in

part, because the country is so large and education decisions are

locally driven.

"We have 50 states with 15,000 separate independent school

districts," said Gerald Kulm, a math professor and researcher at

Texas A&M University. "Our textbooks and other curriculum materials

have to suit at least some majority of the people in those districts,

and so things get complicated."

This month's release of international comparisons of math performance

highlighted the confusion. One study showed that U.S. eighth-graders

made significant gains compared with their counterparts worldwide,

climbing several places -- to 15th out of 45 countries -- since the

international math rankings came out nine years ago.

Yet another recent study suggested the opposite of progress -- that

15-year-olds in the United States lag behind their peers in most

other leading industrialized nations in the ability to solve

real-life math problems.

Some mathematicians and educators even disagree on whether

international comparisons are valid. R. James Milgram, a Stanford

University mathematician, said yes; Jeremy Kilpatrick, a University

of Georgia professor, said different cultures and educational systems

skew the results.

There may be some room for hope of a truce in the math wars,

according to Milgram and Kilpatrick, both of whom attended a "peace

summit" designed to see whether common ground could be found.

Richard J. Schaar, a mathematician and senior vice president of Texas

Instruments Inc., wooed the two scholars, plus three other figures in

math education, to Washington early this month. Also attending was

Harvard University Professor Wilfried Schmid, who, like Milgram,

criticizes "reform" math programs for failing to teaching children

the fundamentals.

Kilpatrick and two other leading math educators at the gathering, the

University of Michigan's Deborah Loewenberg Ball and Joan

Ferrini-Mundy of Michigan State University, hold the view that the

reforms are helping students better understand math because they do

not rely on memorizing correct answers.

To the surprise of all, there was more agreement than they had

imagined, several participants said, suggesting that they may be

moving toward a "centrist position." Among the topics they said they

agreed on:

* Heavy reliance on calculators in the early elementary grades is a bad idea.

* Elementary school children must have automatic recall of number

facts, meaning that, yes, they have to memorize multiplication tables.

* Children must master basic algorithms. The meeting participants

spent time defining the word "algorithm," which means a set of rules

for solving a problem in a finite number of steps.

Schmid called it "significant that we do have agreement in this group

. . . To me, it is an indication that we are moving toward peace in

the math wars."

Participants said parents can take these areas of agreement and look

for them in their children's math programs. The group plans to

continue meeting and to issue a report with math education goals,

Schaar said.

The fact that their discussion centered on such basic understandings

revealed how hardened the sides had become.

Controversy over a National Science Foundation-funded program,

Everyday Mathematics, developed at the University of Chicago, tells

the tale.

The program is being used in many schools across the country,

including Annandale Terrace Elementary School. On a recent day at the

Northern Virginia school, teacher Abigale Braun presented this

problem for 21 second-graders to solve: 15+5+9=__. Then she asked

them how they got their answers.

Dennis Segovia-Ramirez said he put 15 plus 5 together to make 20 and

then added 9. Sarah Velegaleti said she knew 5+9 was 14 and just

added 15. Laila Elahi put down 15 tally marks on her white board,

then 5, then 9, and added them all up.

Braun praised them, telling them that there was no single correct

method and that it was important for them to figure out the way that

worked best for them. She said that in computational skills, her

second-graders are far ahead of students using other math programs.

Her school's principal, Christina Dickens, said the University of

Chicago program helped children improve on standardized tests.

At the opposite end of the country, however, Milgram and other math

educators have persuaded the California legislature not to allow

school systems to use the University of Chicago program without a

special waiver.

The critics believe that it does not teach basic math rules and leads

to computational incompetence. They prefer more traditional

approaches such as Harcourt Achieve's Saxon math program.

In an effort to help bring clarity to the math wars, the Mathematical

Sciences Education Board of the National Academy of Sciences reviewed

147 studies done on the effectiveness of 19 math programs used in

schools today. The conclusion, released this summer: Not one study

had been carried out well enough to prove a program's effectiveness.

"Don't believe a thing said to you associated with the phrase

'research shows,' " said W. Stephen Wilson, a Johns Hopkins

University mathematics professor.

There are programs successful in some schools, but there isn't a

single best one, according to experts, who emphasize it often comes

down to teachers: how well they understand math and how much they

have been taught about the program their school is using.

"All the program can do in the best case is be correct, efficient and

accessible. Then it is up to the teacher," Schmid said.

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A RESPONSE FROM MICHAEL PAUL GOLDENBERG ... Submitted letter to the

Post Editor.

As a mathematics educator, I read with puzzlement Valerie Strauss'

piece suggesting that there is peace on the horizon in the Math Wars:

one need not read between the lines here if one knows the subject,

its recent history and the players.

For those not so informed, please don't be fooled. Note well that the

agreed-upon positions cited all appear to be compromises/concessions

from the reform end (not that Professors Kilpatrcik, Ball,

Ferrini-Mundy or NCTM itself ever advocated for HEAVY calculator use

in early elementary, or against knowing algorithms or knowing number

facts).

Note, too, the utter lack of anything that vaguely looks like a

concession or compromise from Professors Milgram or Schmid. Zip.

Nothing. Nada. Instead, we get more criticism of progressive

mathematics teaching methods and texts, and advocacy for so-called

"teacher-proof" materials like Saxon math, possibly the textbook

series least representative of what mathematicians themselves

actually do and think about. The real goal of the anti-reformers

couldn't be more clear: banning creative programs like Everyday Math

at any cost, as they've already been able to do in California.

Why is what emerged from this "summit" a Roadmap For Peace? If it

really represented the current position of NCTM, it would be a

document of surrender. If this is a peace plan, I'll take another

half century of war, thank you very much. As will, in fact, the

entrenched foes of progressive reform until they wipe out any and all

creativity and vitality in mathematics classrooms for the vast, vast

majority of American kids.

Michael Paul Goldenberg -- mikegold@umich.edu

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