Mayor Bloomberg and his schools chancellor, Joel Klein, deserve credit for moving the city’s public school system in the right direction – and they’re taking it. “Over the last two years we have begun to bring order and accountability to a system that had been dysfunctional for decades,” the mayor said on Wednesday. “By providing students with the resources they need and holding them, their teachers, and ourselves accountable for producing results, our schoolchildren are now receiving the education they deserve.”

This year, New York’s public school pupils in the third, fifth, sixth, and seventh grades achieved the largest one-year gains – as well as the highest overall scores – ever recorded on the English Language Arts and mathematics tests since the city started administering them six years ago. As our Julia Levy reported last week, the proportion of students who passed the city’s English exams this year swelled to 54.8% from 40.4%. Between 2000 and 2004, the overall passing rate had varied only between 39.0% and 40.8%. In mathematics, meanwhile, 50.0% of the pupils taking the exams passed, up from 42.5% the year before.

The city’s fourth graders also achieved dramatic improvement this year: a nearly 10-point jump in the number of pupils passing the state English test. “There is no doubt that our children and our schools are performing better than they were before we instituted the Children First reforms,” Mr. Klein said on Thursday. And he’s right.

The president of the United Federation of Teachers, Randi Weingarten, locked in negotiations with the mayor’s office over the teachers’ contract, has tried to spin the rising test scores in her favor. When the fourth-grade scores were announced in May, Ms. Weingarten told New York Public Radio, “It’s going to be very hard for the chancellor to argue that the contract impedes success, that’s the irony, that’s the great irony of all of this.” When the city test scores were announced last week, she repeated the argument: “With scores rising, it’s really hard to say with a straight face that the contract is an impediment,” Ms. Weingarten said at a UFT rally at Madison Square Garden last week.

Not quite. Test scores for the fourth grade have been rising faster at the city’s charter schools than at the city’s public schools overall. On the eighth-grade state reading test, moreover, just 32.8% of city pupils passed – a decline of 2.8 points from 2004. Among those pupils enrolled in charter schools, however, 48.5% passed – a five-point increase over last year. So it’s hard, even for the union, to argue with a straight face that the extra strictures of the teachers’ contract added to the rise in test scores. If anything, the contract held students back.

At the same time, many of the improvements on the city exams can be attributed to specific innovations. The gains were sharpest in the fifth grade, for example, where students were subject to the mayor’s new promotion policy and benefited from the Saturday Preparatory Academy, a program geared toward at-risk children.

It’s clear that the faux report cards drawn up by the teachers union last week, grading Messrs. Bloomberg and Klein as having failed in their leadership of the school system, were less about promoting students’ educational attainment than winning salary increases for public school teachers, regardless of their performance. The rising test scores across the city give Mr. Bloomberg an opening to resolve the contract dispute not with across-the-board raises, but with individual merit pay for teachers. That would be a victory for taxpayers, parents, and students.

Which makes it all the more disappointing that the other mayoral candidates – Democrats Fernando Ferrer, Gifford Miller, and Anthony Weiner along with Republican Thomas Ognibene – would show up at the United Federation of Teachers rally last week to undermine the mayor’s negotiating position.

Mr. Ognibene told us that he appeared at the rally out of sound conservative principles. The Republican challenger says that individual schools should have the primary responsibility for educating their students, and principals should be given more authority. As for the rising test results, according to Mr. Ognibene, are “totally fudged … It’s all smoke and mirrors, the mayor manipulating the system.”

We’re sympathetic to Mr. Ognibene’s decentralized model for the public school system – up to a point – but the union has been an obstacle to steps such as vouchers and charter schools that would expand the number of options for parents. Mr. Klein, on the other hand, has been pushing to lift the cap on charter schools. There may be room to criticize the Bloomberg team on schools for its failure to pursue vouchers. And now that the mayor finally says our schoolchildren are getting more of the education they deserve, maybe he can forget about soaking the taxpayers in the rest of the state for $23 billion more in aid to city schools. But for all that, a credible political challenger to the mayor on the education front has yet to emerge in this campaign, which must put a bounce in Mr. Bloomberg’s step as the school year heads into summer recess – and the campaign heats up.