Contrary to a report in Friday's Washington Post, the school board associations of Texas and Ohio have not formally opposed the idea of a U.S. Department of Education.

With civil service overhaul and a Department of Energy already under its legislative belt, the Carter administration yesterday went after number three on its government reorganization list: a Cabinet-level Department of Education.

Vice President Mondale, whose visibility on this issue has helped stamp it a serious Carter priority, told a briefing that the bill introduced in the Senate yesterday stands an excellent chance of becoming law this year.

"This is the only major industrial democracy in the world that does not have a department or a ministry of education," Mondale said. Education occupies one-quarter of all Americans, he added, but suffers because its highest official "is not at that Cabinet table speaking directly to the president."

That is the main argument for the proposal, but it failed to impress critics in the House Government Operations Committee last year, where the bill lingered until too late for a full House vote. This year's streamlined version lacks the programs that drew the most fire last time, and the administration hopes to have it through the Senate by March and the House by early summer.

"If we don't get it by July, it's dead," said Howard Carroll of the National Education Association (NEA). The NEA has been trying, largely unsuccessfully, to shed its image as the driving force for the new department. When Carter won an unprecedented NEA endorsement in 1976, he promised the association a department, and now the opposition is calling the idea "'just another pelt to hang on the wall" for both Carter and the NEA.

The new department would include 16,200 employees running about 150 education programs with a budget of $13.5 billion, more money than now goes to the departments of Energy, Justice, Commerce, Interior or State.

Transition would cost $10 million and would mean another 171 administrative positions, but 300 jobs would be cut and the money made up in long-run efficiency savings, according to James McIntyre, director of the Office of Management and Budget. He said yesterday that the new department would restrict itself to coordinating federal programs, to being responsive to state and local education authorities, and to making the federal interest more efficient locally and more visible nationally.

"The new department won't teach people to read or teach them mathematics," he said. "Teachers do that."

The reach of the federal arm into local school jurisdiction is the central debating point. Nobody wants to extend it in theory. The question is whether a new department would extend it in fact.

The Rev. Jesse L. Jackson, president of the Chicago-based Poeration PUSH (People United to Save Humanity), made the department defenders squirm in Senate hearings this week when he endorsed the concept, in part because it could bring more federal muscle to bear on local school boards dragging their feet on desegregation.

"It's essential to have federal responsibility so that we can have equal protection under the law," he said. "That will not happen at the local level."

The measure, like existing law, contains language that would keep the federal government out of curriculum, administration, personnel and textbooks, "but such language alone is not very reassuring," remarked Thomas A. Bartlett, president of the Association of American Universities. "Something much more concrete will be necessary."

He worries, he said, about centralizing education so that it can be "captured" from the top. "I thank God we didn't have this when Nixon was president," Bartlett said in an interview. "He was out to punish [education] and he would have had an easier time of it."

Bartlett muted his worries before the Senate after Carter's domestic policy chief, Sturart Eizenstat argued at a White House breakfast last week that Bartlett's concerns would be taken into account. Mondale also orchestrated what the administration frankly called a "pep rally" last month of the 100 organizations that have signed up to back the department.

"It means the administration is serious this time," said Charles Saunders of the American Council on Education, an umbrella group of higher education organizations. The question, he and others suggested, is whether the AFL-CIO, the Roman Catholic private institutions, the American Federation of Teachers and other opponents will muster their heavy artillery to defeat it.

Some groups are undecided or divided. The National School Boards Association voted in the past to support a DOE II, as it is being called, but that was when there was little chance it would become a reality. "Now some of us are scared we might get it," said one state school board official.

The school board associations of five states -- Pennsylvania, Texas, Kansas, Ohio and Nevada -- have already broken ranks and decided to oppose the measure. The topic will be number one at the group's convention in April.

The issue of federal involvement is a red herring, according to the department's backers. "Wherever we are spending $25 billion we HAVE a policy," said Sen. Lawton Chiles (D-Fla.). The question, he said, is how well that money is targeted.

"A Cabinet-level department of government is created not because the program is run from Washington but because of its importance to the nation," said Education Commissioner Ernest Boyer. It is frustrating, he said, to try to run so many complex programs when they are distributed among 40 government agencies.

The administration bill brings in 10 program areas to join the current HEW education division in the new department, the Defense Department's schools for overseas dependents; the Labor Department's migrant education programs; graduate school of the Agriculture Department; and law enforcement, nursing and health professionals' student loan programs from Justice and HEW, among others.

That list leaves out the hot lunch, Indian education and Head Start programs whose inclusion last year caused such an outcry. "In the real world, we couldn't get them through the Senate," said Sen. Abraham Ribicoff (D-Conn.), who is leading the fight for the department in the Senate.

It also leaves out major programs affecting education -- Labor's manpower training program, the Veterans Administration GI Bill benefits and others -- that together are far larger than the proposed department and were never proposed for inclusion because of political resistance.

Some groups that wanted in, such as the vocational education and rehabilitation programs, were left out, while others, such as some research programs of the National Science Foundation, that wanted to stay out were included.

The product means the department is too weak for some who hope it will soon be expanded, and too amorphous for others who fear that it will expand. Both sides want new language in the bill to guarantee their view.

"The Senate will be easy, but the House will be a zoo." That assessment of the bill's future this spring, from a former HEW official, gets general agreement. The battle will be fought in the House Government Operations Committee, where a staff aide to one of the bill's chief opponents, Rep. John N. Erlenborn (R-Ill.), said the measure had only a 50-50 chance of emerging at all.