John Elfrank-Dana, UFT chapter leader at Murry Bergtraum High School, says his history classes have as many as 37 students.

After three years of budget cuts, the city’s schools started the year with more oversize classes than at any time in the last decade, according to data collected by the United Federation of Teachers.

Union members reported that on the sixth day of the school year, nearly 7,000 classes had more students than the teachers contract allows, mostly in high schools and a large number in Queens. That was almost a thousand more oversize classes than they reported at the same time last year.

The union will soon file a grievance against the contract violations, and many of the classes will shrink as schools shuffle students around in the coming weeks, as typically happens at the beginning of the school year. But union officials said it appears that for the fifth year in a row, average class sizes have inched up again.

“Our worst fears have now been confirmed,” said UFT President Michael Mulgrew at a press conference announcing the numbers today. He urged Mayor Bloomberg to protect the city schools from additional budget cuts in the coming year.

Now, nearly a quarter of all city students are spending all or part of the day in overcrowded classes, according to the UFT. The contract limits classes to 25 students in kindergarten; 32 students in elementary school; 33 students in middle schools and 30 students in middle schools with many poor students; and 34 students in high schools.

“We are still finalizing our class size reports, but we do expect class sizes to rise modestly as a consequence of nearly $1.7 billion in state and federal budget cuts that have forced us to more with less,” said Frank Thomas, a Department of Education spokesman, in a statement. “But we believe that getting effective teachers into every classroom is the most important stepping stone to student success, and we will continue to work toward that goal.”

“Our best teachers cannot do their best in classes of 25 or 30 or more,” said Leonie Haimson of Class Size Matters, who appeared with Mulgrew at the press conference. She said the increase in class size appears to be sharpest in kindergarten through third grade.

Many principals cut teaching positions at the end of last year, leading to a situation that has union officials scratching their heads: ”We have buildings that have oversized classes and open classrooms,” said Myra Cruz, the UFT’s district leader in District 6 in Upper Manhattan.

At Murry Bergtraum High School in Manhattan, where the press conference was held, some classes have as many as 41 students and lunch periods start as early as 10 a.m. and as late as 3 p.m., Mulgrew said.

What’s worse, according to John Elfrank-Dana, Murry Bergtraum’s UFT chapter leader, is that the school is getting more poor and low-performing students than ever, and they need more individual attention.

“The more socially needy the students are, the smaller you need the class to be,” he said. And at a time when teachers are being pushed to improve their practice, he said, “It doesn’t seem to fair to pull the rug out from under us” with even more students.