In a month of hard-hitting speeches on education President Reagan has thrown his critics partly on the defensive by arguing that increased federal aid would hurt schools more than help them, mainly because federal aid is too often accompanied by federal regulation.

But the president has given little evidence of this, and has not been pressed to give more.

Reagan has said, for example, that federal aid to education has increased 600 percent in about the last 25 years but standardized test scores have not. "If a 600 percent increase can't make America smarter," he has asked, "how much more do we need?"

But what demonstrable effects have federal aid, and federal regulation, had in particular classrooms? On this the administration speaks with much less confidence.

Education Secretary T.H. Bell, whose department Reagan had promised to abolish before his recent rediscovery of education, said Reagan is trying to address "the general discontent with education in this country." Asked to be more specific, Bell suggested the "best examples" of the president's theory of federal aid have come in New Mexico and California.

New Mexico, Bell said, does not accept federal education aid for handicapped children because of the regulations accompanying the money. As for California, Bell suggested it was Reagan's years as governor there that first sensitized him to the problems of federal red tape in education.

The Nixon administration tightened the rules for state and local spending of federal aid to the poor under Chapter I of the Elementary and Secondary Education Act. The Nixon Office of Education said the tighter rules were necessary to make sure the aid did go to poor instead of middle- and upper-income children. But resisting state and local officials, including California's Reagan, said the new rules were federal infringements of state and local rights.

New Mexico officials, however, gave a different version of why they had refused federal aid. Elie Gutierrez, state director of special education, said the main problem with federal funds for the handicapped was that they came so late each year.

"The money would come in September and October when we start our program in August," said Gutierrez, noting that under state law special education teachers cannot be hired until funds to pay them are in hand.

He said local politics also were involved, with state legislators wanting constituents to know that New Mexico was paying to help handicapped children, not the federal government. "The state has as good or better a program for handicapped children as the federal program," he said, "and some, not all, of our politicans want our residents to know it is New Mexico that is paying for it."

The new Democratic governor, Toney Anaya, now is pressing to put New Mexico back in the federal program with the rest of the states, arguing the more money the better for children who need help.

Officials in California, where the governor is again a Republican, have objected to federal restrictions on Chapter I money, saying they do not fit what finance director Jess Huff calls California's "large and unique population."

However, Paul Smith, director of research for the Children's Defense Fund, points to inconsistencies in Reagan's position.

"The president clearly understands the need for federal regulations of food stamps and welfare to prevent misuse of federal funds. He doesn't want money for food stamps used for other purposes or welfare money used for cars," Smith said. "It's only in academic areas that he isn't bothered by the idea of federal money might not pay for what it is intended to pay for--directly improving the education of children."

Bell also testified earlier this year that Chapter I is now a "success by any measure."

Some of the Reagan administration's attempts to cut red tape from educational programs and return them to local control are seen by critics as devices for cutting the education budget.

For example, the administration recently proposed new vocational and adult education programs that would reduce federal support while increasing state and local control to avoid such things as training students "for jobs that don't exist" where they live.

One critic, Sen. Lowell P. Weicker Jr. (R-Conn.), chairman of the Senate Appropriation subcommittee on education, recalled one administration official testifying that the proposed cuts "amounted to a mere 4 percent reduction in the 'total universe' of local, state and federal funding for vocational education."

Weicker said he found it more significant that it was nevertheless a cut of 40 percent in federal funding.

In explaining the administration's position on education, Bell said his department is following the president's lead. "He is hearing from many people out there that schools are not working and he is reflecting that general discontent," Bell said. "He recognizes the need for federal leadership on this issue because of his own experience in California and situations like that in New Mexico and he wants the power for the programs returned to the states and cities."

Many experts say federal regulations have exerted their most powerful effect in determining which children shall be served in the schools. Some say American schools did not serve disadvantaged children--the poor, the handicapped, those from minority groups, those who do not speak English--as attentively before federal aid increased.

"It's not really true that the federal government is using its money to control local schools," said Denis Doyle, director of education policy studies at the American Enterprise Institute, a think tank often associated with the administration.

"The fact is the federal presence in education is far more a virtue than a vice . . . . There has been marked improvement in the way schools conduct their business, particularly with regard to minority, handicapped and low-income students, because of the federal government's money and regulations."

Ron Edmonds, a professor of education at Michigan State University who has just completed an eight-year study of American schools for the National Institute of Education, also described the problem as partly one of distribution of services, saying that state and local officials historically have shown little concern for minority and handicapped students. "Federal money has helped to a remarkable extent to open schools to classes of children who traditionally have not profited from schools, the handicapped, minorities, language-minority children," Edmonds said.

"If Mr. Reagan goes through with withdrawing federal funds it will have the effect of returning their educational fortunes to the politics of local government and the history of state and local politics shows them inadequate to respond in a fair way to those children."

On the related question of whether added federal funds could help schools, Doyle added, "It is almost impossible to waste education money because you are buying services for children. The question is really can you devise better ways to spend the money."

"Additional money is not a sufficient condition for improving schools, but it remains a necessary condition for improving schools," said Robert Rosenweig, president of the Association of American Universities. "That ranges from paying for better teachers to making money available for students to take advantage of higher education . . . as well as bringing the best teachers and students back into academic life to do research."

But administration officials say it is this kind of open-ended thinking that helped cause the problem. They want local officials to set priorities and pay for them.

"There is a tendency to feel certain programs are federal programs and are federally financed when maybe they should be a high priority in the school district," said Robert B. Carleson, a special assistant to the president for policy. "I have often wondered why some school districts that complain about the reduction in federal funding for programs don't simply fill in with money from other programs . . . . I'm talking about priorities."

In addition to saying that federal aid has not helped that much, the president has defended himself by denying that he has cut the education budget as much as critics charge. In a recent Saturday radio address, he accused his opponents of "hysteria" on this issue and urged listeners to "ignore the noisemakers."

In one recent forum the president went so far as to suggest that his administration has spent more on education than on defense and has "not cut any budgets." In fact, federal spending on education has fallen from $14.3 billion in fiscal 1982 to an estimated $13.5 billion in fiscal 1984. Critics jumped Reagan on this.

"I can only explain their hysteria by assuming that they were comparing federal spending on education to federal spending on defense," said Reagan in the radio address.

"That of course is ridiculous. The federal government bears overwhelming responsiblity for national defense, but it provides less than 10 percent of all education costs . . . . In the 1982-83 school year government at all levels spent $215.3 billion on education. The 1983 defense spending is $214.8 billion. Actually that $215 billion for education doesn't include Department of Defense spending for remedial education or private corporation spending on employe education . . . nor does it include what parents spend on books."