The Control Data Corp. yesterday donated a $118,000 computer instruction system to the D.C. public schools, the latest and one of the largest in a series of joint ventures between the school system and the private sector.

The Minneapolis-based company will install eight computer terminals at Spingarn High School in far Northeast, where student test scores are among the lowest in the city. Starting in September, some 400 students there will be able to receive computer-assisted instruction in reading, math, social studies, science, career planning and writing skills through Control Data's well-known PLATO educational programs. The total cost to the company, including installation of equipment and teacher training, will be $250,000.

"Public-private partnerships" have been one of the major thrusts of Floretta D. McKenzie's first year as school superintendent. Shortly after she took the job last July, she assigned one of her assistants, former business executive Pete Weaver, to the full-time job of trying to interest corporations in forming joint programs.

As a result, McKenzie and her staff are currently finishing plans for five new "career high school programs" to begin next fall with the help of local and national businesses. And the schools have received pledges of more than $750,000 from private industry for various educational programs.

The career schools will be in the areas of communications, engineering, health services, hospitality (including hotel management and culinary arts) and business and finance. McKenzie said yesterday she could not yet reveal the names of all the corporations involved, but school officials have said previously that the public relations agency of Goldberg/Marchesano and Associates would help set up the communications school.

The total amount of funds the corporations have contributed to the career programs could not be learned yesterday, but Goldberg/Marchesano alone has already committed $20,000 to the communications program and may donate more in the future.

In addition, the Mobil Oil Corp. recently agreed to give the schools a three-year $500,000 grant to fund a performing arts program, according to Janis L. Cromer, spokeswoman for the school system.

Over the past year, the Digital Corp. has donated $25,000 in computer graphics equipment to Ballou; Xerox has committed $42,000 for 60 summer jobs for public school students; C & P Telephone has donated $10,000 towards the production of take-home assignments for parents to do with their children; and IBM loaned one of its executives to the school system this year to help interest the private sector in the schools, Cromer said.

School officials said that the corporations involved with the career high schools will help in training teachers and in writing up curriculum for these special programs.

The career programs will operate as "schools within schools," similar to the math/science program at Ballou High School, Cromer said, which has a different curriculum and set of teachers from the rest of the school.

The communications program will be located at the Lemuel Penn Career Development Center on Third St. NE; engineering at Dunbar High School, 13th St. and New Jersey Avenue NW; health sciences at M.M. Washington, O and North Capitol streets NW and Eastern High School, 17th and East Capitol streets SE; hospitality at Roosevelt High School, 13th and Upshur streets NW; and business and finance at Woodson High School, 55th and Eads streets NE.

Efforts to enlist private sector help actually began more than a year ago when the Geico Corp., the city's major underwriter of auto insurance, gave the school system a one-time $600,000 grant so that it could continue to offer driver education, a program which was scheduled to be cut in the 1981 school year for lack of funds.

McKenzie said yesterday that she hopes Control Data's computer system will help D.C. students "be more attuned to the demands of the job market . . . it also demonstrates that our students are capable and worthy of investment from the private sector."