For anyone who hated math in school, didn't get geometry or grumbled, "What's the point of a quadratic equation?" James Koutsos's sixth-grade math class is a revelation. On a recent day, after organizing pairs of students to play a tick-tack-toe-like game about prime numbers and leading a spirited class activity on Venn diagrams using popular radio stations, he asked his students what they thought.

A forest of hands shot up. "Oooooh. Oooooh. Pick me!"

"The game helped me learn to multiply and divide," said a boy named Jason.

"It was hard to win," said a boy named Darin, draped in baggy jeans and a skull T-shirt. "It's just fun to do."

Fun? Math?

Koutsos and his class at Montgomery County's Col. E. Brooke Lee Middle School are part of an experiment. Lee is one of five county schools testing a new way of teaching math. What is going on in Koutsos's classroom is at the heart of a passionate, often vitriolic debate that has shot through school districts nationwide and has now reached Montgomery.

The program is called Connected Math. It aims to have students actually understand math and how it is used. To understand, for example, that a quadratic equation helps demographers project population trends and Red Cross relief workers estimate how many tents they'll need for a refugee camp.

To do that, Connected Math breaks loose of the drill-and-kill way math has been taught for ages. It attempts to engage all students, not just the 15 percent who always have done well, by relating math to the world they live in. Thus, percentages are taught with story problems about restaurant tips and the sales tax on CDs. Fractions, ratios and perimeters are taught within the context of movie tickets, brownies and bad cat breath.

Students play games, write in math journals and often work together in small groups. They no longer sit in neat rows, all facing the blackboard, as the teacher lectures, scratching out the answers to one problem after another.

"An abomination!" said critic Wayne Bishop, a math professor at California State University. "Utter trash!" said Richard Askey, a prominent mathematician at the University of Wisconsin. It's MTV math. Placebo math. Mickey Mouse math.

Critics' biggest beef is that in the rush to imbue "deep conceptual understanding," Connected Math skips over the computing skills students need.

John Hoven, head of a group of parents of gifted and talented children leading the charge against Connected Math in Montgomery County, calls it "fuzzy math." "The students may be having a good time," he said. "But they're not learning anything."

On the surface, the war of words rages over the value of learning long division; the fact that while there is still one right answer, Connected Math allows for several ways to get there; and whether students learn best when the teacher lectures or students are left to discover answers on their own.

But the debate has near-religious undertones, which focus on fundamental and unresolved questions like: What is math? How do you teach it? And who gets to learn it?

To complicate matters, there is little solid, objective evidence -- state scores, SAT scores -- toward proving that either camp is right because the approach is so new.

"There are people who fervently believe math consists of computational skills and the way you do it is, someone shows you, then you practice, practice, practice," said Bill Jacob, a mathematician at the University of California at Santa Barbara. "Connected Math forces students to make sense of problems, to think. These are two very different views of the world. That's why there's such passion."

And heavy hitters choosing sides.

The U.S. Department of Education last week declared Connected Math one of five "exemplary" math programs. The American Association for the Advancement of Science rated it number one. The president of the National Council of Teachers of Mathematics helped write it, and the National Science Foundation backs it financially.

But it also was rejected by California for failing to meet the state's rigorous new back-to-basics standards. Mathematically Correct, a parents group with a commanding presence on the Internet, gave it an F. And 600 parents in Texas are suing their school district for giving students no other choice.

Passions are running so high in Montgomery that the new superintendent, Jerry Weast, created an expert panel to mediate.

At a meeting of the group for parents of gifted and talented children one evening, Ray Russo, who has a doctorate in math, became agitated as he explained that Connected Math, to him, isn't math, it's math appreciation. "Math is symbolic abstraction and formal proof. It means you don't have to fool with objects," he said. "It makes my eyes light up."

But Nancy Metz, the county's math coordinator, who also taught math and was a mathematician in the aerospace industry, feels just as deeply. "If we are censored from trying this, and I fear that's what's going to happen," she said, tears brimming, "I will regret it as long as I live."

Ironically, both camps are motivated by a fundamental concern: that U.S. students perform abysmally on national and international math tests. In the latest international math comparison, high school seniors scored above their peers in only Cyprus and South Africa. And both sides agree that middle school math has, for years, been a wasteland. Students are able to compute or memorize formulas. But when faced with solving a story problem, they freeze. Many have no idea how to use what they know.

"We've had the longest-running experiment in human history about whether rote memorization of math facts and skills works. And it doesn't. Students are coming to universities and into the workplace not understanding math," said Glenda Lappan, president of the National Council of Teachers of Mathematics and one of the authors of Connected Math. "Why wouldn't I want to try something new?"

In Montgomery, 75 percent of seventh-graders passed the math part of the 1999 Maryland functional test, while 94 percent passed the reading test. Black and Hispanic students' reading scores lagged 10 percentage points behind their white and Asian counterparts; the gap yawned to 30 or more points in math.

"If anything, the math score should be equal to or better than the reading score in most places, because of language problems and the immigrants who have the tools to solve math problems but don't have the language," Weast said. "I don't think there's any doubt we want progress in the math program. There's no doubt we need teacher training to do that."

