Kirsten Rasmussen knew she had a problem. The 16-year-old sophomore at T.C. Williams High School in Alexandria had always done well in school, but last February she suddenly began to flounder in her world history class. She even got an F on a unit exam.

Her teacher wrote her a note asking if there was something wrong, but "there was nothing really wrong, it just got harder," said Kirsten.

The teacher offered to help, she said, "But it didn't really work out. Teachers don't have a lot of time and they just review it [the material]. The problem was I just didn't understand it."

Kirsten knew she needed help, so she and her parents made a decision that more and more families are making. They hired a private tutor.

Once she started working with her tutor, Bill Wanamaker, her history grade "picked up right away," Kirsten said. Her other grades began to improve as well. More importantly, her entire attitude about school began to turn around. Sharon Rasmussen, Kirsten's mother, said, "The biggest difference it [the tutoring] made was her positive attitude about herself and her studies."

While figures for the number of students who receive private tutoring are difficult to obtain, educators say the private tutor business is booming.

"More and more, we are seeing kids being tutored and taking SAT [Scholastic Aptitude Test] prep courses," said Ann Hargrove, director of guidance at Langley High School in McLean. "There's a definite trend."

Sue Gurland, director of Traveling Tutors Inc., a Silver Spring-based company that tutored more than 700 students last year, half from Northern Virginia, said, "You can go down the block in many suburban neighborhoods and every other house has a kid being tutored."

There are more than 50 private tutoring firms in the Washington area, including more than 20 in Northern Virginia. Experts expect the boom to continue indefinitely.

One reason is the changing nature of who is being tutored. Traditionally, private tutors worked with students doing poorly in school. These days, tutors often work with good students who want to do even better.

"We used to work mainly with kids who were falling behind," said Gurland, a former high school French teacher who founded the company in 1977. "Now, we get a lot of kids who want to get ahead of the game, who have a tutor [help them] in geometry before they take it, for instance."

Another reason tutoring is becoming popular, say parents and students, is that schools, both public and private, often do not give struggling students the individual attention they need.

"My calculus teacher just expected you to be born with it or something," said 18-year-old Helen Bird, a senior at the private Bishop Denis J. O'Connell High School in Arlington. "He just couldn't spend the time on me to explain it well."

By contrast, her tutor, John Mathews, "would explain something a million times if you needed it," said Bird. "He'd come to my house at special times, like if I had a test, and I could call him on the phone any time I wanted. If I had a rough homework problem, he'd explain it to me."

Helpful as such an arrangement may be, hiring a private tutor isn't cheap. Area firms charge $17 to $26 an hour, and students generally are tutored once or twice a week for an hour or two at a time. But parents say the investment is worth the money.

"Like all parents, I want the best education my child can get, and if I have to pay a tutor, I'll do it," said Susan Monroe, a writer whose 17-year-old daughter Nicoletta, a junior at the private Holton-Arms School in Bethesda, was tutored in algebra last year. "The point is for your child to do well, have a good self-image and learn the stuff . . . . By God, she passed algebra."

While few educators question the value of tutoring a student who otherwise might fail a course, some believe that hiring a tutor to help a B student get A's is unnecessary, especially when the schools themselves offer assistance. Private tutors, say critics, prey on the fears of achievement-oriented families.

"Unfortunately, in education as in anything else, there is always somebody who thinks, 'If I pay enough, that's going to make a difference,' and there are people who are going to make money on achievement-anxiety," said guidance director Hargrove.

Hargrove said she has "no standard answer" on whether hiring a private tutor is worthwhile. "So much depends on the individual situation," she said.

Fairfax County offers many forms of help for those who need it, Hargrove said. Teachers, for instance, spend an extra "seventh period" three days a week helping students. Schools also have reading specialists and guidance counselors for those with academic and psychological problems.

Critics also say that because of the high cost, students who are tutored for standardized tests such as the SAT have an unfair advantage over those who can't afford it. Tutoring firms, however, say their business is just like any other offering a professional service.

"I'd love to see the information we give about SATs available to everyone without people having to pay for it, but the reality is that they do [have to pay for it]," said Traveling Tutor's Gurland.

The firms also point out that not all clients are well-to-do. Robert Miller, director of Tutors Inc. of Rockville, which tutored more than 300 students last year, said, "We have students throughout the area, from the inner city to Potomac."

Added Gurland: "Tutoring is not a luxury like horseback riding or a VCR; it's an investment. If tutoring can help a kid who sees herself as a B student break through to get A's, we've done a lot for that kid's self-concept."