TUCSON, ARIZ. — LIKE millions of other parents, Herberta Millett was unhappy with the atmosphere and standards at her local public high school. ''The kids were swearing and teasing my daughter, pulling her hair,'' Mrs. Millett says. ''Her grades were starting to fall.'' Millett decided to enroll her daughter in the Heritage Academy, a small school with a back-to-basics curriculum and strict codes of conduct. Although Heritage is public and nonsectarian, it closely reflects the traditional values of Millett and others in the Mormon-dominated community of Mesa, Ariz. Millett said her daughter came home after the first day of school and told her, '''Oh mother, it's so wonderful not to hear cussing and swearing.''' Heritage Academy is emblematic of an innovative - and controversial - reform movement in American education: charter schools. Set up to be free of regulations and experiment with new teaching methods, hundreds of charter schools have now sprung up in 19 states nationwide. Arizona, with some of the least-restrictive education laws in the nation, is providing one of the clearest views of where the movement is headed - and the problems that can crop up. In Arizona, the controversy lies not with the concept of charter schools but with the minimal requirements placed on them. Charter schools must meet minimum health, safety, and academic standards; not discriminate against applicants and not charge tuition; and avoid religious instruction. Arizona doesn't require charter-school teachers to be certified. Since the charter-schools movement began in Minnesota in 1991, many educators have hailed it as a promising way to improve public education in America. Charter schools offer parents choice in the kind of education their children receive, and they encourage more ''ownership'' of the school among teachers, students, and parents. But it remains to be seen what kind of lasting effect charter schools will have on the broader public education system. As one teacher says, ''We don't want to reinvent the wheel.'' Educators are especially interested in what's happening in Arizona because charter schools here are among the nation's least restricted. Anyone - teachers, parents, businesses, community groups, even religious organizations - can charter a school here. Arizona also allows applicants to obtain charters from two statewide boards as well as from local school districts, which makes it easier to charter a school here than elsewhere. Although Arizona's law allowing charter schools was passed just last year, the state has about 50 opening this fall, second only to California, which has about 100. Freedom to teach Roughly half of Arizona's charter schools were formerly private or community-based schools. The rest are new. Many of them are the realization of teachers' lifelong dreams to run their own shops. The schools range in size from about 50 students to several hundred, and they are located in such diverse places as shopping centers, meeting halls, and church buildings. Heritage, for example, leases space from the Temple Beth Shalom in Mesa. Among Arizona's charter schools are some for ''at-risk'' youth, Montessori schools, bilingual schools for native Americans, and schools emphasizing business or arts education. Officials say most of these schools already have waiting lists. Despite the enthusiasm and energy surrounding charter schools, some experts are cautious. ''I think in our zeal to try something new, we may have opened the door a bit too wide,'' says Raymond Kellis, the former superintendent of a Phoenix-area school district and a member of the state Board of Education. Dr. Kellis says Arizona may have done better to limit the number of charter schools and to nurture them more carefully. The casualty rate may be high. Members of Arizona's public-school teachers' union, while not opposing charter schools, also are concerned about how the state intends to account for the $16 million it appropriated for charter schools this year, as well as ensure that students are being educated properly. The state already has had to tighten requirements beyond what the charter-school law requires by instituting background and credit checks for applicants. As for financial and academic performance, officials say they are still in the process of setting up procedures to monitor charter schools. Arizona may also be opening itself up to lawsuits by allowing religious groups to operate public schools. Although the law specifically forbids religious education in charter schools, some question how religious organizations can be held to that requirement once the classroom door closes. ''It's a slippery slope,'' Kellis says. Religious discrimination? Conflict already has arisen with the Church of Immortal Consciousness near Payson, Ariz., which was given a preliminary charter for its school, only to have it denied later after an investigation found tax and credit problems among some school officials. Steve Rensch, a lawyer and church member whose children attend the school, says he believes the alleged financial problems are merely a pretext for the denial. ''What we've got here is religious discrimination,'' Mr. Rensch says. ''The utter unfairness and heartbreak they've caused leaves me no choice but to go after them in court.'' State officials insist the denial had nothing to do with the church's beliefs. Lawsuits may force the Arizona legislature to fine-tune its charter schools law, as Michigan did in 1994. Nevertheless, charter schools are shaking up public education across the country, and some say that alone makes them a success.