Alexandria's Schools have now published figures comparing the average test scores of black students with those of white students. The magnitude of the disparity between them is dismaying. Like the Prince George's County schools, which made similar data public last month, Alexandria's school system is risking reinforcement of the familiar stereotypes about black and white. But as the schools know, these test scores don't tell you anything about race. They tell you a great deal about rich and poor, and the enormous handicaps of the children of poorly educated parents. Both Prince George's and Alexandria hope that these comparisons will draw public concern and support to a strenuous effort to raise achievement levels that can, in fact, be raised.

Children's school test scores usually correlate closely with parents' incomes. The challenge for schools is, among poor families, to break the iron link between parents' economic status and their children's report cards, while preserving and reinforcing that link among the well-to-do. Alexandria's demography is peculiarly unbalanced.

Unlike Prince George's, Alexandria has almost no black middle class. The reason is a pattern of housing that became engrained when Virginia was segregated by law. Alexandria's black families generally have low incomes, while most of its white families range from average to very high incomes. The growing numbers of Hispanics and Asians usually fall in between.

Last spring the average score for white 11th graders in the city's schools, on the standard achievement test that they use, was at the 75th percentile; it means that 75 percent of the 11th graders taking that test throughout the country scored below that level. But the average score for Alexandria's black 11th graders was at the 27th percentile. What does the school system propose to do about that?

One immediate response, already under way, is to break down those averages by school to look for clues in those classrooms where performance is better than family incomes would predict. Superintendent Robert W. Peebles says he also intends to call on the city's civic and service organizations for help in persuading black children that middle-class achievement is not necessarily associated with one race, or poverty with another. But the most important part of the job will be done, as always, by teachers and principals. Perhaps, as Mr. Peebles suggests, the crucial step has already been taken. The schools have already decided to treat this gaping difference in test scores not as a mere reflection of an intractable social reality, but as a failure that possibly could -- with much hard work by the schools and their friends -- be gradually corrected.