AMERICAN CHILDREN'S progress in school is slowly but clearly improving. High school students are taking more academic subjects, the College Board reports, and more students are taking advanced placement courses. The change is not large, but it's in the right direction. Teachers seem to be grading more rigorously. As a result, not surprisingly, the College Board reports that the average scores in its Scholastic Aptitude Test have also risen.

The long fall and recent rise in SAT scores trace an important passage in this country's social history. The fall began in 1964, at first because more youngsters were taking the test and going to college. But by the late 1960s the scores were dropping for another and less promising reason -- widespread relaxation of the traditional disciplines, in the spirit of the times. The long decline ended at the beginning of this decade, and for the last four years the average scores have been rising, at first hesitantly but in the past year more substantially. The test is taken by nearly a million students each year, a third of all high school seniors. Since they include most of the brightest students, a great deal depends on what they know.

But the same hopeful pattern emerges from broader testing. The National Assessment of Educational Progress has been measuring the reading achievement of American schoolchildren for the past 15 years and has found general improvement. While black and Hispanic children still read, on the average, at levels below those of white students, the National Assessment shows that they are improving more rapidly. Among children in middle-class urban families, there has been little change in reading ability over these 15 years. But among children in poor, urban neighborhoods, the gains have been striking. Although the gaps among class and race in these kinds of averages are still wide, these tests provide persuasive evidence of progress in closing them.

Not all of the news is good. Reading achievement among young children, particularly young black children, rose rapidly in the 1970s but not since then. The scores leveled off in the same years in which the enrollments in pre-primary school programs such as Head Start began to level off. Scores among black high school students, which showed no improvement in the 1970s, are rising now -- but they reflect, apparently, gains made when they were much younger.

Taken all together, these tests suggest that for bright students the quality of a high school education, and its focus on serious subjects, makes a difference. But the crucial period is much earlier. Reading achievement among high school seniors depends heavily on what happened in the primary grades, in even earlier education, and at home.

Education, both early and later, is expensive. But spending on schools can produce results that are visible, among other places, in these test scores.