Back when I was growing up there was a young woman slightly older than I was who left town for nearly a year. Literally. Just disappeared. She had gone to live with her aunt, was the explanation that surfaced after a while. That explanation was just mysterious enough to make everyone wonder, even though the rest of the girls on the block were too young to understand precisely what they were wondering about. Within a year, however, the secret was out.

She had not gone away to live with her aunt. She had not gone to school that year. She returned to the same grade she had left, having lost a year of her life. She had had a baby.

No one ever mentioned it, of course, and she never talked about it. It was a source of shame and embarrassment and it got swept under the rug along with every other source of shame and embarrassment families had in those days. The prevailing social standard was that having a baby when you are not married, when you cannot support a child or care for it, was simply dead wrong. The cruel part, of course, was that many girls did get pregnant, and they could not or would not get abortions, and they went away to homes for unwed mothers and returned to be treated like pariahs.

It wasn't the greatest system ever devised for coping with teen-age pregnancy, but it did keep the problem under better control than in the decades that followed. Moral and religious pressures were intense and sometimes ruinous, but they worked.

Now, more than 25 years after that memorable episode, we are engaged in a heavy debate over how to prevent, stop, limit or somehow manage teen-age pregnancy, which is now widely viewed as an epidemic. Last month, the Center for Population Options released a study that found that American families started by teen-age mothers cost taxpayers $16.5 billion in 1985 alone. That includes only the minimal benefits such as Aid to Families with Dependent Children, Medicaid and food stamps, not the various social service, housing or educational programs that are called into play to assist teen-age mothers. The study also estimated that babies born to teen-age mothers in 1985 will cost taxpayers $6.4 billion by the time they become adults, but that $2.4 billion of that could be saved had the mothers waited until they were 20 years old to give birth. As things stand, however, 385,000 teen-agers give birth to their first baby every year, and half of them are under 17 years old, according to the study.

The center supports family planning counseling for teen-agers and experimental family planning programs that are directly in schools and that have had some noteworthy successes. The center also supports an end to what amounts to a ban on contraceptive advertising on television.

The cost to teen-age girls of becoming mothers while they are too young is enormous and well-known. Their future is essentially behind them, and so is their opportunity to get an education, a job and a decent shot in life. The cost to society, however, is also enormous, as the new study points out. Family planning programs and educational programs will help, but what is really needed is a fundamental change in attitudes that underscores the notion that having a baby you can't support and care for is simply wrong and socially irresponsible.

Here's where television can help, precisely as it has helped reshape attitudes toward smoking and drunk driving. The argument against advertising contraceptives on television is that contraception is controversial. A more cogent argument would be that given the history of contraceptive advertising practices, false claims of efficacy could be broadcast to an even greater audience and all manner of damage might ensue. Then, too, there is the matter of good taste, which is already routinely violated in television advertisements. One shudders to imagine what Madison Avenue, which brought us talking toilets during this television season, would do with contraceptives.

Somewhere within these parameters, however, there must be some room for maneuvering, for tasteful, educational advertising and public service announcements that stress personal and social responsibility not to have children you cannot care for. Judith Senderowitz, executive director of the Center for Population Options, makes the point that the public cost of well into the billions makes teen-age pregnancy "everyone's problem." It's costing all of us a bundle of money, good cause in these times to rethink our attitude toward what is going on. Like the girl I grew up with, we can ignore it, but it's a problem that won't go away.