WASHINGTON (AP) _ Secretary of Education William Bennett on Tuesday criticized fathers who leave their children's upbringing to the mothers, and said the educational system should teach boys how to be good parents.

One fifth of all American children live in homes without fathers, to the detriment of the youngsters' educational progress, the secretary said in a pre-Fathers Day message to a group of educators involved in child and maternal health issues.

''If you look at the breakup of the American family, you very quickly find that the fathers are the ones who are missing. Generally the mothers are there struggling,'' he told the luncheon gathering at the Networking Community Based Services conference. ''But for nine out of 10 children in single parent homes, the father is the one who isn't there.''

While there has been much focus on the question of women trying to divide their time between home and career, Bennett said, not much attention has been paid to the role of the fathers.

''We are beginning to hear the question coming from many quarters: Where are the fathers? Where are the men?''

Turning to the familiar Reagan administration theme of the importance of traditional family values, Bennett said, however, ''There is no shame, there is no second-class status in raising a child by oneself.

''There is honor for those who can do it well,'' including his own mother, he added. But he said research has shown single-parent households are more likely to produce children who have trouble in school, have emotional or drug problems, and get in trouble with the law.

''The decline of the traditional American family constitutes perhaps the greatest long-term threat to our children's well-being,'' he said, adding that societal changes have contributed to that erosion.

The government must help by ensuring ''that federal social policies are not doing things that weaken the fabric of the family,'' and also by teaching children in school about the importance of family, he said.

''I do not mean that we should create classes on 'parenting,''' he said. ''Rather, schools must teach in the classroom the value of the family and how it is the spring of so much that is good. They must do this explicitly, through stories and studies in history, literature, and civics.

''They should teach our children about the importance of being parents so those children whill someday be good parents. And in doing so, teachers should not forget to talk to the boys, they should tell the boys what it is to be a father. ... And they should tell them how the readiness and responsibility of being a father should precede or at least accompany the acts which might make them fathers.''

Bennett said that in addition to President Reagan's leadership in stressing family traditions, he sees other hopeful signs for the ''future health of the family,'' including the success of Bill Cosby's ''The Cosby Show'' on television.