Student test scores rose in New York City this year – and in some classrooms and schools, kids made truly significant gains. Consider Region 5, a poor district of eastern Brooklyn and Queens. As Julia Levy reported in The New York Sun, the district was an “educational wasteland for decades,” with two-thirds of the schoolchildren failing at everything. But this year, the district’s elementary- and middle-school students pulled off testing gains of 17 percentage points in English and 10 percentage points in math, outpacing the city’s average gains in both areas. At P.S. and I.S. 41 in the district, 48% of fifth-graders met reading standards this year, up from 32% last year, while 37% of the seventh-graders did okay or well this year, more than double last year’s figure.

It’s no mystery why scores are going up: a gifted, determined manager who motivated teachers to succeed. The district’s leader, Kathleen Cashin, established clear expectations for principals and teachers, and pushed the schools in the district to meet them. P.S./I.S. 41 principal Myron Rock enthuses that his teachers worked evenings, Saturdays, and vacations to push students.

The teachers must be glowing with pride from the praise they’ve garnered. But they won’t see more money for their feat, unless every New York public school teacher also sees it. In mid-June, the United Federation of Teachers, led by Randi Weingarten, released its latest pay demands, and rewarding the best teachers is not part of them. Instead, the union wants a 19% pay hike for teachers across the board, raising top salaries to nearly $100,000 within three years. Partial funding for this hefty raise would come from the new billions in city school money the union expects from the state to settle the Campaign for Fiscal Equity lawsuit – money that may (and should) never materialize.

But without the introduction of merit-based pay, new money won’t do much to build upon this year’s rising scores, as a recent study, conducted by Harvard economics professor Caroline Hoxby and Andrew Leigh of the National Bureau of Economic Research, makes clear. The study examined worker aptitude (native smarts, basically) as it relates to worker pay. In most professions, the best workers usually receive the top pay – a situation that once held in teaching, before the unions arrived on the scene and began to mandate lockstep salaries. Ms. Hoxby and Mr. Leigh found that smart women (the study looked only at females), frustrated by the absence of reward for ability in the public schools, have looked elsewhere for more rewarding career paths, as you’d expect.

Forty years ago, as unions were just gaining control in public schools, Ms. Hoxby and Mr. Leigh report, 16% of American female teachers were of low aptitude in relation to other college graduates (determined by mean SAT scores at their respective universities). By 2000, a full 36% of women teachers were of low aptitude. In 1963, 5% of women teachers came from the highest aptitude group; by 2000, that figure had plummeted to 1%. The primary reason for this startling decline in teacher quality, Ms. Hoxby and Mr. Leigh conclude, is the elimination of financial rewards for talent. Back in 1963, the smartest teachers earned more money than average teachers, while the lowest-aptitude teachers earned less; by 2000, all teachers earned pretty much the same for the same level of experience, regardless of talent.

If New York wants to attract and keep the best teachers, then, the solution isn’t to increase teacher pay across the board. That might attract more people to teaching, but not necessarily smarter or harder-working people. Mayor Bloomberg and Schools Chancellor Joel Klein should instead seek to structure financial incentives to reward teachers like the ones who performed so well this year at P.S. 41.

Mr. Klein already supports school-based merit pay for teachers – that is, if a school improves, he wants everyone teaching there to receive a financial reward. But for merit pay to work best, Ms. Hoxby pointed out to me last week, it should offer bonuses or raises based on individual teacher performance. Otherwise, she asks: “What happens if you’re a great teacher in a school with problems?” Answer: The best teachers will just leave bad schools for good ones, perpetuating a race to the bottom in the worst schools.

If he could get the teachers to cooperate, Mr. Klein might take his proposal at least a step further and award schools bonus pools that would vary from year to year based on each school’s individual performance. The principals could then distribute the bonuses among teachers at the schools, based on test-score improvements in individual classrooms as well as on more qualitative evaluations of individual teachers. Teachers would have an incentive to work together in a school to get the whole school to do well, but would also be encouraged to excel in their own classrooms.

But the UFT remains hostile to any merit pay for individual teachers. Striking a Marxoid note a little while back, Ms. Weingarten declared that merit-pay plans “pit teachers against each other instead of encouraging a collaborative school culture.” What Ms. Weingarten and the union do not see – as the rest of America fervently believes – is that competition is healthy: In a merit-pay system, for instance, a teacher who could potentially be effective but who has lost any incentive to improve under the existing system might see her colleague down the hall try, succeed, and get rewarded for her successes – and want to emulate that colleague. Until Ms. Weingarten budges, though, virtue will have to be its own reward for New York’s teachers.

Ms. Gelinas is a contributing editor for City Journal, from whose Web site, city-journal.org, this is adapted.