Test scores of students in several big-city school systems have risen significantly this spring, an encouraging development to educators who regard poor scores as a symbol of the weaknesses of inner-city public schools.

Improved performance, particularly among black or Hispanic students in lower grades, has appeared in tests of achievement and basic skills in cities as diverse and geographically scattered as Washington, D.C.; New York City; Trenton, N.J.; Atlanta and Oklahoma City, according to an informal survey.

Moreover, at a meeting in Boulder, Colo., this week sponsored by the Education Commission of the States, many of the 200 state education officials attending noted that local testing revealed increased mastery of basic skills.

Weighed against the good news from Washington and other cities, however, are inconclusive or deteriorating results in some other urban school systems. While pleased over the improvements, professional educators warn against drawing premature conclusions as to the national trend.

To some extent, demographics may be helping some schools. As the number of elementary schoolchildren decreases sharply in the wake of the population explosion known as the "baby boom," instructors can concentrate attention on fewer children, although in many areas the number of teachers is being cut as enrollments drop.

Educators also caution that along with indications of improved mastery of basic skills by younger children, nationwide tests are turning up indications of a decline in the ability of older students to apply those skills, to solve problems, to think clearly and to express themselves logically and succinctly. These results could reflect the fact that the older students did not receive the benefits of intensive grounding in basic skills that is now being extended to younger children.

Interpreting the changes is further complicated because several major systems, including those of Boston and Chicago, have not received this year's test results, and results from earlier years appear inconclusive.

Even so, the recent results have cheered many big-city school administrators, for whom test scores increasingly have been the touchstone of performance and political survival. The results are certain to provide ammunition for education groups fighting to save federal programs targeted to help blacks and minorities.

Roy H. Forbes, president of the Denver-based National Assessment of Educational Progress, said his organization would soon release a report showing a connection between rising test scores and federal money spent in schools to aid disadvantaged children.

"If federal funds are cut, this can't help but hurt the scores," said William Mathis, deputy assistant education commissioner in New Jersey. "We've got hard evaluations that show payoffs."

Mathis said tests of students receiving extra language arts or reading instruction financed by federal aid have improved their ranking against other students nationwide by as much as 16 percentile points.

Improved scores provide a brief respite for school officials under enormous pressure to reverse the downward trend. The chief executives of several big-city school systems attributed the higher scores primarily to introduction of academic programs aimed at improving basic skills, raising scores and, indirectly, deflecting public criticism.

In announcing dramatic gains in math scores by District of Columbia ninth graders, Acting Superintendent James T. Guines said Wednesday that the socres were "the best hard-nosed testimony" that the school system's three-year-old competency-based curriculum is working.

Test results in Atlanta were even more dramatic.Forty-three percent of the city's students read at or above the national norm on the California Achievement Test, up from 31 percent in 1980. In math, 47 percent were at or above the norm, up from 33 percent a year earlier.

Atlanta school administrators credit the improvements to more classroom training in test-taking and efforts to identify quickly and concentrate educational service on students whose progress flags. A computerized monitoring system tracks each student's progress and issues monthly progress reports. Armed with these reports, administrators call up extra teachers to work with pupils with problems.

Oklahoma City Superintendent Tom Payzant introduced a new reading curriculum in the lower grades. It involves frequent testing, with results printed out by computer within 24 hours to provide for speedy classroom follow-up.

Payzant said improvement has been so substantial that the system will be introduced in reading and math in the system's middle schools next fall.

Pleased as administrators are with such results, other statistics from a variety of cities caution against overly optimistic conclusions at this stage.

In Los Angeles, scores of third, fifth and eighth graders in basic reading and math skills declined this year. School officials blame the confusion caused by busing, a steady influx of Mexican children with language difficulties and too much television watching.

In st. Louis, the percentage of eighth graders passing three minimum-skills tests rose slightly this year, but the percentage passing the crucial reading and math portions of the series dropped.

In Oklahoma City, where Payzant reports "substantial improvement" for the third consecutive year by pupils tested in kindergarten through fifth grade, results did not improve significantly for children in the lowest quarter of students in the system.

Trenton provides a telling example of how far city schools must go even after making substantial improvements. The percentage of students in grades 3, 6, 9 and 11 passing a state test of minimum skills has risen 17 percent in three years. But the number failing is still 49 percent, compared with a failure rate in many New Jersey suburban schools of less than 10 percent.

School officials describe the test as a fairly simple one that measures basic skills needed to survive in society, such as ability to complete an income tax form, balance a checkbook or read want ads.

In New York City, where 49.6 percent of students in the second through ninth grades were at or above grade level in the California Achievement math test this year, scores dropped sharply in the upper grades. City officials acknowledge that students who adequately acquire basic skills seem to have trouble applying the skills to solve problems in higher grades.

That problem has been detected in the reading, math and writing tests given every five years by the National Assessment of Educational Progress. While these tests have found improvements at lower grades, particularly among blacks and minorities, the ability of 17-year-olds to write a persuasive essay, to solve a math problem or to answer a question when the answer is implied but not given have declined steadily.

Despite the improvement in big-city basic skills, scores of college-bound seniors taking the Scholastic Aptitude Test declined this year for the 15th consecutive year. And some educators question the usefulness of the skills being inculcated by the back-to-basics curriculums now popular.

"My sense is that schools are focusing their instructional activities in areas that show up in the testing mechanisms that are around," said Vito Perrone of the Boston-based National Consortium on Testing. "I'd be surprised if that didn't translate into scores. Whether it translates into enlarged literacy, problem-solving skills or ability to use the culture, I'm not convinced.

"When I visit schools, I don't have the sense that kids write or read very much. They write paragraphs or sentences, but the reading is textbook-oriented and doesn't include many books. I guess I'm not very impressed with the [school systems] that talk about imnproving these particular scores," Perrone said.