After a year's experience with the Reagan administration's controversial "block grant" method of giving federal money to local schools, federal support of urban desegregation efforts has fallen off dramatically. At the same time, more districts are using federal aid to expand libraries, buy computers and teach people how to use them.

These are conclusions reached in half-a-dozen private and federal studies examining the effect of one of the two block grants in the Education Consolidation and Improvements Act of 1981, a centerpiece of the administration's effort to restructure domestic spending.

The studies, coming at a time when the block grant concept is under increasing criticism, diverge on many key points, but they agree on the overall conclusion that the losers in the new system tended to be poor urban school districts, while the winners tended to be private schools and districts that had fared poorly or opted out of the competition for the 27 programs which were were replaced by the block grant.

The dramatic falloff in federal support for desegregation efforts meant urban districts such as St. Louis, Philadelphia, Seattle and Chicago had to dip into other programs, lay off teachers or go to court to find money for desegregation plans, according to information collected by a congressional committee.

But at the same time, the number of participating districts increased sharply, and more than a third of districts sampled in a survey by the national school administrators' organization reported that their federal grant money doubled under the block grants.

Overall, the same survey showed, districts that received less than $7,500 under the old system nearly doubled their receipts, while school districts receiving more than $100,000 lost, on the average, more than 85 percent of their money. The survey was done for the General Accounting Office, the investigating arm of Congress.

"What you are experiencing," said Education Department assistant secretary Lawrence Davenport, is "the local educational agencies, the elected school boards and their superintendents making decisions on how they best feel they can utilize their dollars."

The report by the American Association of School Administrators had a slightly different perspective: "First, federal block grant funds are helping local school districts move into the high technology era. Secondly, this block grant delivery system is creating a serious equity problem."

In June, the House passed legislation to reestablish a modified version of the Emergency School Aid Act, the original program providing backup support for school districts with voluntary or court-ordered busing plans.

The block grant at the focus of these varied reports is Chapter 2 of the Education Consolidation and Improvement Act of 1981, a $450 million program combining 27 earlier programs. The forerunners of the block grant, aside from the ESAA, which was incorporated in the block in 1982, offered federal aid to rural districts, to school libraries, to programs for the gifted, to programs in environmental or metric education.

Chapter 2 is one of two major education block grants coming under increased congressional scrutiny. A hearing on the impact of the block grant is scheduled Tuesday in the intergovernmental relations subcommittee, of the House Government Operations Committee, headed by Rep. Ted S. Weiss (D-N.Y.).

The block grant system makes state education authorities the prime actors in figuring which schools get money and how much they get. Instead of the old system, where districts asked the federal government to include them in programs for special needs, such as those for the gifted or those for improvement of library resources, states develop distribution formulas and local districts can use what they get under the formulas for any or all of the original 27 purposes.

The block grant law asks the state agencies to develop formulas on the basis of two broad criteria: how much money should go out on a per-pupil basis, and how much should go out to so-called "high-cost" students--the poor, the gifted, the handicapped, the students in rural districts, and so on.

The formulas adopted have varied widely, from Mississippi, which allocated 95 percent of its funds on the basis of enrollment and 5 percent on a "high-cost" basis, to Connecticut, which allocated 21 percent of its grant on the basis of enrollment and 79 percent on the basis of "high cost" factors. Low-income and economically depressed districts received about 60 percent of the funds in Connecticut.

Overall, according to Education Department figures, at least 37 states gave out more than half their funds on the basis of enrollment--a device that tends to spread the money around to more school districts and give each one less.

Some critics, including those interviewed by Education Department consultants examining the effect of the block grant, have charged that this method of distributing the funds, combined with the uncertainty of continuation of the funds, predetermines the use districts will make of them.

A Pennsylvania advisory committee established to set up that state's allocation formula found "a fundamental tension between the purpose of the statute and the funding mechanism. Dealing with the problems of equity and of improving school programs in specific areas the areas covered by the forerunner programs just does not occur on a per capita basis."

Other observers pointed out that, no matter whether one agrees with the philosophy of block grants, there is some local skepticism as to the continuation of the Chapter 2 program. That, combined with the allocation formulas which spread the existing money over a broader area, tends to predispose local administrators to make one-time purchases--such as books and computers--instead of longer-term investments in programs or teachers.

"Until the program settles down to being long-term, schools are going to be conservative," said Richard Jarrell, an official of the Texas Education Department. "They're going to look at what they can do with the funds right now." Jarrell added he found the new system "is doing a pretty good job."

But Davenport disagrees with the notion that there is any uncertainty about the program. "They do know the money is coming again," he said. "It's not a one-year program."

The Council of Great City Schools, an organization representing 30 major urban school districts, has been among the most vociferous critics of the new system, pointing out that federal block grants have forced city schools "to exchange approximately $135.7 million in categorial aid for $50.3 million in block grants, a decline of 63 percent. The losses in several cities, Buffalo, Cleveland, St. Louis and Seattle, for example, has exceeded 85 percent in two years."