Mayor Bloomberg has drawn the wrong lesson from the example of Franklin K. Lane High School in Brooklyn, where a little more than a quarter of the students graduate, violence abounds, and a fifth of the student body transferred out last year under the federal No Child Left Behind Act. “I don’t think anybody can really run a [high] school of 3,000 people,”Mr. Bloomberg told reporters Monday, referring to the 3,400 student population of Franklin Lane.

This has become the prevailing wisdom among many education reformers. It’s one of the reasons why the Bill and Melinda Gates Foundation is spending more than $50 million to transform big schools into smaller, nimbler ones that give teenagers individual attention and ensure that nobody falls through the cracks.

When a school is too big, the theory goes, it’s just unmanageable. Remember how they used to say the same thing about New York City itself? But Stuyvesant High School has more than 3,000 students. More than 4,000 students attend Brooklyn Tech. Both are among the best high schools in the city and the nation. The same is true of Benjamin Cardozo High in Queens, Midwood High School in Brooklyn, and many others. Some have selective admissions policies that weed out all but peak performers, others do not.

Sometimes big schools get bigger precisely because they’re doing such a good job, and more parents do whatever they can to help their children attend them. P.S. 321 in Brooklyn, which The New York Sun recently reported is bursting with students, is a case in point. That’s the way the market works, when it works. Breaking up a failing high school is fine if it leads to teachers and administrators being held accountable, discipline being enforced, parents being engaged, and students being challenged. But it is no panacea — and the size of a school is no barrier to a good education when a culture of learning fills the halls.