The federal government's $266-million-a-year migrant education program often serves children who don't change schools, while failing to reach the "truly migrant," a new Department of Education study concludes.

The study also said that while children participating in the program showed academic gains on test scores, the advances could not be attributed to migrant education.

As a result, it said, the department should consider changing the name and mission of the 14-year-old program, which was designed to serve the children of migrant farm workers, or make essential changes in it and increase efforts to identify and recruit "highly migrant" children.

The $3.7 million study by Research Triangle Institute of North Carolina was immediately challenged for design flaws by several supporters of the migrant education programs, which served about 550,000 youngsters nationally last year.

The policy implications are unclear, because Secretary of Education Terrel H. Bell has been briefed only on the broad outlines of the study, a department official said yesterday. Migrant education is part of the so-called Title I program for disadvantaged children, which has remained separate from the Reagan administration's new push for block grants.

The study said that nearly half of the students served by the migrant program were enrolled in one school district for the entire year. But Bruce Hunter, a former staffer for the Education Commission of the States' migrant task force, noted the statistics don't account for children who may have moved just before enrolling for the school year.

The apparently static population also could be skewed, others said, because the program is open to children for five years after their parents leave the migrant stream, because of the presumption that constant moves have disrupted their education.

Gerald P. Burns, the department's project officer on the study, acknowledged yesterday that the study included several caveats about its key findings. A summary of the four-year study noted, for instance, that its enrollment data didn't count any moves that didn't lead to an enrollment.

Vidal Rivera, acting director of the department's Office of Migrant Education, said yesterday that "there's no doubt we have to improve identifying and recruiting migrant children. They're just not going to walk into class. You have to go out into the fields and the camps." He said his office has encouraged states to do that.

The study said that migrant children are generally recognized as the most educationally disadvantaged group in the nation. They are usually older than children in the same grade, and show rapid dropout rates beginning in the eighth grade. Burns said the data showed only about half as many migrant eighth-graders as fourth-graders, presumably because they enter the work force then.

Migrant children miss about six weeks of school a year, but when they are enrolled their attendance rates are somewhat higher than the general school population, the study found.

Those in grades two, four and six showed significant gains in reading and mathematics scores, but their achievement seems to fall farther behind the general population's as they grow older, it said. Although the study could find no evidence the gains were attributable to the program, Burns cautioned: "We couldn't find an impact, but we're frightened to say the program didn't have one."

The study was critical of the Migrant Student Record Transfer System, which is supposed to follow the moves of children. It said a "disproportionately large segment" of the children purged from the system in early 1979 for inactive files were eligible for the program. They had moved and just not been picked up by the system, Burns said.