About 2 percent of American students are now taught at home. Educators are confused about how this growing practice should be regulated, and also wonder whether  children who are not fully registered in school should get some public services. The issue  shows how dim the line between public and private education can become, even when  that private education is delivered at home.        Probably about half the parents who teach at home are religiously motivated and use  lessons by mail  (or Internet) from church schools. Perhaps an additional fourth have some doubts about public education, think schools are unsafe or the fact that their children have special needs that regular schools don’t meet. In some cases, parents home-school to escape compulsory(义务) education; they do least teaching while  having older children care for younger sisters or brothers or work in home businesses. Although children often learn well at home, weak regulations in most states mean that officials rarely challenge or monitor parents who say they are home-schooling. With growing frequency, however, public schools offer services to the home-schooled.Districts may permit them to enroll part time for instance; educators fear that otherwise these children could later return full time with serious academic weaknesses, and in any case some districts wanting to qualify for state aid can benefit from part-timers filling empty seats.        Here in Helena, Mary Brown has taught her 12 children at home while manufacturing clothing there in her non-teaching hours. Mrs. Brown says her motive is to give more training in basics, like phonics(发音学) than public schools offer. Most of her curriculum is from a church school, with tests returned by mail.        Two years ago her seventh child, Andrea, wanting to join regular athletic programs, enrolled at Capital High School. Andrea soon changed her mind and continued home study. But she had liked gym and chorus(合唱), so Mrs. Brown asked that she be allowed to continue in them while taking other courses at home.