LEBANON -- Lori Haley and Mya Corbett hunch over a pile of yellow hexagons, trying to figure out how many hexagonal tables it would take to seat 25 guests.

The pair want to get the answer, but what they're really itching to do is to come up with a formula that will tell them how many people they could seat for any given number of tables.Suddenly, the girls detect a pattern, and one shouts: "(t x 4) + 2 = s!" They try it on one table, two tables, eight tables -- it works.

They beam, flashing smiles that still feature baby teeth. Lori and Mya just started third grade.

While most high schools in Oregon and across the nation struggle to get freshmen to pass algebra, one school district is trying something very different.

Are you smarter than a fifth-grader? Click on the graphic

Lebanon, which educates 4,000 students in eight schools, is pushing algebra on students as early as first grade. And the kids are getting it.

More than 80 percent of Lebanon eighth-graders passed the state math test, compared with 66 percent at schools with similar demographics. No other large or medium-size Oregon district outdid its peers by 15 percentage points.

Still, Lebanon leaders say they expect better results this school year and next, as more teachers adopt early algebra and pupils who've been solving for x since primary school advance into higher grades and take state tests.

They also acknowledge that their successes in elementary and middle schools are not matched at Lebanon High, which posts some of the worst math scores in Oregon. Math coach Joe Vore and others say they expect that will turn around as students who got a solid grounding in math during the early grades reach high school and as district efforts to improve math teaching shift to the high school.

No flash cards

Visit a Lebanon elementary math class, and you will see:

First-graders set up and solve formulas such as 9 - x = 5, as they did when Raylene Sell talked with her class about "some teddy bears" walking away from the classroom rug, leaving five behind.

Third-graders suggest mathematically complex ways to arrive at 9: -219 + 228 or (10 x 5) - 40 - 1, or even (3 x 3) + (8 x 8) - ((4 x 4) + (4 x 4)) - 32.

Students don't do worksheets, use flash cards or memorize multiplication tables. Yet by third and fourth grade, most of them add, subtract and multiply quickly and accurately.

Fifth-graders grasp how small one-thousandth is compared with one-tenth, as is reflected on a typical gas meter -- a magnitude of difference that many adults get wrong. And the kids actually seem to like the stuff. When student Dakota Rose closed his folder after the gas meter lesson, he said to no one in particular: "I wish we could do more. That was fun. I liked the dials."

Lebanon officials are loathe to proclaim their program perfect, noting that math instruction is evolving, that some teachers still use traditional methods and that the biggest payoffs are yet to come.

But they say they are confident that their new approach to teaching math is the way to go.

Among the key elements: Begin simple algebra and multiplication by first grade; have every child talk extensively about his or her mathematical reasoning; let students set up their own problems and equations and allow them to use big numbers if they choose; cover few topics in great depth; use lots of visual and hands-on modeling to make math ideas concrete.

"Something happens when they play with numbers every day -- numbers they come up with themselves, equations they write themselves," says Marla Ernst, a teacher who also coaches fellow teachers. She is largely responsible for finding the approach and spreading it districtwide. "They get an innate sense of what is seven, what is a fraction."

Smarter than you think

The Northwest Regional Education Laboratory, a Portland-based research and training agency, helped train more than 60 Lebanon teachers in the new math approach.

It is based largely on a teacher training technique called Cognitively Guided Instruction, or CGI, developed by education researchers at the University of Wisconsin at Madison.

Among the core ideas, according to CGI co-developer Thomas Carpenter:

Young children know more about math than most adults think they do. Ask kids to talk a lot about their mathematical reasoning and then add to what they already know. In Lebanon, teachers strive not to say "That was the wrong answer." They lean toward, "Can you tell me about your thinking?"

Lebanon schools shine in math

Percent of students who met state math benchmarks in 2008:

Lebanon:

• Grade 3: 77

• Grade 5: 86

• Grade 8: 82

Similar schools*:

• Grade 3: 77

• Grade 5: 78

• Grade 8: 66

State average:

• Grade 3: 77

• Grade 5: 77

• Grade 8: 69

* Schools similar to Lebanon, where about half the students qualify for federally subsidized meals based on low family income.

-- Source: Analysis by The Oregonian of Oregon Department of Education figures

Kindergartners intuitively know how to add -- "you can have two more cookies" -- and subtract -- "put three of those toys away." They can create and solve much more interesting problems than 2 + 2 from their first weeks of school. Children should also be asked to multiply and divide (without necessarily using those terms or the division sign) by first grade.

Perhaps more than anything else: Don't mislead kids, as most schools do, about the meaning of the equal sign.

Part of what converts teachers to the new approach is watching videos in which typical U.S. schoolchildren as old as third and fourth grade invariably give the wrong answer to this simple question: 8 + 4 = _ + 5. Most answer "12," because they have mistakenly learned that the equals sign means "give me the answer to the problem so far" rather than "make things equal on both sides of me."

Which is why Sell's first-graders are encouraged to think about problems in which the unknown -- the classic x of algebra, often discussed in Lebanon as "some" teddy bears or "some" cookies -- comes at the beginning or middle of the problem, not just at the end.

Other tools in the Lebanon math toolbox include lots of visual modeling of math ideas. Plastic blocks represent hundreds, tens and ones; kid-sized balances show ways make both sides equal to balance the scale; number lines make it easy to see that 3/4 and 0.75 mean the same thing.

Lebanon's approach is in line with recent national reports about what's wrong with U.S. math classes and how to fix them.

The Center for Data-Driven Reform in Education at Johns Hopkins University reported this month that getting teachers to change their daily teaching practices does more to raise math achievement than buying new textbooks or computerized math programs.

And the National Math Panel, appointed by the president to find research-backed ways to improve math skills, concluded that the reason so many high school students fail first-year algebra isn't poor teaching in high school; rather, it's that they got through elementary and middle school without grasping the basics, including fractions, percentages and decimals.

In primary classrooms in Lebanon, students deftly use number lines, work with negative numbers and solve basic algebraic equations. Few students sit stumped on the sidelines.

The day that (2 x 19) - 16 was one of the warmup equations in Beth Moore's third-grade classroom, every hand went up when she asked how they'd solved 2 times 19 in their heads so quickly.

Says 9-year-old Casey McEuen : "Sometimes the problems can be very hard and difficult, but we can figure it out."

-- Betsy Hammond; betsyhammond@news.oregonian.com