In their studies, the children of Ruth and Peter Nobel were working well above grade levels with a teacher they loved and respected.

Their classroom was free of foul language, drugs and overcrowding.

But their classroom was their living room, not that of a local school, and Mrs. Novel was not licensed to teach. So local authorities arrested the Nobels and put them on trial.

The Nobels, devout Calvinist Christians, rejected conventional schooling for religious reasons. About 10,000 families -- probably not as successful as the Nobels, but ignored or tolerated by local governments anyway -- have their own justifications elsewhere in the United States. For some it simply may be the notion that they can do a better job than the schools.

The issue is educational standards: who sets them and who enforces them. The issue also is children: who is in charge of them, the parent or the state? And, for the Nobels and a relative handful of like-minded families, the issue is the fundamental one of religious freedom.

The family had little legal precedent on its side when it went into court late last year.

In 1972 the U.S. Supreme Court had ruled that an Amish family could withdraw its children from the schools for religious reasons at age 14, two years before Wisconsin law allowed. But the court carefully drew the line at 14, saying nothing about younger children, alternatives to conventional schools, or government supervision of what the Nobels consider a religious exercise: education.

Each year since, small cases scattered around the country have been won or lost on lesser legal questions than the First Amendment.

Last December the Nobles became the first family in recent times to win on the Bill of Rights, when Michigan District Court Judge Gary Stewart ruled that both conventional schools and teacher certification interfered with their religious freedom.

The Nobels' trial, in the rural Allegan County courthouse, lasted one day. It was, said the bailiff on duty then, an extraordinary day, as churchgoers from all over Michigan filled the courtroom and crowded the lawn outside, peering into the courthouse and listening through the windows.

The Nobels and their seven children, five of school age, live about two miles from the Dorr Elementary School.

"Now write the word 'smiling,'" says Ruth Hobel, who is at a table with her daughter Charity, 7, teaching spelling. "Now remember a rule you learned yesterday. If it ends in 'e' what do you do?"

"Drop the 'e' and add the 'ing'" Charity responds.

"Now write the word 'pile,'" says Ruth. "Now 'piling.'"

"Is this the last one?" says the child. It is not, because school in the Nobel home ends at 3:15 p.m.

The other children, on a couch, are reading and writing, getting up to consult an atlas, copying the flags of different countries from The World Book.

Hope, 18 months, and Luke, 4, weave in and out of the living room, demanding carrots from their mother, who gets up to help. Finally, Luke grabs a book, firmly places Hope in a chair and proceeds to imitate his mother's teaching.

"Read this, Hope," he says, putting a book on the toddler's lap.

The schedule is precise for all the children. Abigail, 12, is up at 7 a.m. At 8 there are chores. At 9, prayer; 9:15, math; 10:15, break; 10:30, English; 11:30, reading; at noon, a break; 1 p.m. Bible (except on Fridays when a book report is due); 2, break; 2:15 government or science or art.

Ruth Nobel, 37, who was graduated from Calvin College in education, and Peter, 28, a carpenter, structure the teaching around a home-study course provided by the Christian Liberty Academy in Illinois. Each program is individually tailored to the child.

During the preparation for the Nobels' trial, a psychologist had given each of the children standardized tests for learning achievement. The results played a major role in the judge's decision.

Abigail tested at freshman college level. Charity, then 6, scored at the level of a second-grader, Naomi, 11, who would have been in sixth grade at an ordinary school, scored at an 11th-grade level. Priscilla, 10, and Eve, 9, performed equally well.

Peter and Ruth Nobel take the Bible seriously. It is, they explain, their entire life, which they are obligated to pass on to their children.

Doing so -- even in the town of Dorr -- was not easy, they say. Public schools were out of the question from the start.

"Immorality, the dress, the attitude, the speech, and they can't turn out good students," Ruth Nobel declares.

The family tried a local Christian school but dropped it in August 1978 because of what they describe as "doctrinal" differences.

That was when they started teaching at home. The absence of five children from school in a twon of several hundred did not long go unnoticed.

Under Michigan law, as in many other states, home-based schooling is permitted. But nearly all of these states impose conditions. In Michigan the condition is certification -- the process of licensing teachers. Ruth Nobel, though qualified to be certified to teach, refused to take the examination on religious grounds.

"We had to enforce the standards," said Michael Buck, an Allegan County prosecutor. "We need minimal standards to protect the state's interest in quality education."

Authorities issued a warrant for the Nobels' arrest on charges of contributing to truancy charges, with a maximum penalty of two days in jail, $50 fine, or both. Peter and Ruth turned themselves in and were booked in February 1979.

The couple are fundamentalists, as were their parents. They believe that neither the public schools nor a religious school would continue this heritage in their children.

They accept the U.S. Constitution the way they accept the Bible: literally.

"It [the Constitution] says that government is there to see that citizens keep their rights," says Ruth Nobel. "The government has no rights.

"It would have been so much easier to get certified. But for me, it would have been sacrilegious, giving an honor to the state that belongs only to God. I would not have kept my rights."

The Nobels went into court with many friends, but little law, on their side. One of the couple's supporters was the Rev. Paul Lindstrom, headmaster at the Christian Liberty Academy in Illinois.

Through a network of religion-oriented lawyers, Lindstrom helped provide expert witnesses and attorneys for the Nobels, who were represented by Washington lawyer John Whitehead and others.

Sometimes, in small rural courthouses, judges include their personal handwritten notes from a trial in the public record. Judge Stewart's notes summarizing the arguments presented in the case tell the story:

"It would violate her belief to send them to public school. It would violate her Religious Beliefs to accept certification."

"Would go to jail," he wrote on the final page of yellow legal pad, underlining the words three times.

In his 12-page opinion, Stewart said that "an evaluation of the Nobel children has indicated that all five are intelligent and appear to be well-adjusted and normal."

The state, he said, "has failed to produce any evidence whatsoever on the interests served by the requirement of teacher certification, and the [Nobels'] experts, to the contrary, demonstrated that there was no rational basis for such requirements. . . . For her to accept certification would not make her a better teacher, nor would it make her children more intelligent. . . ."

"It would, indeed," the judge concluded, "interfere with her freedom to exercise her religious beliefs."