"To many parents," says Jane Norman, "nothing is more impenetrable than the teen-age mind. Despite our best intentions, somehow, when they turn 13, we seem to lose touch."

Norman, a former elementary school teacher and kid-show hostess, learned about the "tight-lipped teen" in 1979 when she co-produced the "National Kids' Quiz" for NBC.

"We asked kids questions about everything -- shoplifting, school, sex, drugs. Afterward we got hundreds of letters from parents, educators and kids saying how much they appreciated our presenting a program about what kids had on their mind.

"Parents and teachers were starved for this information. And kids wanted so badly to talk, but often couldn't talk to their own parents. It seemed logical to find out more."

With psychologist Myron Harris -- and some suggestions from her teen-age son -- Norman designed an 80-question survey. It was published by Xerox Educational Publications in magazines read by millions of school-age children. More than 160,000 teen-agers across the country answered the questionnaire anonymously.

To get a nationally-representative demographic sampling, Norman and Harris polled an additional 857 teen-agers. They also conducted one-on-one interviews with more than 100 teen-agers in about 12 cities, including New York, Chicago, Kansas City, Philadelphia, Tampa, Los Angeles and Great Falls, Mont.

The result of this three-year effort, The Private Life of the American Teenager (Rawson, Wade Publishers, Inc., 311 pgs., $14.95) is a sometimes disturbing, occasionally reassuring and frequently enlightening look at American adolescents.

"We found they really would like to be able to talk to their parents," says Norman. "But what turns them off is that parents jump to conclusions or over-lecture instead of really listen to what the teens are trying to say.

"They want to know what our values are . . . some equate lack of discipline with lack of caring. But while they would like to hear our advice, they don't want us to insist that they must take it."

Many teen-agers, she says, share adult concern over adolescent sexual activity and substance abuse. For example:

"Almost half believe that adolescents are too involved with drinking and drugs. Kids say it's not even the 'in' thing to smoke pot anymore. One 15-year-old girl told me, 'I don't like most teen-agers. They don't take things seriously and don't care about much.'

"And most teen-agers (67 percent) feel that sexual intercourse is less important than dating and friendship. They like to spend time with someone who is easy to be with and in whom they can confide."

A sampling of the survey:

Teens on Parents

"I try to explain things to my parents, like why I cut school one day, but they don't react very well. They only hear what they want to hear . . ." --Jack, 16

* Believe they can tell one or both parents how they think and feel at least sometimes--83 percent.

* Think parents listen and care about their ideas and opinions--60 percent.

* Think parents are not helpful when giving advice--51 percent.

* Most want advice from parents on getting a job; least want advice on drugs.

* Teens pick mothers, three to one, as the parent "easiest to speak to and get along with."

* More than 80 percent of teens whose mothers work outside the home say they approve.

On School

"There are some classes where everyone cheats . . . In this school the emphasis is on grades and getting into college." --Lenore, 18

"I'd love to take a course to really learn something and not feel pressured to do well in it. That would make school okay." --Debby, 17

* Study only to pass tests, not to learn--60 percent.

* Admit that they cheat--55 percent.

* Say teachers play favorites--76 percent.

* Believe teachers don't care about student ideas and opinions -- 54 percent.

* Fairness is the quality most teens "like best" in a teacher.

Family Members

"I offered to pay for half of my parents' marriage counseling, but when it still didn't work, I gave up. I'm glad they split, though. It's a lot better for me now." --a 16-year-old

* 81 percent think parents have a happy marriage to some degree, although this view is altered as teenagers (particularly girls) get older.

* 75 percent see divorce as "preferable" to staying together if parents are truly unhappy.

* More girls than boys favor divorce.

* 82 percent like their brothers and sisters "most of the time."

* Only 3 percent don't like their siblings at all.

* Lack of privacy is the number- one complaint among children with siblings.

Home Rules

"I wish that I could have a curfew that's reasonable that we could both work out. I think that would be fair." --Jack, 16

* More than 80 percent believe keeping their room neat is a chore they "should do" (although they don't necessarily comply).

* Teens believe a sexist division of chores still exists, although less pronounced than in the past. "My brother sleeps in a bed the same as I do. Yet how come my mother feels he should just sleep in it, but I should make it?" --Dora Lee, 14

* Punishment is equated with caring--if the methods are fair and not excessive. "I can do anything I want and my parents never punish me. If you want to know the truth, I don't think they give a . . . My father's always working and my mother is tied up with organization work." --Dolores, 14

Vandalism And Shoplifting

"I think people that vandalize don't have anything better to do." --Mark, 14

* One out of three teen-agers think vandalism could be curbed if parents paid more attention to them, and if they weren't so bored.

* Most believe nothing will stop the shoplifter except getting caught and facing the consequences.

* Very few would tell on a shoplifting friend.

Drinking and Drugs

"You always think of something to say when you're drinking. The things I say when I'm sober are usually just small talk. When I'm drunk I can start a real heavy conversation, and I can relate better. Open and secure. I really like that feeling." --Andy, 17

* Drink more than once a week--1 out of 4 high schoolers.

* Smoke marijuana regularly--40 percent

* Have tried marijuana--7 out of 10 high-school teen-agers.

* Most feel that their parents know they drink, but only 29 percent say their parents know they smoke pot.

* Will lie to parents about their pot use--50 percent.

* Say their parents have never discussed drugs--55 percent.

* Believe pot is bad for their health--55 percent.

* Believe drinking is bad for their health, even though they do--62 percent.

Sex and Marriage

"All my sex education came from dating. You might call it on-the-spot training. My parents would be so embarrassed to talk to me about sex." --Jim, 16

* Nearly 60 percent of 16- to 18-year-olds and 33 percent of 13- to 15-year-olds have had sexual intercourse.

* Nearly 6 out of 10 sexually active teen-agers do not use birth control or use it only some of the time.

* Nearly three-quarters have never discussed birth control with their parents.

* Almost all want more information about intercourse, birth control and venereal disease (in that order).

* If they became pregnant, 13 percent of teen-age girls would marry the baby's father; about one-third would get an abortion.

* 90 percent believe in marriage.

* 74 percent say they'd live with someone before or instead of marriage.

* Twice as many girls as boys fear that marriage would interfere with their freedom and career plans.