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.