From the Washington Post, Tuesday, December 21, 2004; Page A10. See
Math Educators Find Common Denominators
By 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
"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
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
* 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,
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 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
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.
A RESPONSE FROM MICHAEL PAUL GOLDENBERG ... Submitted letter to the
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
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 -- email@example.com