• Highly effective teachers routinely propel students from below grade level to advanced in a single year. There is a substantial gap at year's end between students whose teachers were in the top 10% in effectiveness and the bottom 10%. The fortunate students ranked 17 percentile points higher in English and 25 points higher in math.
• Contrary to popular belief, the best teachers were not concentrated in schools in the most affluent neighborhoods, nor were the weakest instructors bunched in poor areas. Rather, these teachers were scattered throughout the district. The quality of instruction typically varied far more within a school than between schools.
• Although many parents fixate on picking the right school for their child, it matters far more which teacher the child gets. Teachers had three times as much influence on students' academic development as the school they attend. Yet parents have no access to objective information about individual instructors, and they often have little say in which teacher their child gets.
• 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."