Saying Mayor Bloomberg’s budget proposal would unfairly harm schools, union leaders, advocates, elected officials, and principals are concocting alternative strategies for weathering the bad economy.

Some of the ideas that have been percolating were pitched at a rowdy meeting last night in Manhattan attended by about 150 people. The principals union president, Ernest Logan, and the teachers union president, Randi Weingarten, were among those demanding more belt-tightening at the central Department of Education, people who attended the meeting said.

The meeting was closed to reporters.

The department’s bureaucracy is one area of concern among the critics. A report compiled by the City Council shows the number of people employed at central administration is rising, growing to 2,337 full-time employees in the latest available figures, for November 2007, from 2,148 in July 2007.

A department called the Office of Accountability is an area of particular concern. An e-mail message dated January 9 announced 13 new hires at the office.

A copy of the message mailed to The New York Sun that hid its sender’s identity included a handwritten note: “We thought there was a hiring freeze.”

After obtaining the message, the city’s public advocate, Betsy Gotbaum, mentioned the memo at the meeting last night, a source who attended said.

A Department of Education spokesman, Andrew Jacob, said none of the new hires on the city payroll are newly created positions, but merely filling vacancies.

Advocates and union leaders are also examining a number of multimillion-dollar no-bid contracts the Department of Education holds with outside companies.

One five-year contract, for $80 million, is with the educational publishing company CTB McGraw Hill, which agreed to write new diagnostic tests called periodic assessments for grades 3 through 12.

The contract is costing the department $30 million this year, Mr. Jacob said.

The contract is getting attention because high school principals haven’t yet received a single assessment.

Speaking anonymously because they said they feared they would lose their jobs, several high school sources said they have been asking for the assessments every week for months.

Mr. Jacob said the assessments were initially scheduled to be released this month, and a Power Point presentation written in July of last year says the same thing.

But principals in the next few days will be told that the assessments will not be released until after February, and that only two will be given rather than three. Mr. Jacob said the change is a result of conversations with educators, who told the department February was not a good time to give a diagnostic test.

He said the department will save money from the change, but he could not say how much.

“We only pay for the assessments we actually administer,” Mr. Jacob said.

A change in the number of assessments given in lower grades, to four from five, was listed as a budget savings of $1 million in Mr. Bloomberg’s budget. No changes in high school assessments were listed as a savings.