It's 10:30 in the morning at the Kimball house, and in a book-cluttered upstairs room Rebekah, 12, is scrawling a report on the "Secrets of the Shopping Mall." Nearby, six-year-old Benjamin, his sandy hair tumbling out from under a Yankees baseball cap, thumbs through a fat edition of the "Children's Guide to Knowledge."

Welcome to the Kimball school of learning. No need to check in with the hall monitors (there aren't any). Don't worry about attendance, either (everyone is her -- mom, dad, son, and daughter).

While millions of youngsters troop off to school each morning, Benjamin and Rebekah Kimball roll out of the sack and into the next room or cluster around the kitchen table for their instruction.Their lessons: a hodgepodge of math, science, reading, geography, composition, and other subjects culled from library books, games, educational television, and just plain everyday life. The teachers: mom, and occasionally, dad.

"How do you spell 'national'?" Rebekah yells out.

"How do you think?" replies her mother.

"I know," Benjamin pipes up, "n-a-s --"


"Wait," he says groping through the alphabet, "n-a-i --"


He shrugs and breaks into a singing rendition of the ABCs. Moments later the topic changes from spelling to Spanish.

Que es esto [what is this]?" the mother quizzes.

"La pluma [pen]," Benjamin shoots back.

From Spanish the lesson will probably go on to some addition and subtraction, then more work on the book reports, and then maybe gym class -- a jog around the neighborhood with dad.

"What I am trying to do is to instill a love of learning, a love of knowledge ," Mrs. Kimball says.

The Kimballs are part of a small but mushrooming number of people across the country who are bucking traditional schooling in favor of teaching their children at home. Worried about everything from drugs to discipline in public and even some private institutions, an estimated 10,000 to 30,000 families are believed to be involved in home schooling today --These people are joining the thousands of traditional home-schoolers -- the disabled, slow learners, and children of migrant workers and servicemen.

The nation's classrooms are in no danger of becoming obsolete. But enough people are becoming living-room lecturers to prompt some concern in the educational community, particularly at a time when school enrollments are dropping sharply and the computer revolution may one day turn the household into an information hub. It has also evoked a fiery response from some educators, who believe home-taught children may be growing up in a den of ignorance and will perhaps be ill-equipped to cope with the future.

The reasons for the frontier-spirited drive are many: concern about an "antireligious" atmosphere in schools; uneasiness over the growing problems of sex, drugs, and violence; a desire to tailor-fit instruction to an individual's needs. For some rural dwellers, it is a way to avoid busing their children to distant schools that they think only stifle their curiosity and creativity, anyway.

But the bedrock of the movement is the belief that children can learn as much at home as in school -- and probably more.

At least 32 states have legal provisions allowing schooling outside the classroom. Yet in most cases the home-instruction program must still be approved by local school authorities. Cooperation has prevailed in many areas, with a few home-taught children even continuing to participate in band, choir, and other extracurricular activities at school.

As often as not, however, it has led to legal tussles or threats of legal tussles over an issue as basic as reading, writing, and arithmetic: the parents' right to control their own children vs. the state's right to ensure an adequate education. As yet, the courts have not blazed a clear-cut ideological path, experts say.

In one widely publicized case, the Van Daams of Providence, R.I., have been arrested twice for violation of compulsory-education laws. A judge dismissed the first case and told school officials to draft an application form for private instruction. They did, but the Van Daams rejected it and made up one of their own.A second suit against them is pending. Providence school officials did, however, recently approve another family's request for home schooling.

The Van Daams slipped into home education by happenstance. Both former schoolteachers, Peter and Brigitta Van Daam always advocated sending their children to school, whatever its shortcomings.

But it was their oldest child, then seven years old, who objected. From the moment she stepped into kindergarten, at a private school, she thought it too regimented. After two subsequent years at public schools, she balked altogether. The Van Daams have been teaching their children -- Julia, 10, Jessica, 8, and Percival, 4 -- at home ever since.

"We do not recognize the right of the state to regulate the behavior of the family," says Mr. Van Daam, who installs hot-water systems.

Home-schoolers don't exactly go by the book in their teaching. Some subscribe to correspondence courses and other home-study programs that provide detailed, day-by-day study guides and books. Others map their own curriculum, tapping everything from TV to box-lunch poetry sessions at the local library.

Julia Van Daam, for instance, is taking conversational French with a group of adults. She also works on her classical Greek at a Brown University language lab, takes art at a Montessori school, studies poetry in a class at the public library, and tinkers with electronic hardware under the tutelage of a Brown professor.

The Kimballs, too, have worn a path to the local library. Rebekah alone takes out about 11 books a week. Their makeshift second-floor classroom is a cornucopia of books, games, solar kits, flash cards, and papers.

