Last month, former Los Angeles School Superintendent Roy Romer said that high school algebra "triggers dropouts more than any single subject. I think it is a cumulative failure of our ability to teach math adequately in the public school system."

Mr. Romer, former governor of Colorado, headed a massive school system that in 2003 required students to pass a year of algebra to graduate. The following year, 44 percent of the 48,000 ninth-graders taking algebra flunked it, and 17 percent had D's.

It is that kind of dismal performance that Steve Ritter is dedicated to overcoming.

Dr. Ritter is the chief scientist at Carnegie Learning Inc., a Downtown company that markets one of the leading computer-based math teaching programs in the United States. The company's a spinoff from Carnegie Mellon University.

The company's Cognitive Tutor programs in algebra, geometry and integrated math are being used by 475,000 students in 1,300 school districts across the country, and the Rand Corp. is currently testing it against traditional math classes in several school districts nationwide.

The program recommends two days of computer work a week and three days of classroom sessions.

The Cognitive Tutor's software lets students learn at their own pace, Dr. Ritter said, and can automatically change the mix of problems a student sees to help him work on the skills he is struggling with the most.

And, in an unexpected benefit, the company has found that during the computer-learning sessions, teachers interact with 91 percent of their students -- far more than they would during a regular classroom session.

"In a standard class," he said, "teachers tend to talk to the best students because they're the ones whose hands go up."

Not only are the struggling students talking to their teachers more than normal, but they are more apt to raise their hands to ask questions during the computer lab sessions. That's because "it's more acceptable for the computer to tell you you're wrong than for a human teacher to tell you you're wrong, and besides, all the questions are being asked privately," he said.

That may explain why studies have shown that the Cognitive Tutor program not only outperforms traditional algebra teaching, but also is especially effective in raising the scores of special education students.

A comparative study of the program in one Washington school district showed that Cognitive Tutor algebra students raised their test scores overall between 10 and 15 points, about three points more than students in conventional classes. And special education students using the computer-based program showed gains of almost 35 points, compared with fewer than 20 points for such students in regular classes.

When he and his colleagues were developing their curriculum, Dr. Ritter said, he didn't ignore the advice of math teaching experts, but "my doctorate is in cognitive psychology, and the main thing you learn in that field is that you don't necessarily trust experts -- you trust data."

As students worked with the software, he said, the company discovered that teaching experts had a blind spot about how children learn algebra.

"When you're an expert," he said, "you sometimes lose the intuition of what's difficult about a task.

"Think about reading. If you know how to read, it's impossible not to read. If you see an exit sign on the highway you just read it -- you don't think about how to do that. It's kind of hard to bring back your intuition about what's hard about that task.

"It's the same with mathematics. People who are doing math a lot, when they look at a linear equation, like 3x + 5 = 10, they immediately understand that language in the same way most adults read. They've lost the insight into the struggle students are going through to understand that language."

Many teaching experts thought the hardest challenge for most students was translating an algebra word problem into a formula, but that once they had written the formula, solving it would be easy, he said.

They were only partially right, he said.

It turns out that many students are pretty good at understanding a word problem well enough to try to solve it using common-sense reasoning.

What they struggle with is converting that into an algebraic formula, and then solving the formula.

"If you give students a simple word problem, like 'You make $15 an hour. How many hours would you need to work to earn $150?', they'll use common-sense math and say, '10 hours.' "

If their teacher then goes to the blackboard and says that the solution is 15x = 150, "the students say, 'That's an easy problem and I already solved it, and now you're giving me a harder way to solve it.' "

Cognitive Tutor lets students solve problems initially using a common-sense approach and introduces the algebraic formula later.

"Now, when some people hear that," he said, "they say, 'That just proves that algebra's useless because you can solve the problem without using algebra,' but we say that in fact, when problems become much more difficult, that's when there is a lot of value in translating a complex real world situation into a simpler mathematical formula that abstracts away all the complexity of the real world."

Help from a 'skillometer'

A key gimmick to build up their motivation, he said, is a set of bars on the computer screen dubbed the "skillometer." The more correct answers a student gets, and the less he needs to ask for help in solving a problem, the higher his skillometer rating is.

"It's always been a little surprising to me that that is really highly motivating," Dr. Ritter said. "You'll hear them kind of cheering in the class when they get their last gold bar and move on to the next section."

Field tests so far have shown that the Cognitive Tutor program improves test scores for African-American students as well as it does for white students, but that much of the gap in their respective test scores remains.

The initial gap goes back to poor preparation in earlier years, Dr. Ritter said.

"That's the thing that people focus on a lot, but unfortunately the only thing that means is the high school teachers blame the middle school teachers and the middle school teachers blame the elementary school teachers and the elementary school teachers blame the parents, and that doesn't solve the problem."

What can make a difference, Dr. Ritter said, is not only boosting the motivation of African-American students to learn algebra and geometry, but giving them the extra time they need to begin to catch up.

Some school districts have implemented double math periods or longer "block scheduling" classes to try to provide that extra time, he said, but ultimately, the gap may not shrink much until the less-skilled students are able to spend even more time outside of school working on their math.

For American students to improve their world standing in math, however, an even bigger cultural change will be needed, Dr. Ritter said.

One reason many Asian students excel in math, he said, is that their families simply expect it of them.

"People in the U.S. and a lot of Western countries will say, 'You know, I'm just not a math person; I don't get it.' But no one ever says that about reading.

"In Japan it's very different. In Japan, you would be just as embarrassed at a cocktail party to say I'm not a math person as you would be in the U.S. if you said, 'Well, I just never read books.' "