District School Superintendent Floretta D. McKenzie recommended yesterday that D.C. public schools use new standardized achievement tests in reading and mathematics starting in May 1987, the first time the tests would be changed here in 12 years.

Of the three tests under final consideration, McKenzie asked the school board to adopt the 1981 edition of the Comprehensive Test of Basic Skills (CTBS). It is the oldest test in the group and the one on which city students scored highest in a sample testing last spring. McKenzie said it should be used because it best matches the schools' present curriculum and would produce the least change in reported scores.

According to results released yesterday, D.C. students taking the newer CTBS averaged from one month to 1.4 years below the scores they made on the older CTBS, used by the school system since 1975. The norms on that test are based on sample nationwide testing conducted in 1972-73 with questions that are still being used.

On the California Achievement Test, whose sample nationwide testing was conducted in 1984-85, the D.C. students averaged from 2 months to 1.5 years below their old CTBS scores. On the Stanford Achievement Test, prepared in 1981-82, the D.C. average scores ranged from 2 months to 2.7 years below those on the old CTBS.

"We knew the scores would go down," said David L. Huie, the school system's director of quality assurance. "The kids around the country have become smarter than they were in 1973 . . . . We're putting a higher hurdle in front of our kids."

He added that the lower scores do not mean that actual achievement of District students has declined, but that their relative standing, compared with other children around the country, is not as high as it was when measured against the easier standard of more than a decade ago.

The grade-equivalent scores, used by the District for reporting its test results, are based on the number of test questions that at least half the children in any grade answered correctly during the nationwide sample testing.

Scores of District students have improved substantially on the old CTBS since 1979. In the test results for last spring, the median or mid-point scores here were comfortably above the national norms in both reading and math for third and sixth grades, at the norm for ninth grade mathematics, and one year below it for ninth grade reading.

On the newer CTBS, the D.C. scores were above the national norm only in third grade mathematics. They averaged several months below the norm in math for sixth and ninth grades. In reading the averages were seven months below the norm for third grade, 1.3 years below the norm for sixth grade, and 1.5 years below in ninth grade.

McKenzie had been scheduled to recommend a new test in October for use city-wide this spring. However, officials said she delayed picking a new exam so the school system would have another year to change its curriculum to tie it more closely to the new test.

Yesterday Huie told the school board's research and evaluation committee that school officials also wanted to keep the old CTBS in grade 11 this year to measure the impact of the program to raise high school achievement, which still lags far below the test norms.

No sample testing with the three different exams was conducted last spring in 11th grade, although, under McKenzie's recommendation, the 11th grade test would be changed next spring along with the others.

The recommendation was approved by the board committee yesterday and is scheduled to be considered by the full board March 19.

A new edition of the CTBS test is tentatively scheduled to be issued in mid-1988, the CTB/McGraw Hill company said yesterday.

Public schools in Maryland use the 1977 California Achievement Test and those in Virginia use the 1978 test of Science Research Associates. Both states report their scores in percentile ranks -- from 1 at the bottom to 99 at the top, the method most widely used around the country, instead of grade equivalents.