A teacher training grant is what sparked the controversy here. Patricia Flynn, director of academic programs for Montgomery schools, and other administrators applied for a \$6 million grant from the National Science Foundation to help get more middle school teachers into college math classes and certified as math teachers. In Montgomery, 57 percent of the middle school math teachers lack secondary math certification, and 20 percent have not satisfied Board of Education college math requirements.

But Hoven and others protested that the grant would only train teachers the new way, which they say is aimed at low-performing students who don't get math at the expense of their children, who do.

Across the country, it is largely the parents of gifted children who are fighting Connected Math and similar programs. They fear two things: that forcing their bright children to work in groups with others will hold them back and that relating math to the world they live in won't boost their college-entrance SAT scores.

"The hidden secret of Connected Math is that some gifted students don't perform as well, and their parents become enraged," said Lynn Raith, mathematics curriculum specialist in the Pittsburgh school district, one of the first to test the program. "They were good at memorizing and moving numbers around, but if you asked them to explain something, they couldn't. Now, they have to think. But the truth is, once you win the kids over, you win the parents over."

That didn't happen in the case of Cathy Berninger, a Montgomery parent of a gifted child who lived in a San Diego district using a similar approach. "We recognized very soon that our seventh-grade daughter was rapidly losing interest in her honors math class," Berninger said. "We basically had to hire a tutor for her."

With fears so basic and convictions so strong, Weast's expert panel is unlikely to end the war in Montgomery.

On Friday, the panel, which included a Nobel laureate, issued a short report, saying, in essence, that the county didn't treat the objecting parents very well but that the current math curriculum needs improvement and the critiques of Connected Math aren't convincing enough to keep it from classrooms.

Within hours, Hoven shot down the report.

Against this swirling backdrop, Steven L. Bedford, principal at Lee Middle School, has one simple goal, which sounds just like Hoven's: to use challenging programs like those used in Singapore and Japan to get more students into Algebra I by eighth grade. And to give them the foundation to do well on the SAT.

"Connected Math is just one more tool to get there. It's only a pilot. If it doesn't work, we'll try something else," Bedford said. "If what we're doing works for a small part of the population, let's keep doing that right. But if it's not working for everyone else, and it's not, let's not keep doing something that hasn't worked for 20 years."

In James Koutsos's sixth-grade class, over lunches of barbecued chicken, blue Gatorade and goldfish crackers, four 11-year-old students recalled once hating math.

"I just used to stare at my work. I was confused," said Candy Rosel. "The teacher would give an example, and I still didn't understand."

Now they write in their math journals about the "special numbers" they've picked, like 40, for a mother's age, and 18, for when they can leave home, and 24, because it's how many hours are in a day. They diligently list the factors and some multiples of each.

"This is good. It helps you learn in a fun way," said Chelsea Vogel. "Last year, we'd just sit in class and just talk about math. It was so boring."

They listen to the teacher, Koutsos, then work in pairs. Then he summarizes what they've learned. The class likes that.

"It kind of feels good when you're helping someone out," said Shayla Hines, who for the first time is thinking about becoming a teacher, a math teacher, even. "It helps me know more, too."

New Math

Below are sample math problems that are being used as part of the Connected Math program for sixth-graders. The program is designed to make math more fun and accessible to students and is being piloted in Argyle, Col. E. Brooke Lee, Shady Grove, Silver Spring International and Sligo middle schools.

Problem 1

At Loud Music Warehouse, CDs are regularly priced at \$9.95 and tapes are regularly priced at \$6.95. Every day this month, the store is offering a 10 percent discount on all CDs and tapes.

Joshua and Jeremy go to Loud Music to buy a tape and a CD. They do not have much money, so they have pooled their funds. When they get to the store, they find that there is another discount plan available just for that day -- if they buy three or more items, they can save 20 percent (instead of 10 percent) on each item.

A. If they buy a CD and a tape, how much money will they spend after the store adds a 6 percent sales tax on the discounted prices?

B. Jeremy says he thinks he can buy three tapes for less money than the cost of a tape and a CD. Is he correct? Explain your reasoning.

A. They will spend \$16.12. The solution involes several steps:

Step 1: Find the total cost before the discount: \$9.95 + \$6.95= \$16.90

Step 2: Compute the 10 percent discount: 0.1 x \$16.90= \$1.69

Step 3: Calculate the discounted price: \$16.90- \$1.69=\$15.21

Step 4: Compute the tax: 6% x \$15.21= \$0.9126, which rounds to \$0.91

Step 5: Compute the total cost including tax: \$15.21 +\$0.91= \$16.12

B. Jeremy is incorrect.

Step 1: Compute the cost of three tapes: 3 x \$6.95=\$20.85

Step 2: Compute the 20 percent discount: \$20.85 x 0.2=

\$4.17 and \$20.85 - \$4.17= \$16.68

Step 3: Compute the tax: 6% x \$16.68= \$1.00

Step 4: Total cost is \$17.68. This is more than the \$16.12 for a CD and a tape.

Problem 2

Element Portion of Earth's crust

Oxygen 0.4660

Iron 0.0500

Silicon 0.2772

Aluminum 0.0813

Sodium 0.0283

Calcium 0.0363

Potassium 0.0259

Magnesium 0.0209

A. Order the elements in the earth's crust from most abundant to least abundant.

B. Estimate how much of the earth's crust is made up of the three most abundant elements.

C. About what percent of the crust is made up of the three least abundant elements listed in the table?