A fire door in a brick school building separates two worlds.

On one side is P.S. 149, a New York public school where educating a student costs $19,358 per year, 29 percent of the students were proficient in English in 2009-10, and 34 percent were proficient in math.

On the other side is Harlem Success Academy 1, a charter school where 86 percent of the students were proficient in English that year and 94 percent were proficient in math. The charter costs $980 less per student.

That’s right: The charter is cheaper and better. So why wouldn’t all public schools in America turn into charters? That question is at the heart of a war over public education.

In Class Warfare, media entrepreneur and Yale-educated lawyer Steven Brill chronicles the efforts of education reformers as they mobilize to fight the teachers’ unions that insist on maintaining the status quo of American public education.

It’s a war about children, fought by adults.

The conflict has even inspired a critically acclaimed 2010 documentary, Waiting for Superman, a call to action that shocked and infuriated the public.

The problems of American education are well-known, and so is the solution, according to Brill. The answer is to hold teachers accountable for student achievement. Yet accountability is elusive, in Brill’s view, when a union such as the American Federation of Teachers becomes deeply involved in politics. The AFT is one of the largest donors to Democratic political campaigns, Brill writes. In response, education reformers have mobilized a sizable army of politicians, educators, parents and donors to counter the union’s political clout, as Brill shows in astounding detail.

Brill features 152 people, a number that is impressive but makes it hard for a reader to remember who is who. Organized in short chapters that don’t always seem connected, Brill’s book skips around the reform army, profiling the struggles of individual soldiers.

On the front line are people, such as Michelle Rhee, the former chancellor of public schools in Washington, D.C., who are unyielding when dealing with the union. Depending on where you stand in the battle, Rhee is either a dream for demanding accountability or a nightmare for firing hundreds of teachers and trying to break up the union by offering an alternative teacher contract with higher pay but no job security. She inspired such fear in unions around the country that she helped pave the way for change elsewhere.

Then there’s President Obama, who gets high marks from Brill for championing education reform despite the political risk for a Democratic politician. Obama rolled out a grant contest called Race to the Top, which dangled a $5 billion carrot in front of states to improve education. Brill has problems with Race to the Top. He chronicles how an elegant idea morphed into a head-scratching conundrum, in which states that offered few real reform policies, such as New York, received money. But Brill adds that even though Race to the Top was not perfect, the contest forced states to draw up plans for change. Whether these plans will be carried out remains to be seen.

Brill also writes about star charter schools like Harlem Success Academy 1, where teachers work tirelessly because they believe that the fate of the students are in their hands and not determined by race, family, and poverty.

Taking us inside urban classrooms across the country, Brill tells the stories of new college graduates who are teaching there because of programs like the nonprofit Teach for America. They may lack experience and be terrible in the beginning, but they experiment until they get it right.

Just when Brill seems to get too idealistic about Teach for America, he argues that the program sometimes forgets that the war is for children, not adults. In that vein, he criticizes TFA founder Wendy Kopp for refusing to make available data that link test scores and TFA teachers.

Behind all of the action are the financial backers, billionaires including Bill and Melinda Gates, Eli Broad, Rupert Murdoch, the Walton family, and the hedge-fund managers who donate millions to reform organizations and political action committees.

Brill’s survey of the reform side of the war is impressive, but it leaves the reader wondering about the status quo side.

He writes that he spent more time interviewing AFT president Randi Weingarten than he did anyone else in the book, but a reader can’t help question whether his portrayal of Weingarten as a frequent liar who cares only about the interests of teachers is entirely accurate.

Brill depicts the union in general as being so selfish about its own gains that it steadfastly pushes against any measures for reform. He profiles only a few union teachers. And readers develop a sense that union teachers simply don’t care to be better because they’re not held accountable, which is exactly what Brill intends to convey.

So it comes off as a surprise when Brill concludes the book by endorsing a “Nixon to China” strategy of old enemies coming together: Weingarten should be the next New York City schools chancellor — a fantasy fit for a sequel.