ALREADY THE RITES of June have begun in the classrooms of the District's public schools --not the formal closing ceremonies, but the final fortnight of gathering in books, fanning out on field trips and wrapping up most of the intensive instruction to meet teachers' quitting time for the summer. But also this month, more students than ever will be back in school--in what looks to be the most promising program of its kind in years.

Only two summers ago, in one of its weaker moments, the city's school system canceled its entire summer schedule as part of its budget-cutting. Like other of its ill-directed attempts at economy--eliminating foreign languages in elementary schools and cutting way back on music instruction--the closing of summer school merely compounded the educational challenge for teachers during the rest of the year. It was, and still is, a matter of basic math:

Q: If Earl and Roberta are a year behind their grade level in reading skills in June and can't go to summer school, where will they be in September?

A: No closer, even if for no good reason they happen to be "promoted" to the next grade anyway.

But come June 30 this year, an estimated 13,000 students will begin summer classes, from remedial help in basic English, mathematics, science and social studies to various enrichment courses, including a computer camp, theater study and radio work. The price tag? School officials say that about $1.9 million has been earmarked for the program. That, out of a budget of more than $300 million, has got to be money well spent.

Summer may be a traditional time for fun, for a change of pace and for different kinds of "education." But when students are struggling just to keep even for nine months of the year, it can mark the difference between valuable time wasted and a feeling of confidence and progress.