When a child asks: 'Can I help?'

''Can I help?''

It's a question children are forever asking parents. How it's answered can make a big difference for a family.

''So often, we as parents say, 'No, I can do it faster,' but that's not always the best response,'' says sociologist Helen Mendes. ''For one thing, it's not the best way to teach a child how to contribute to the family.''

Dr. Mendes speaks from a wide professional and personal background. A professor of social work at the University of Southern California (USC) with 17 years experience in family counseling, Dr. Mendes is a pioneer in research on single-parent families. She herself was the single parent of two adopted children for eight years before her recent marriage.

''I remember when my son, who was then four and one-half, wanted to help by learning how to cook,'' Dr. Mendes recalls. ''I told him he was too young, but I promised to teach him when he turned six. So on the morning of his sixth birthday, he woke me up by whispering, 'This is the day.' ''

Mother and son started out with scrambled eggs, and they have since progressed to teriyaki burgers, spaghetti and meat sauce, and barbecued pork chops, among other delicacies. ''Both my children, who are now 13 and 10, are a real help to me in the kitchen,'' Dr. Mendes adds. ''I know that when I have to work late at night, I can leave a note for them, and dinner will be ready when I get home.''

According to the latest US Census Bureau figures, some 12.7 million children under age 18 are living in single-parent homes - or one child in every five. With 20 percent of American families now headed by single parents, it's a life style that's getting a lot of helpful attention from researchers like Dr. Mendes.

''As a single parent, I knew that I liked my chosen life style and that my children were thriving,'' she explains. ''I also knew I couldn't be the only one like that, and I decided to investigate further.''

Dr. Mendes began doing research on single fathers in 1974, as part of her doctoral work at the University of California at Los Angeles. Since then, she says, the body of scholarly literature about single mothers and fathers has grown considerably. While she's on sabbatical this year, Dr. Mendes hopes to finish two books on the subject.

A recent USC-based study of 45 single parents turned up several significant findings, according to Dr. Mendes. She discovered that single parents who were the most successful in rearing happy, productive children were those who had dependable support systems. ''They didn't try to do it all themselves,'' she notes. ''And with help from relatives and friends, their children had richer relationships.''

When it came to their views of the child's role in the family, single mothers and fathers often responded differently, however. Many men felt that children should share in household tasks, while some women tended to ''baby'' their offspring.

''It may be because men are brought up to be more task-oriented and to think that having children help around the house is perfectly natural,'' Dr. Mendes explains. ''They don't feel guilty about asking them to do certain chores.

''Women, on the other hand, often feel that mothers are supposed to do everything - and even when their life situations change, they continue to try to function in the same way that they did when there were two parents to do the work.''

As a result of her research and counseling background, Dr. Mendes has a number of practical suggestions for today's single parents:

* Don't try to be a ''superparent.''

Ask for help from friends and relatives. Ask children for help with housekeeping chores and explain why it's needed. It may take a while to teach young children how to wash dishes or make their beds, but it's an investment of time that will help children develop skills and will also pay off for the family in the long run.

* Don't isolate yourself.

Children learn how to be friends and retain friendships by watching their parents. Isolating yourself from other adults may mean that you're overworking yourself. Parents need to exchange ideas and emotions with other adults; time away from children can be refreshing and renewing.

* Don't join parenting or self-help groups to look for a new mate or to wallow in self-pity.

''Nobody has ever told me a prospective mate is likely to be found at a single-parent club,'' Dr. Mendes notes. ''People usually say the Sierra Club, or the NAACP, or church. If they go to those places and don't find a mate, they're still better for the experience. They're rewarded by the activity itself, and they're meeting more people all the time.''

The benefits to be gained from single-parent groups depend on the motivations for joining, according to Dr. Mendes. ''There usually are experienced parents in the group who have worked out solutions to various challenges and can share those with others. In terms of emotional support and information exchanged, these groups often have a lot to offer.''