They may not know it, but the chief justice of the United States and a Montgomery County teacher have something in common.

Chief Justice Warren E. Burger and Damascus High School teacher Sally Walsh are trying to find remedies for chronic problems that many Americans think have no remedies.

Washington Post staff writer Al Kamen told us in yesterday's paper that when Burger addressed 400 graduates at the George Washington University law school commencement he didn't content himself with deploring the nation's prison system. He made some concrete proposals for improving it.

He said we ought to have a national training center for prison guards, and he suggested some practical and economical ways to establish one.

Burger also proposed mandatory schooling for inmates. He thinks that all prisoners who cannot read, write, spell or do simple arithmetic should be enrolled courses designed to teach them to do so.

Burger pointed out that there are an appalling number of functional illiterates among the young people who are sent to prison. He said it is essential that we teach them reading, writing and arithmetic. "Without these basic skills," he asked, "what chance does any person have of securing a gainful occupation when that person is released and begins the search for employment, with the built-in handicap of a criminal conviction?"

Burger also urged a large expansion of vocational training for inmates, so that when they are released they will qualify for honest employment. He said society has a "moral obligation" to improve prison conditions and help inmates improve their lives.

Sally Walsh is trying to provide similar help to young people who are still in school. She teaches an 11th grade writing class -- a thoroughly frustrating undertaking in a era in which sloppy speech and worse writing are the norm -- not merely for high schoolers but for their parents and teachers as well.

Washington Post staff writer Kathryn Tolbert informed us in her story in yesterday's paper that Sally's emphasis is on straightforward expository writing, not creative writing. In order to help her pupils put together simple, declarative sentences that will convey a practical message, she must first help them organize their thinking. And sometimes she must go one step further and teach a generation of passive TV watchers what the thinking process involves.

It is not enough to give a student a writing assignment and later hand back his paper with a grade on it and the comment, "Needs more detail" or "Needs better organization." Unless the teacher goes over the paper with the student, sentence by sentence -- and if necessary, word by word -- the student is not likely to learn what he did wrong, or how to do better.

And if somebody doesn't teach him to communicate with clarity and precision, he'll have two strikes against him for the rest of his life. He won't be able to write a successful application for a job, he won't be able to make his supervisor understand what's in his mind, he won't even be able to communicate satisfactorily with his spouse or children. Very likely the inadequacies of his own training will be perpetuated in the next generation.

So in a very sense, the chief justice and the writing teacher are embarked upon the same course. They are like-minded people who refuse to surrender to the notion that nothing can be done to make life better or easier for the inarticulate portion of our population that is now being shunted aside to inferior status both socially and economically.

My hat is off to Chief Justice Burger and to teacher Sally Walsh. I hope that President Reagan, the Congress, and school boards throughout the land will note what they are trying to do and give them the support they deserve.

Burger has been criticized for saying that judges have been too lenient and that too many criminals have been turned loose to commit additional crimes. I think that criticism was undeserved, especially in the light of Burger's call for positive programs designed to make every inmate a better and more useful person while he is in custody.

It is relatively easy to stand on the sidelines and deplore existing conditions, as we columnists often do. It is considerably more difficult to suggest practical remedies, and to be willing to work for their adoption.