A platoon of curriculum-support groups has sprung up to help home-schoolers. One, the Home Education Resource Center, was launched last summer by Margaret Johnson of Ridgewood, N.J., who has been teaching her children at home for four years. She has received about 100 requests for materials so far. The Christian Liberty Academy in Prospect Heights, Ill., now enrolls more than 3,500 people in its home-study program, and its ranks are swelling by several hundred each year.

Yet, the nagging question remains: Do the children learn enough at home? Many teachers and parents think not. Keeping children at home only insulates them from a valuable sice of everyday life, they argue, not to mention the extracurricular activities -- everything from band to basketball --they may miss out on.

Further, critics say, few parents are capable of teaching subjects such as algebra and chemistry.And even if parents do have qualms about the quality of public education, there are plenty of other options -- private schools and professional tutoring, for instance -- short of mother's becoming a schoolmarm.

"I believe the school is something larger than supplying what the ABCs are," says Roger Lulow, assistant superintendent for public intruction with the Ohio Department of Education. "It is learning to get along with other people. It is socializing. A youngster gets deprived of that when not in the school building."

"Going to school is something special," adds Robert Snider of the National Education Association, the country's largest teachers union. "You make friends. You make enemies. It's a miniature world. A kid deprived of that experience is going to miss out on a lot."

Not so, home-school advocates argue. In fact, some contend that home-taught children mature much faster than other youngsters. But what about that algebra? Parents say they will either learn it themselves or find someone who does know it. Home schooling isn't for everyone, they add. But it should be an option.

"Home schooling gives the impression that the kids are shut up inside the house," says John Holt, a maverick educator, author, and philosopher-king of the home-schooling movement. "But they go more places, see more things, and do more than the kids locked up inside schools."

"Most learning is not the product of teaching," Mr. Holt adds, immersed in a sea of papers and books in his fourth-floor Boston office. "There is this idea that if we don't teach you something, you can't learn it. This is not true. Most of what people learn they figure out.Occasionally they may ask a question. Humans are a curious, question-asking, answer-finding animal. The human race has been passing on information to its young for millions of years without schools."

Nor do home-school advocates worry about college. There are plenty of schools that don't require high school diplomas, they point out, and many believe their children could score well on college entrance exams. If a diploma is required, they can take high-school equivalency tests.

Kevin Gavitt pulled out of a New York public school when he was in sixth grade. He passed a high-school equivalency test when he was 16 and entered Bard College in New York a year or two later. "The admissions director was startled to have a sixth-grade dropout apply for college," says Arthur Harris, Kevin's father. "The wide-ranging discussion he had with my boy rather surprised him." Kevin has completed three years and is doing "above average" work, Mr. Harris says, trying to avoid mentioning grades. Grades have always been a testy subject around the Harris house. "We always used to sign his [Kevin's] report card blindfolded," Mr. Harris says. "We didn't want that kind of pressure on him."

The Kimballs aren't worried about college, either. Like many other families, they are taking their home schooling one year at a time. If Rebekah and Benjamin decide they want to go back to the classroom, fine. But for now the verdict is a resounding no. Becky has already been to two private schools, neither of which offered the individual attention Mrs. Kimball thought her daughter needed. In addition, she thought the last one was too far away and too expensive.

So home instruction it is. Mrs. Kimball usually spends several hours a day with the children -- but the time varies according to their interest. When Benjamin bolts into the other room to watch TV, she lets him go. They take it up later. "I don't let them run wild, either," she says. "But I don't discipline them for discipline's sake. If children have an interest in learning something, they will knock themselves out to learn it rather than if someone says, 'You are in the second grade, so you have to learn this.'"

Minutes after she says this, six-year-old Benjamin struts up toting the overgrown "Children's Guide to Knowledge" book. "Mom, would you find me something about inventions?" he asks, plopping it in her lap. She does. He sits down to read. Some of the lessons have a homey touch: Family lineage often crops up during history discussions; favorite recipes, friends, and neighbors show up in word problems.

"I think I would like to be, what do you call that, an ologist?" Benjamin says of a possible career. "One who studies bones and dinosaurs. Or I might be an artist or a writer."

In the meantime, he won't be taking any tests that might tell him he'd be better suited for something else. Mrs. Kimball thinks mosts exams are more a handicap than a help. But she does keep a daily log of what the children do and has enrolled them in a home-study program through a community school in Santa Fe , N.M. A tutor also visits twice a month -- a condition laid down by the local school committee.

Mrs. Kimball, who has had one year of college, may be learning as much as the children. "We get into some pretty good discussions," she says.

But don't the children miss the food fights in the lunchroom?

"Not really," says Rebekah. She pauses, then adds: "Sometimes I might wish to be with a best friend passing notes in class . . . or even getting yelled at."

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