The public school year that begins today is said to be a pivotal one in making the case for an extension of what is known as mayoral control. It is so called to distinguish the present regime from the old Board of Education, which included some mayoral appointees but also individuals appointed by the presidents of the boroughs. The present system is an improvement over what came before and deserves to be extended by the legislature.

But to say that the system is now under the “control” of the mayor is an exaggeration. Mr. Bloomberg must contend with a politicized teachers union that has negotiated a contract curbing management authority over teachers. The principals have their own union. The politicians in Albany who appropriate $8.2 billion a year to the city’s schools and those in Washington who appropriate another $1 billion or so a year do it with plenty of strings attached.

We’re not trying to make excuses for the mayor or for his schools chancellor, nor to belittle them. They are powerful. But as doors open today to more than a million students, the idea that these schools are under the control of the mayor is a fiction.