Reading and mathematics achievement in Washington's public schools fell slightly last year, according to a new test report that shows that average performance here was considerably below that in other big cities as well as far behind national norms.

Supt. Vincent Reed, who issued the report, said he "didn't anticipate any improvement" in the tests taken last spring at the end of his first full year in office.

"Hopefully, we will see some signs of improvement this spring," Reed added. "I don't want to go with a pie in the sky, but we are going to do everything we can to make (improvement) possible."

Reed's new curriculum, being tried this year in 26 schools, stresses step-by-step instruction in basic skills and uses tests frequently to measure achievement. It turns away decisively from the de-emphasis of tests and structure that marked the innovations of the past decade.

The standardized tests, whose results are contained in the new report, were given last May to a 10 per cent sample of students throughout the city.

They showed D.C. first-graders scoring as high in reading as national norms. However, second-graders averaged six month below the norms, and by fourth grade, students here were 1 1/2 years behind.

At the end of senior year in high school, the report said, the average reading performance of D.C. students was the same as the national average for the start of 10th grade - a deficit of 2.8 years.

The city's 12th-graders scored even lower in mathematics, avdring the same as ninth-graders nationwide or 3 1/2 years below grade level.

Until ninth grade, the report said, mathematics scores were slightly above those in reading, but still below both national and big-city norms.

For example, in most elementary and junior high grades, Washington students scored two to six mohs below the big-city average in mathematics. However, both 11th- and 12th-graders here were more than two years below the big-city mathematics norms.

Compared with tests taken a year earlier, the performance of D.C. students in reading fell in all grades in 1977, except grade one where there was a slight improvement and grade three where there was no change. Mathematics performance dropped in grades two, four, eight, nine and eleven, rose in grades three, five, six and seven and was unchanged in grade one. There was no comparison for 10 or 12.

Since 1971, only D.C. first-graders have shown sustained improvement on the standardized tests. All other grades have fluctuated around roughly the same low levels. Most upper elementary classes have ranged from the 25th to the 35th percentile nationwide (compared to the national norm of 50). Junior and senior high classes have usually averaged from the 20th to the 25th percentile.

The multiple-choice tests are prepared by the California Testing Bureau, a division of McGraw Hill Publishers. They last about three hours for reading and mathematics together.

During the 1960s, the tests were administered to all D.C. students in several grades. In 1970 and 1971 they were given to every student in elementary and junior high schools as part of the reading mobilization plan, prepared by psychologist Kenneth B. Clark.

Under both arrangements, the school system issued data on the average performance of students in particular schools, permitting school-by-schoocamparisons that showed a wide range of achievement.

After the Clark plan was dropped, the test were given to only a 10 per cent sample of students to show a system-wide average.

his year the testing policy is scheduled to change again with standardized tests being given this spring to all students in grades 3, 6 and 9 as part of Supt. Reed's competency-based curriculum. Reed said that school-by-school averages will be issued next summer for the first time since 1971.

Reed and other school officials refused to speculate on the reasons for the test results. School board member Betty Ann Kane suggested, however, that the strong performance of first-graders probably reflects the success of the school system's unusually widespread program of free nursery schools for 4-year-olds and all-day kindergartens for children aged 5. She said no comparable effort had been made in later grades.

"Some people see these (early education) programs as an expensive luxury," Mrs. Kane said, "but I think they're needed educationally, and they've paid off.

Several testing experts suggested that the fact that D.C. students generally fall further behind national norms the longer they stay in school reflects both the nature of the standardized tests and the school curriculum.

In the lower grades the tests measure relatively few concrete skills, and the range of achievement is narrow. However, the school curriculum and the tests change markedly in fourth grade, when students are expected to apply skills they have already learned.

There are more substantial changes at grades seven and 10, the start of junior and senior high schools, with test quesitons reflecting school work that is increasingly analytical and varied.

At each of these points of major change there is a substantial drop in the relative performance of Washington students.

In addition to the standardized tests in reading and mathematics that contain "school-type" questions and problems, the school system administered a special test to all its 10th-graders last year, measuring "everyday skills." These included finding information in a telephone book, figuring discounts on merchandise, and filling out a job application.

The test had no expected level of performance.

Generally, the results were better in reading than in mathematics. For example, about 80 per cent of the 10th-graders could follow recipes or the instructions on medicine bottles. However, only 70 per cent could make change correctly, only 35 per cent could fill out a job application, and only 13 per cent could figure the sale price of an article when they were given its regular price and a rate of discount.