• Many of the factors commonly assumed to be important to teachers' effectiveness were not. Although teachers are paid more for experience, education and training, none of this had much bearing on whether they improved their students' performance.
Other studies of the district have found that students' race, wealth, English proficiency or previous achievement level played little role in whether their teacher was effective.
"In the past, too often we've just gone with gut instinct and haven't been careful about whether those things are important," said Richard Buddin, a senior economist and education researcher at Rand Corp., who conducted the statistical analysis as an independent consultant for The Times.
Many teachers and union leaders are skeptical of the value-added approach, saying standardized tests are flawed and do not capture the more intangible benefits of good instruction. Some also fear teachers will be fired based on the arcane calculations of statisticians who have never worked in a classroom.
The respected National Academy of Sciences weighed in last October, saying the approach was promising but should not be used in "high stakes" decisions — firing teachers, for instance — without more study.
No one suggests using value-added analysis as the sole measure of a teacher. Many experts recommend that it count for half or less of a teacher's overall evaluation.
And in Los Angeles, the method can be used for only a portion of the district's roughly 14,000 elementary school instructors: California students don't take the test until second grade and teachers must have had enough students for the results to be reliable.
Nevertheless, value-added analysis offers the closest thing available to an objective assessment of teachers. And it might help in resolving the greater mystery of what makes for effective teaching, and whether such skills can be taught.
On visits to the classrooms of more than 50 elementary school teachers in Los Angeles, Times reporters found that the most effective instructors differed widely in style and personality. Perhaps not surprisingly, they shared a tendency to be strict, maintain high standards and encourage critical thinking.
But the surest sign of a teacher's effectiveness was the engagement of his or her students — something that often was obvious from the expressions on their faces.
Study in contrasts
On a spring day at Broadous, all eyes in Room 26 were on the white board.
Miguel Aguilar had brought his fifth-graders to the edge of their seats — with a math problem.
Aguilar, a stocky 33-year-old who grew up in the area, is no showman. Soft-spoken and often stern, he doles out praise sparingly. It only seems to make his students try harder.
"Once in a while we joke around, but they know what my expectations are," he said. "When we open a book, we're focused."
It seems to work: On average, his students started the year in the 34th percentile in math compared with all other district fifth-graders. They finished in the 61st. Those gains, along with strong results in English, made him one of the most effective elementary school teachers in the district.
On this day, Aguilar had invited a student to the board to divide two fractions — a topic on the upcoming state exam. As his classmates compared notes in whispers, the boy wrote out his answer. Aguilar turned to the class.
"Do you agree?" he asked, without hinting at the correct response.
"Yes!" they called back in unison.
"Good," he said softly, allowing a faint smile. "You know this."
John Smith's students in Room 25 were studying fractions too.
Speaking in a slow cadence, he led his class in reciting a problem aloud twice. He then called on a student slouched in the back. The boy got the answer wrong.
"Not so much," Smith said dryly, moving on to another pupil without explanation.
It was only 11a.m., and already it had been a tough day: Three of Smith's students were sitting in the principal's office because of disruptive behavior. All were later transferred permanently to other classrooms.
In an interview days later, Smith acknowledged that he had struggled at times to control his class.
"Not every teacher works with every kid," said Smith, 63, who started teaching in 1996. "Sometimes there are personality conflicts."
On average, Smith's students slide under his instruction, losing 14 percentile points in math during the school year relative to their peers districtwide, The Times found. Overall, he ranked among the least effective of the district's elementary school teachers.
Told of The Times' findings, Smith expressed mild surprise.
"Obviously what I need to do is to look at what I'm doing and take some steps to make sure something changes," he said.
Jobs with security
Public school students are graded and tested all the time. Schools are scored too — California rates them in an annual index.
Not so with teachers.