It's a Wednesday morning, and Zenaida Tan is warming her students up with a little exercise in "Monster Math."

That's Tan's name for math problems with monstrously big numbers. While most third-graders are learning to multiply two digits by two digits, Tan makes her class practice with 10 digits by two -- just to show them it's not so different.

On this spring day, her students pick apart the problem on the board -- 7,850,437,826 x 56 -- with the enthusiasm of game show contestants, shouting out answers before Tan can ask a question. When she accidentally blocks their view, several stand up with their notebooks and walk across the room to get a better look.

The answer comes minutes later in a singsong unison: "Four hundred and thirty-nine billion, six hundred and twenty-four million...."

Congratulations, Tan tells them, for solving it con ganas. That's Spanish for "with gusto," a phrase she picked up from watching "Stand and Deliver," a favorite film of hers about the late Jaime Escalante, the remarkably successful math teacher at Garfield High School in East Los Angeles.

The Los Angeles Unified School District has hundreds of Jaime Escalantes -- teachers who preside over remarkable successes, year after year, often against incredible odds, according to a Times analysis. But nobody is making a film about them.

Most are like Zenaida Tan, working in obscurity. No one asks them their secrets. Most of the time, no one even says, "Good job." Often even their own colleagues and principals don't know who they are.

As part of an effort to shed light on the work of L.A. teachers, The Times on Sunday is releasing a database of roughly 6,000 third- through fifth-grade teachers, ranked by their effectiveness in raising students' scores on standardized tests of math and English over a seven-year period.

The findings are based on an approach called value-added analysis, which is designed to allow fair comparisons of teachers whose students have widely varying backgrounds. Although controversial, the method increasingly has been adopted across the nation to measure the progress students make under different instructors.

L.A. Unified has had the underlying data for years but has chosen not to analyze it in this way, partly in anticipation of union opposition. After The Times' initial report this month showed wide disparities among elementary school teachers, even in the same schools, the district moved to use value-added analysis to guide teacher training and began discussions with the teachers union about incorporating data on student progress into teacher evaluations.

The results of The Times' analysis are not a complete measure of a teacher by any means, but they offer one way to see whether an instructor is helping -- or hindering -- children in grasping what the state says they should know.

The Times found that the 100 most effective teachers were scattered across the city, from Pacoima to Gardena, Woodland Hills to Bell. They varied widely in race, age, years of experience and education level. They taught students who were wealthy and poor, gifted and struggling.

In visits to several of their classrooms, reporters found their teaching styles and personalities to differ significantly. They were quiet and animated, smiling and stern. Some stuck to the basics, while others veered far from the district's often-rigid curriculum. Those interviewed said repeatedly that being effective at raising students' performance does not mean simply "teaching to the test," as critics of value-added analysis say they fear.

What's clear from the data is that these teachers have an immediate and profound effect on how much children learn. On average, their students leapt 12 percentile points on tests of English, from the 58th to the 70th. In math, the gains were more stark: a 17 percentile point jump, from 58th to 75th. All in a single year.

The idea of publicly rating teachers by name has generated enormous controversy among educators and experts across the country. The debate has focused on whether the method is sound and the publicity is fair to those with low rankings.

Often lost in that discussion are the benefits of singling out those who consistently succeed.

U.S. Education Secretary Arne Duncan said as much in a speech last week, denouncing a culture in public education that has long been averse to talking about success stories.

"The fact is, rather than shining a light on effective teachers, our education system hides them," he said.

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