Many are the sons and daughters of Latino immigrants who never finished high school, hard-working parents who keep a respectful distance and trust educators to do what's best.
The students study the same lessons. They are often on the same chapter of the same book.
Yet year after year, one fifth-grade class learns far more than the other down the hall. The difference has almost nothing to do with the size of the class, the students or their parents.
It's their teachers.
With Miguel Aguilar, students consistently have made striking gains on state standardized tests, many of them vaulting from the bottom third of students in Los Angeles schools to well above average, according to a Times analysis. John Smith's pupils next door have started out slightly ahead of Aguilar's but by the end of the year have been far behind.
In Los Angeles and across the country, education officials have long known of the often huge disparities among teachers. They've seen the indelible effects, for good and ill, on children. But rather than analyze and address these disparities, they have opted mostly to ignore them.
Most districts act as though one teacher is about as good as another. As a result, the most effective teachers often go unrecognized, the keys to their success rarely studied. Ineffective teachers often face no consequences and get no extra help.
Which teacher a child gets is usually an accident of fate, in which the progress of some students is hindered while others just steps away thrive.
Though the government spends billions of dollars every year on education, relatively little of the money has gone to figuring out which teachers are effective and why.
Seeking to shed light on the problem, The Times obtained seven years of math and English test scores from the Los Angeles Unified School District and used the information to estimate the effectiveness of L.A. teachers — something the district could do but has not.
The Times used a statistical approach known as value-added analysis, which rates teachers based on their students' progress on standardized tests from year to year. Each student's performance is compared with his or her own in past years, which largely controls for outside influences often blamed for academic failure: poverty, prior learning and other factors.
Though controversial among teachers and others, the method has been increasingly embraced by education leaders and policymakers across the country, including the Obama administration.
In coming months, The Times will publish a series of articles and a database analyzing individual teachers' effectiveness in the nation's second-largest school district — the first time, experts say, such information has been made public anywhere in the country.
This article examines the performance of more than 6,000 third- through fifth-grade teachers for whom reliable data were available.