THE hand that rocks the cradle may rule the world, but it doesn't necessarily control the on-off switch on the family TV set.
That power often rests in the hands of young children, leaving parents ignorant about the quantity and quality of television their offspring watch.
Advocates for children hope to shift that balance by urging parents to exert more influence over youthful viewing habits. Calls to ''mobilize'' and ''empower'' parents ran as a recurring theme through a national conference on the role television plays in shaping children's values. Sponsored by Children Now, a California advocacy group, the meeting this month at Stanford University in Palo Alto, Calif., drew top leaders from the television industry.
''Many busy parents are completely unaware of the programs their kids are watching,'' says Donald Kennedy, president emeritus of Stanford. ''Parents are hungry for advice. We need a comprehensive, long-term, multi- faceted effort where the TV industry and parents and those who have access to parents work collaboratively to help parents become stronger.''
Winston Cox, chief executive officer of Showtime Networks Inc., calls the on-off switch ''parental-discretion technology'' and says, ''We must empower parents to take control of viewing again.'' At the same time, Mr. Cox concedes that the entertainment industry itself needs to do a better job of informing viewers about programs ''so they can make decisions about what they're going to watch. If parents have some knowledge, they can exercise discretion.''
Yet some parents and educators bristle at the idea that parents bear total responsibility.
''It's unrealistic to expect parents to sit with children,'' says Betty DeFea, public-relations chairman of the California State PTA. ''You're not going to bring back the situation of the 1940s and '50s where most mothers were home. We do need to help families control TV. But we also need to do a better job of educating TV decisionmakers and encouraging them to focus on what children need.''
Ann Pleshette Murphy, editor in chief of Parents magazine, shares that view. ''To blame working mothers for the fact that because they're not home supervising, kids watch too much TV, is a duck blind to attack working moms,'' she says. The larger problem, she adds, is that ''there isn't enough good programming for young children.''
Many parents do monitor programs, of course. When Parents magazine surveyed its readers, 70 percent said they prescreen what their children watch. Even so, 40 percent admitted their children watch too much television.
BUT even parental vigilance has its limits. A new poll by Children Now finds that 54 percent of young people between the ages of 10 and 16 have a television set in their own rooms, which gives them relative autonomy over their viewing choices.
Elizabeth Thoman, director of the Center for Media Literacy in Los Angeles, describes the primary solution as a tripod -- a three-way relationship involving parents, children, and ''that box.''
One of Ms. Thoman's first messages to parents is: Watch what you do yourself. ''If Mom and Dad come home and plop down and watch for six hours, the kids will pick that up,'' she says. ''We have to model the behavior we want kids to emulate.''
As one way of helping families develop critical viewing skills that can make TV a positive activity, Thoman's group distributes a parent-education course, ''Parenting in a TV Age.'' The course, involving four two-hour sessions, can be conducted by PTA groups, parent organizations at day-care centers, churches and synagogues, and adult-education programs.
Some critics argue that busy parents have no time to attend such workshops. Thoman counters by saying, ''If children are going to watch 20,000 hours of TV before they graduate from high school, don't parents have eight hours to invest to be sure that viewing time is productive, or at least not damaging?''
As parents take charge in their own homes and become more aware of what their children watch, Thoman observes a second benefit: They are better able to express their opinions to networks and local stations in letters, calls, and polls.
Instead of complaining in a general way -- ''I didn't like that show, take it off the air!'' -- a parent might say: ''I wasn't pleased with characters X, Y, and Z,'' or ''I didn't like the portrayal of minorities.'' That kind of specific criticism, Thoman says, gets Hollywood's attention.
Some media watchers also emphasize the importance of involving advertisers and advertising agencies. James Steyer, president of Children Now, says, ''Many ad agencies want to get the most number of eyeballs watching at the least possible price. They don't think of the message they're sending to children.''
In Germany, where private television stations air many American programs, parental concern about too much viewing and excessive violence has led some stations to shift children's programs to weekends, when parents are more likely to be home.
Dieter Czaja, head of the standards commission for RTL Television in Cologne, says he also cuts certain violent scenes from children's shows. ''We must play our part in this big work for the future of our children,'' he says.
If American programming is to improve, child advocates say, parents and other concerned viewers must hold television executives accountable.
''We need a national conversation about the role and function of mass media in our culture,'' Thoman says. ''There is no Ralph Nader of the media world blowing the whistle'' on the industry.
''Television is part of our culture,'' she continues. ''We need to shape it and interact with it. We can't just pretend it's mindless entertainment. That's false.''