Starting in September, the District of Columbia school system will begin requiring first through third graders to master a set of "critical skills" in reading and mathematics each semester before they will be promoted to the next semester's work.

Under a detailed Student Progress Plan announced Friday by Superintendent Vincent E. Reed, the pupils in the three grades will have to pass tests showing they have learned all the required critical skills each semester and at least 70 percent of a broader list that includes these skills as well as less important ones.

Reed's plan -- a refinement of the D.C. School Board's policy to end "social promotions" of students when each school year ends will also sharply increase parential involvement in the children's education.

Parents will be told at the beginning of each school year what skills the children will be expected to master that semester. Then, halfway through the semester and at the end of the semester, the checklist will be attached to the pupil's report card showing whether the child learned the various items. Teachers will be expected to give parents tips on how they can help their children master the various skills.

Reed has staked his reputation as superintendent on a range of programs designed to upgrade the quality of the city's publis schools, where, in the past, numerous students have graduated from high school without being able to read. The D.C. School Board has already raised high school graduation requirements to make them the stiffest in the Washington area.

"It's almost criminal to pass kids" simply because the semester or school year has ended, Reed said. "We're saying. 'Stay down there till you get that work.'"

He said teachers and parents should not worry so much about the stigma" of being held back to fully learn various skills.

"It's a greater stigma when you come ut of the 12th grade and can't read," he said.

The reading checklist for the first semester of the first grade, designated 1A, for example, contains 71 items, when 24 of them identified as critical, meaning that a pupil must be able to perform them before he can go on to the next semester's work.

Reed said the reading checklist concentrates as well as writing ability at an early age.

The mathematics program for semester 1A includes 19 skills to be mastered, with nine of them deemed critical. One such critical math skill for a first semester, first grader is to be able to look at two basic fractions, such as 1/2 and 1/4, and know that 1/2 is larger.

If the pupil passes the tests showing that he has mastered the various skills required in the first, or A, semester of the school year, then the pupil is promoted to the second, or B, semester.

But if the pupil has not learned enough, he will be held back until he has mastered the necessary skills, Reed said. If the pupil is weak in math or reading, then he will be advanced in one but not the other. Children who need help in either reading or math will be placed in a "transition" class for intensive work on their weak skills.

Reed said that last year 18 percent of the first through third graders were not promoted to the next grade. But he said that with the school system's introduction in all schools this year of the Competency Based Curriculum, a citywide learning program of basic skills, he is hopeful that the failure rate will be reduced to 10 percent or less.

Reed said the new program listing various skills to be learned at each grade level should reduce the number of failures still further.

The superintendent said the Student Progress Plan with its lists or requirements for each grade level will be expanded to include the fourth through sixth grades in the 1981-82 school year. Three more grades will be added in each of the successing two school years as well, Reed said.