IN ANY SCHOOL SYSTEM, however important the principals are, the quality of education depends fundamentally on the quality of classroom teaching. Following that axiom John C. Alwood, the highly successful principal of Fairfax County's huge Lake Braddock Secondary School, says that in September he will return to the classroom to teach math.

School systems have the bad habit of pulling excellent teachers out of their classrooms and putting them into administrative jobs. The destructiveness of that practice is a point repeated many times in the long shelf of studies of American education that have recently appeared. "The notion seems to be that, if you are good, you will move out of the classroom and become a school counselor or a principal -- or a football coach," Ernest Boyer wrote in the Carnegie Foundation's book, "High School." As an answer to that presumption, Mr. Alwood's decision has special meaning.

There's no doubt that he's good. He opened Lake Braddock 13 years ago and, under his management, it has become the biggest, and one of the best, schools in Northern Virginia. When he returns to teaching students he will have the special and senior standing that Mr. Boyer of Carnegie has urged school boards to establish to hold more of their best people in teaching careers.

Evidently a lot of people have begun to think that teaching needs more support than it has been getting, both within school systems and from the public generally. Several weeks ago, in one notable example, a group of Prince George's County businessmen offered to support the recruiting of teachers for their schools. Mr. Alwood is making a contribution of a different sort, but it pushes toward the same admirable purpose.