CHICAGO, Nov. 23 - On weekdays, during what are normal school hours for most students, the Billings children do what they want. One recent afternoon, time passed loudly, and without order or lessons, in their home in a North Side neighborhood here.
Hayden Billings, 4, put a box over his head and had fun marching into things. His sister Gaby, 9, told stories about medieval warrior women, while Sydney, 6, drank hot chocolate and played with Dylan, the baby of the family.
In a traditional school setting, such free time would probably be called recess. But for Juli Walter, the children's mother, it is "child-led learning," something she considers the best in home schooling.
"I learned early on that when I do things I'm interested in," Ms. Walter said, "I learn so much more."
As the number of children who are home-schooled grows - an estimated 1.1 million nationwide - some parents like Ms. Walter are opting for what is perhaps the most extreme application of the movement's ideas. They are "unschooling" their children, a philosophy that is broadly defined by its rejection of the basic foundations of conventional education, including not only the schoolhouse but also classes, curriculums and textbooks.
In some ways it is as ancient a pedagogy as time itself, and in its modern American incarnation, is among the oldest home-schooling methods. But it is also the most elusive, a cause of growing concern among some education officials and social scientists.
"It is not clear to me how they will transition to a structured world and meet the most basic requirements for reading, writing and math," said Luis Huerta, a professor of public policy and education at Teachers College of Columbia University, whose national research includes a focus on home schooling.
There is scant data on the educational results of unschooling, and little knowledge about whether the thousands of unschooled children fare better or worse than regularly schooled students. There is not even reliable data on how many people are unschooling, though many experts suggest the number is growing.
Here in Chicago, a group called the Northside Unschoolers has 100 families registered on its online list. There are similar organizations coast to coast, including the San Francisco Bay Unschooling Network, Unschoolers Unlimited in Guilford, Conn., and the Unschoolers of the Ozarks, serving Missouri, Oklahoma and Arkansas, although accurate figures for the number of families they serve are hard to come by. Adherents say the rigidity of school-type settings and teacher-led instruction tend to stifle children's natural curiosity, setting them up for life without a true love of learning.
"When you think about it, the way they do things in school is mostly for crowd control," said Karen Tucker, a mother of three boys who is an unschooler in Siloam Springs, Ark., and belongs to the Unschoolers of the Ozarks. "We don't duplicate the methods of school because we've rejected school."
Coming under the umbrella of home education, unschooling is legal in every state, though some regulate it more than others. The only common requirement is that students meet compulsory attendance rules.
In states with the most permissive regulations - many of them in the Midwest, including Illinois, Indiana, Kansas, Michigan and Nebraska - the idea of unschooling has flourished in recent years, with families forming online communities, neighborhood-based support groups and social networks for their children.
Members of such organizations form a united front against sometimes fierce criticism from outsiders.
"When you are in a subculture of a subculture, you often get painted as the freak family," Ms. Tucker said, "and people believe that what the expert says is true, instead of thinking the alternative viewpoint portrayed has some merit."
Ms. Walter, a natural-childbirth instructor, has had to assuage tense feeling from some of her peers.
"Sometimes people take it personally, like,