Teachers at Gregory Elementary School in the heart of the west side ghetto here became concerned when Arthur, a slight, friendly eighth-grader who serves as the basketball team's mascot, fell two years behind his class in reading.

The youngster was bright, they said, but he rarely applied himself to his studies and he was getting little attention at the rundown housing project across the street, where he lives with his mother and a dozen brothers and sisters.

But Arthur's teachers expect to improve his performance with a new remedial reading program for small groups of students that features special tape-recorded lessons on vocabulary and comprehension.

That reading class is being paid for by a $3 billion program called Title I, the nation's largest federal education program. For Gregory, an all-black school with 575 students, it means another $140,000 this year for more teachers, programs and equipment.

But the coming of the Reagan administration has meant tough times for advocates of federal aid to education.

The administration proposed cutting Title I appropriations by a third for the current school year. Congressional friends of the politically popular program -- it reaches 5 million children in 14,000 of the nation's 16,000 school districts -- held the cuts to $100 million instead of $1 billion.

Program directors say the cuts still hurt. In Chicago, for example, funding will drop from $60 million to about $56 million. That means 4,000 of the 67,000 students in the system who got extra reading, math or other help last year are not getting it this year.

In St. Louis, administrators dropped Title I classes from the high schools because of budget cuts, and Detroit had to drop students from the program as well, officials said.

"We have a chance to reach the kids we couldn't reach any other way, who are behind for a thousand reasons, and now they're taking that away from us," said Michael Striegel, principal at Gregory Elementary. "The progress has been measurable and real. If these kids don't make it, we're all going to end up paying for it anyway."

More than two-thirds of the students at Gregory qualify for Title I aid, but there isn't enough to go around.

So the school is trying to help about 160 students through the reading classes, an early intervention program for 6-year-olds who can't recite any colors or numbers and aren't ready for first grade, and a guidance program that focuses on study habits and career goals. Still, previous cutbacks forced school officials to abandon their most successful program, one that placed troubled students in separate classes half the usual size.

Even Education Secretary Terrel H. Bell, who is generally enthusiastic in cutting his department's budget, is a fan of Title I.

"It took us a while to learn how to teach disadvantaged children," he told a congressional hearing earlier this year.

"But now that's a program you can brag about." Test scores in many area are on the rise, he said.

Striegel agrees with Bell. "In the early years of the program, Washington was literally throwing money at us and the schools didn't know what to do with it," he said. "But it has grown into a fantastically good support program."

While most educators call the program a success, a few critics say its very popularity makes it too scattered and poorly targeted to be of much lasting benefit.

And although local and state studies show some impressive test gains, a new $16 million national study sponsored by the Education Department does raise some doubts about its effectiveness.

The latest reports from the Systems Development Corp. of Santa Monica, Calif., show that Title I students make some gains over their disadvantaged peers in math in grades one through six, but in reading only in the first three grades. The study suggested an examination of the selection system, contending that the extra help is going to too many students who aren't behind.

"In general, regardless of how many years students participate in compensatory programs, they lose ground to their regular peers," one of the reports said.

"Although society cannot merely write off the chronic low achievers, it is clear that present compensatory efforts . . . do not lift them anywhere near to the levels of their non-participant peers."

Marshall Smith, a professor of education policy at the University of Wisconsin and an aide to former education secretary Shirley Hufstedler, is one of the few experts openly skeptical of the program. He said the Santa Monica firm's study, and others like it, show that Title I "is barely moving test scores while kids are in the program. It has no proven effect on dropout rates or employability."

But most, like Maryland Superintendent of Education David W. Hornbeck, praise Title I. Hornbeck said that last year Baltimore youngsters scored at the national levels for the first time. He gives much of the credit to the extra work for poor achievers.

Others say the program's advantages go far beyond the rise in test scores. Some say it has been worth the expense simply because it made school districts pay attention to poor children.

Paul Smith, director of research for the Children's Defense Fund, echoed the feelings of many Title I supporters when he said the program's biggest advantage has been "showing teachers that they can reach and teach disadvantaged kids."