The number of elementary and middle-school classrooms defined as “overcrowded” under the teachers’ contract has more than doubled since last year, and the total number of overcrowded city classrooms is more than 6,000, the teachers union said yesterday, though both the union and the city caution that the numbers are imprecise.

A survey of teachers by the United Federation of Teachers found there were 1,719 overcrowded classrooms in elementary and middle schools as of September 19, up from 668 last year. Including high schools, there were 6,339 overcrowded classrooms in total, up from 5,761 last year.

September 19 was the last day of a two-week grace period at the beginning of the year during which schools can reduce class sizes. After the grace period, teachers can file grievances.

The teachers union has long fought for the city to reduce class sizes.

“It’s hard for teachers to reach students when classes have as many as 4 or 5 kids over the already too-high class size limits,” the union’s president, Randi Weingarten, said in a statement. “And it’s hard for kids, who should have continuous classroom instruction from the first day of school.”

A class is defined as overcrowded when the number of students exceeds the limits set in the teacher’s contract. Pre-kindergarten classes are required to have 18 or fewer students, kindergarten classes are set at 25, grades one through six are set at 32. The city council has set aside funding so that elementary school classes can be limited to 28. Middle school classes are set at between 30 and 33, and high school classes are set at 34.

Department of Education representatives responded by saying that numbers from a week ago were too old to reflect the current status of city classrooms, adding that principals have been working hard since the school year began to rearrange classes that were too full.

“These are unreliable numbers,” said an education department spokesman, Andrew Jacob. “At this point the numbers just aren’t meaningful.”

The teacher’s union also cautioned that the numbers were fluid and could go down as classes are rearranged and once arbitration begins next week between the department and teachers. Already, the union said, the number of overcrowded classrooms at James Madison High School in Brooklyn had dropped to zero from the 361 reported at the beginning of the year.

“We know that some administrators tried extremely hard to get their schools into compliance — and some have done so since we collected these numbers after the 11th day of school,” Ms. Weingarten said. “But we still have some 6,000 classes over the limit. Going through this annual game of musical classrooms is very hard on students and teachers alike.”

Other advocates for smaller class size echoed Ms. Weingarten’s concerns.

“In the process the kids have lost the first few week and few months,” said Leonie Haimson of Class Size Matters, a critic of the department and vocal advocate for smaller classes. “And anyone will tell you it’s the most important part of the year.”

According the Mayor’s Management Report from 2006, class sizes have gone down steadily since 2002 and the proportion of overcrowded city schools has also declined.