One of his campaign’s television ads informs New Yorkers that reducing class sizes has been one of the highlights of Mayor Bloomberg’s record on education. Flashing the words “Reduce Class Size” on the screen, the ad tells potential voters that the mayor has pledged to build more schools to help reduce class sizes.

Under the Bloomberg administration, average class sizes have indeed dropped slightly for students in kindergarten through sixth grade, and the administration has allocated $1.8 billion in its capital plan to cut class sizes for the early grades. The administration’s top officials in charge of class-size issues testified yesterday at a City Council hearing, however, that the Department of Education has questions about the value of reducing class sizes.

The deputy chancellor for teaching and learning, Carmen Farina, testified: “For a school to become successful, to stay successful, each principal must have the flexibility to use the school budget in the way that is most effective for students in that building.” She said teacher quality is more important to student outcomes than the number of students in the classroom.

“You can choose between the most sought-after master teacher in the school with 28 students, a competent but not inspiring teacher with 23 students, or a new teacher with 17 students in the class,” she said. “I guarantee most parents would opt for no. 1.”

Ms. Farina cited a recent study released by the Progressive Policy Institute, the Democratic Leadership Council’s think tank in Washington, to back up her argument. The report states that cutting class sizes has been the most expensive education “reform” in recent decades.

The report, published this spring, said: “While smaller class sizes are popular with parents, teachers, and politicians, they can have an unintended detrimental effect on teacher quality. Across-the-board, class size reductions force school districts to rapidly find new teachers.”

That focus on teacher quality is reflected in the administration’s plan for how to spend the additional $5.2 billion a year in education aid expected as a result of the Campaign for Fiscal Equity school finance case. According to a plan Mr. Bloomberg announced in April 2004, the administration would spend $51 million on reducing class sizes in kindergarten through third grade, while it would spend $830 million to increase the quality of teachers and principals.

With class size emerging as one of the key differences between the mayor and his political opponents, the four Democrats who want to be New York City’s next mayor jumped on Mr. Bloomberg for claiming class size reduction as an accomplishment, while his administration is, at the same time, questioning its worth.

The council speaker, Gifford Miller, is championing a proposal to reduce class sizes in public schools to 17 in kindergarten through third grade by extending a surcharge on personal income tax for New Yorkers earning more than $500,000 a year.

He is perhaps the most vocal critic of the mayor on the issue.

“He’s done next to nothing on reducing class sizes,” Mr. Miller said. “I haven’t seen much evidence of it being one of his priorities.”

The speaker said research supports his contention that reducing class size allows teachers to devote more individual attention to children.

A spokesman for C. Virginia Fields, Nick Charles, said the candidate wants to reduce class sizes by expanding existing school buildings, constructing new schools, and allocating Campaign for Fiscal Equity money for that purpose.

“For effective learning to take place, there must be some kind of manageable class size, where a teacher can have the ability to have rapport with each and every student,” Mr. Charles said.

A spokeswoman for Fernando Ferrer, Jennifer Bluestein, also said the answer to the issue of class size lies in the decision in the Campaign for Fiscal Equity case.

“Freddy Ferrer is the only candidate to propose a School Investment Plan to leverage the funds needed to reduce class size throughout our schools, which he believes is a priority,” Ms. Bluestein said. “Without the $23 billion owed to our schools by Albany, which Mayor Bloomberg has absolutely failed to get, small classes will remain a dream for too many of our kids.”

The president of the United Federation of Teachers, Randi Weingarten, is working with a coalition of small-class activists to gather signatures to put a measure on the November ballot to reduce class sizes in all schools across the city.

She said class size is emerging as an issue because the mayor hasn’t backed up his claims about class size with money.

Like Ms. Farina, Ms. Weingarten said teacher quality has to be the first priority, but she said the administration’s contract proposal to her union doesn’t indicate that it cares about either.

The union president, who has yet to endorse anyone in the mayoral race, said Mr. Miller’s proposal is the “most fully formed,” but she said her proposal, which would put 25% of the Fiscal Equity money toward class size reduction in all grades, would be better for students and teachers.