The Times today has a new profile of Eva Moskowitz, the politician-turned-school operator who is at the helm of the four Harlem Success Academy charter schools. I say new because this is actually the second full-length profile of Moskowitz the Times has run. (The first is here.)

Why pay so much attention to this charter school operator, amid the sea of them? I’ll give two reasons.

First, Eva Moskowitz is not just trying to improve public schools by creating better ones in Harlem. She is testing a theory of politics. Three years ago, after becoming a living legend in her tenure as head of the City Council education committee, holding drama-filled hearings that took on the mayor as strongly as the teachers union, Moskowitz tried to take her political career to the next level by running for Manhattan borough president. She lost in 2005 to Scott Stringer, a defeat that was in no small part thanks to the enemies she made as a tough committee head.

But Moskowitz did not jump out of the limelight. In fact, the opposite: she still declares her intention to run for mayor one day. Whether she really will run for mayor, she is trying to prove a point: that it doesn’t matter that she infuriated the teachers union and other labor groups. Moskowitz’s arguement is that school improvement efforts, done well, can build a natural constituency all their own.

If she succeeds, she will shake up what is permitted in the politics of running schools. As the Times story points out, so far she is making impressive inroads. She has built a parent group to advocate for policies that help charter schools and has held events that attract impressive audiences and, increasingly, elected officials, too. I even once was standing with Moskowitz at a cocktail party when a young woman walked up to us bashfully. Extending her hand to Moskowitz, she explained that she was a “big fan”: she had written her undergraduate thesis on Moskowitz’s challenges to work contracts.

The second reason to pay attention to Moskowitz is that, if she succeeds, her political playbook wouldn’t be the only thing being replicated. People would also be eyeing her schools.

The New York Times story, by Elissa Gootman, is fascinating as a portrait of the day-to-day of Moskowitz’s second coming. We learn that, although she has recently been a strong public ally of Mayor Bloomberg and Chancellor Joel Klein, privately she is still the tough, demanding woman who will challenge anyone she doesn’t think is doing their job correctly: Gootman excerpts some cross e-mail messages she has sent to school officials. We also learn that her son, Culver, is one of a tiny number of white students at one of Moskowitz’s charter schools, Harlem Success 3.

But it also paints a picture of how Moskowitz’s schools are actually run. Moskowitz says her curriculum is a mix of, on one hand, the liberal Bank Street ethic — there are dress-up corners in the kindergarten rooms — and, on the other, the drill-and-kill of programs like Success for All, which she uses for literacy. And she has not been afraid to fire staff; in the first year, an assistant principal and two teachers were let go.

Finally, she appears to ask as much of parents as she has of elected officials, making requirements that a traditional public school would have a hard time pulling off:

She demands a lot from Harlem Success parents: They must read their children six books a week, year round, and attend multiple school events, from soccer tournaments to Family Reading Nights. If children are repeatedly late, the parents must join them to do penance at Saturday Academy.

Nefertiti Washington, 28, whose son is a kindergartner, said some parents walked out of a springtime information session when Ms. Moskowitz made her expectations clear by saying, “If you know you cannot commit to all that we ask of you this year, this is not the place for you.”