IN SOME of Washington's poorest areas, the average household income is less than $7,000 per year. As few as two of every 10 adults have earned high school diplomas. Not surprisingly, these are homes without any of the ordinary educational support that kids from other backgrounds routinely get. There are no dictionaries or encyclopedias or books of any kind. To schoolchildren who live in such an environment, a trip to the library on their own can also be a daunting experience. That is why the District's Home Study Program is such a promising idea.

The city's Housing and Community Development Department and the D.C. public schools have opened study rooms at the James Creek and Sibley Plaza public housing complexes. There are desks, encyclopedias and other reference books -- and even computer terminals. A director and volunteers are there Monday through Thursday from 6 p.m. to 8 p.m. to help children complete their homework. Coordinator Robert Abney says that about 200 elementary school students have signed up at the two sites. About 70 youths come at least one evening each week. Teachers say that many of those children have turned in completed homework and are learning how to use reference books at a much earlier -- and critical -- age.

Mr. Abney wants to open 10 more study centers at other public housing complexes. The D.C. Board of Education should welcome the idea, and it might not have to foot the whole bill. The Riggs National Bank, for example, donated $10,000 to one study center, and 15 bank employees signed on as volunteers. Another study center is being run by the St. George's Episcopal Church in Northwest with money from the Episcopal Church's Office of Black Ministries.

As a result of all this, a lot of children have a quiet place to study with materials that their families could not have afforded on their own. The program should be expanded.