COLUMNIST WILLIAM RASPBERRY recently took what he admitted to be the perilous course or arguing with two Harvard psychiatrists who contended that children in a two-career family should not be overburdened with household responsibilities lest they be cheated out of their childhood. Raspberry thinks they may be wrong. He thinks some of the trouble with America's youth is that they feel useless.

"The problem for modern parents is to find ways to give their children a sense of usefulness, to make them feel that they are a part of a general family enterprise, and not just impediments to their parents' career."

I couldn't agree more. We have, in fact, been trying for more than a decade to give our children a sense of usefulness.

And we have ended up throwing up our hands on any number of occasions and concluding that useful is the last thing they want to be. Modern children, it seems, are far more interested in being stereo experts, dreamers, short basketball players, bicycle riders, skateboarders, marathon telephoners and television critics. They have been observed on occasion reading books ("Pro Basketball's Super Scorers") and magazines, "Sports Illustrated" and "Seventeen," but their idea of being part of a general family enterprise is to read the TV Guide out loud.

There was a time several years ago when our Vietnamese housekeeper ran away from home to find her fortune in computers. We enrolled the toddler in a play group and decided that the household chores would become a general family enterprise. The family that cleans together saves money. Now, Raspberry quite correctly points out that there aren't any obvious counterparts to farm chores in the typical affluent, urban or suburban household, but that doesn't mean there isn't plenty to do. We do have to vacuum and change beds, do laundry, clean up the kitchen and mow the lawn and weed the garden. (We stopped short of the really ambitious projects such as washing cars, wallpapering bathrooms, and fixing dripping faucets. We knew our limits.)

The resident 12-year-old was assigned the task of vacuuming the living room, dining room, and stairway steps. It nearly killed him. Mind you, this was not a short, weak person at that time, nor was he a known anemic, but the efforts that went into moving the dining-room table and chairs and pushing the vacuum cleaner across the carpet sent him diving onto the sofa, gasping about pains in his legs, shortness of breath and terminal exhaustion. Lying down was the only known cure. It was almost as if he were allergic to being useful.

Now, I remember years ago when I was a teen-ager, having major wars with my parents over mowing the lawn. It seems they were of the Raspberry school of thought, that children who did useful things built characters. But I could never see the connection between pushing a lawn mower and building my character, and would stop at nothing to get out of it. I feigned illness. I hid out in my brother's room. I even studied one entire weekend nonstop.

Looking back from the cool vantage point of motherhood, I assumed I acted that way because I was a girl, and girls don't usually do lawns. There are, in other words, distinct sexual roles in life, at least when it comes to lawns. I can tell you now, as the mother of a male teen-ager, that there are not. Boys will not resort to anything quite as desperate as studying to avoid lawn mowing, but they will take their best shot.

"I want you to mow the lawn today," will produce the following responses:

"It's too wet." (Good in this area until the end of June.)

"We're out of gas." (Good any time of the year.)

"The lawn mower's broken." (Particularly good the first time you try to use it each year, and any weekend from August on when the lawn mower's worn out.)

I know a woman who has produced one useful teen-age son, but she's practically given up on her daughter. "I think they should do things. I get all the meals and that's not fair to me, and it's not fair to her either, because she's not learning a darn thing. She can think of every reason why not to do something, or else she'll just ignore you and hope that in half an hour you'll forget it.

"I'll say I need help with this, and she says 'oh, I was going to play the organ, ma.' Her bed's not made, she has clothes all over the chair, everything's on the floor and it doesn't bother her one bit. Then, when I talk to her about it I get myself so upset that I just have to walk outside and cool off. And then when I come back in, she's lying asleep on the couch."

"My husband used to tell me I didn't give the children enough responsibilities," says the mother of four teen-age girls. "He'd say give them a specific amount of time to do the chores and then lower the boom. How are you going to lower the boom when they're bigger than you are? I asked the girls to clean up the kitchen today, and when I came home from work it hadn't been touched. I don't go in my second daughter's bedroom anymore. It's a fire hazard. I don't know," she says, "something's funny about teen-agers." She says she's given up trying to get her children to be useful.

We tried lots of different approaches, including the power of positive thinking. Last summer, we gave our resident teen-ager exclusive rights to the lawn-mowing concession. He, of course, saw right through this, and before we knew it the lawn was too wet, the lawn mower broken, and the gas can empty. Then, by July, we were noticing something else.

Everytime he started to mow the lawn, he began acting weirdly. Even for a 13-year-old. He began to sneeze, and cough, and tear and wheeze. He began acting a little like he acted when he had the exclusive rights to the vacuum cleaner.

He began acting like he had allergies. Which, the doctor announced $149 later, he did.

To dust.

And to grass.

I will not attempt to repeat in a family newspaper what my husband said upon learning that he had spent $149 to find out our son was allergic to lawn mowing. All our efforts to make him useful, to build his character, not to mention to get the lawn cut, were submarined by the kind of act of nature that is supposed to get insurance companies, not teen-agers, off the hook.

We tried, Bill. We tried.