Saving children lost in the system; City Kid, by Mary MacCracken. Boston: Little, Brown & Co. $12.95.

Luke is silent and withdrawn as he hunches over a piece of drawing paper, oblivious of his teacher and classmates. He is only seven years old, but he is already in big trouble. He is failing second grade, and his 24 arrests for arson, theft, and truancy have labeled him a "socially maladjusted juvenile delinquent."

But Luke, the "city kid" in this true story, is fortunate. He is found by the author, Mary MacCracken, who comes to School 23 in Falls City as therapeutic tutor. She is part of an experiment to see if emotionally disturbed children can be reached and saved through one-on-one help from skilled, loving, teacher-counselors.

Mary MacCracken's approach is unorthodox. She doesn't see Luke as a problem, but as a person -- a sensitive boy coping as well as he can with the overwhelming problems of abject poverty and a broken home. Young as he is, he cooks and cares for his mother, who is often ill, and his younger brother and sister.

Mary MacCracken approaches Luke not as an authoritarian figure but as a friend he can trust -- someone who genuinely believes he is worthwhile and capable of learning.

She goes to his world -- she doesn't ask him to come to hers. On his turf, she sees the depths of his despair -- the squalor in which he lives, the loneliness he feels. They share adventures, going to a corner donut shop, crossing a stream and falling in, sitting in Luke's secret "mountain" retreat under a water tower on a hillside overlooking the town.

Mary MacCracken doesn't have any tools to work with except broken crayons, paper, and imagination. She writes down stories she draws out of Luke to go with pictures he has madE. She meets his mother and enlists her aid in making him do homework. And she doesn't give up. When Luke withdraws again, disheartened at having to repeat the second grade, she starts all over, and this time the two are so successful; he skips third grade and rejoins his original class.

For Luke, the story has a happy ending. For Louisa Mae, it does not. Louisa Mae, so badly abused she once runs screaming down the street in her underwear, disappears one day. She is nowhere to be found.

Unfortunately, there are more Louisa Maes than there are Lukes, more children who get lost in cities or in educational systems which can't provide people like Mary MacCracken to save them.

Mary MacCracken wrote two other tender stories -- "A Circle of Children" and "Lovely," both TV specials -- based on her earlier experiences teaching seriously emotionally disturbed children. She meets Luke when she has gone back to college, at age 44, to get her certification to teach in a state-approved school.

WE glimpse her struggles with math, after being away from school for 25 years , and share her frustrations with mid-terms, bullying professors, and seemingly unrelated courses. We also glimpse a warm, rich, private life with her own children and step-children and a new marriage partner who is very supportive of her goals.

The story is told in a simple, straightforward narrative, almost as a "how-to" primer, which is the more valuable for being real. There are limits to the first person, however, and at times I yearned for a third person account, which might have probed more deeply into both teacher and student.

Still, there is much to appreciate. Mary MacCracken pays tribute to teachers who deal daily with rooms full of unruly, unkempt kids and manage to do so with an almost comic-tragic combination of toughness and compassion. She acknowledges the importance of leadership from principals like the one at School 23, who set the tone for good teaching, no matter what.

And while we are helped to see flaws in the overall educational system and the educating of teachers, we also see there are solutions such as the tutorial program which involved the schools, the colleges, and a community mental health group.

Most of all, we see what one inspired teacher can do. "None of these children seemed so terrible to me," Mary MacCracken says. "Where was the hostility that I had read so much about? These kids seemed to crave attention rather than reject it. Maybe the secret was getting them while they were young . . . . What all these kids seemed to want most was somebody to talk to. Could it possibly be that simple?"

It could. Somebody to talk to and somebody in their corner. When Mary MacCracken hears Luke called "the rottenest kid in the neighborhood," she fights back. "Luke isn't rotten," she says. 'He's good and he's smart. He was just scared and angry and he didn't know how to tell anybody so he set some fires instead."

When Mary MacCracken is through with Luke, he doesn't set fires anymore. Only his newfound yen to learn burns bright within him.