SOME OF THE country's largest corporations are taking close looks at Washington's public schools and, thanks to the sales skills of Superintendent Floretta McKenzie, are finding it a pleasure to do business in the classrooms. In less than a year, Mrs. McKenzie and assistant Pete Weaver, a former business executive himself, have drummed up more than $1 million from private industry for a range of imaginative programs. Only this week, the Control Data Corp. announced one of the largest in this series of joint ventures: "PLATO," a sophisticated computer instruction system will be available this fall for 400 students at Spingarn High School in Northeast.

Eight computer terminals and an array of instruction programs in reading, math, social studies, science, career planning and writing skills will be made available at a total cost to Control Data of $250,000. Students can test themselves with signals to the terminals, proceeding individually through various programs, in a system that has been tested out elsewhere by unskilled adults, by students needing remedial work and by colleges.

Why is Control Data's chairman of the board, William C. Norris, interested? He considers the project an "investment" that, if successful in the nation's capital, can have a "ripple effect throughout the urban systems" that will be good for business. The payoff, he believes, comes in a "better prepared, more productive work force capable of using advanced technology."

Another reason for the interest, Mr. Norris notes, is the "enlightened approach" and spirit of Superintendent McKenzie. He has a point: among her other projects are five new "career high school programs" to begin in the fall with the help of national and local businesses--in communications, engineering, health services, hospitality (including health management and culinary arts) and business and finance.

An incomplete list of contributors of anywhere from $10,000 to $500,000 includes the Digital Corp., Goldberg/Marchesano and Associates, the Mobil Oil Corp., Xerox, C&P Telephone, IBM and Geico, with still others making arrangements for their donations.

It is not a matter of merely taking money from any corporation seeking publicity. Mrs. McKenzie and her staff are weighing serious, practical proposals for projects that will link students in the schools with careers afterward. "Sometimes I feel discouraged that so many of us in public education still see corporate 'involvement' as a matter of volunteerism or philanthropy," she says. "Productive working relationships seldom endure without a quid pro quo. . . . It's time for the managers of public resources to stop trying to pick corporate pockets, and to start helping our private sector companies find cost-justified approaches to coupling business interests of their shareholders with the educational interests of our young people."

It's a deal.