Q)My daughter is having a very hard time with the sleeping patterns of her 3-year-old. He's always been difficult to put to sleep. My daughter worked and the child was -- and is -- walked in his stroller by his nanny for his afternoon nap.

Night bedtime was also difficult but at least he couldn't get out of his crib. His parents gave him a 'big-boy bed' when he was age 2 1/2, however, and though it delighted him, he now gets out and walks around until he falls asleep at 10-11 p.m. The matter has gotten even worse since my daughter and her husband now have a 3-month-old daughter.

The boy's parents have tried many things. They read to him, they sing to him. For a while they tried rewarding him the next morning if he stayed in bed, but he began coming into their room at 5 a.m., asking for his surprise. Now his father tries to put him to bed, but again, it's not working very well.

He's a very bright little boy and it seems to me he's getting attention by not going to sleep.

I am concerned about his lifelong sleeping habits and also the disturbed sleep of his parents. They are loving and seem to give him plenty of attention, but I don't think they act consistently in the sleep area.

Is it too late to correct this problem, and how should they go about it?

A)Almost any behavior can be changed, especially in someone as young as your grandson, but his parents will have to change their approach. As you know, a child repeats the behavior that gets him/her the most attention, whether the behavior is good or bad.

Once they start giving more positive attention, they'll find it much easier to help their child learn how to put himself to sleep. It's an important skill. The more a child can exercise control over his own young life, the more independent he'll be, and independence is the basis of self-esteem.

An afternoon nap is not the answer, however. This is probably keeping your grandson awake at night as much as anything else. Instead, he needs a later lunch, so he'll be more tired, and then 60-90 minutes of quiet time in his room.

The timer is set and he's left there to rest and read -- and heaven knows what else -- but he stays in his room until the bell rings. If he tries to leave any sooner -- and there should be bells on his doorknob to let the grown-ups know -- he's walked back to his room, without any stories or much conversation, even if this has to be done a dozen times. He needs to learn that some things can't be negotiated.

After his rest he gets a high-protein snack and then he's strolled to the park to climb on the equipment or taken for a walk on his own two pins. Tired children sleep much better at night.

Even without the exercise, a nap-free afternoon will make your grandson tired enough for an earlier dinner and an earlier bedtime.

Now he gets a couple of stories, including that treasure, Goodnight, Moon, by Margaret Wise Brown (Harper and Row; $2.95), with its fine nighttime ritual. If the family is religious, it's also a good age to start his prayers. A few minutes to kneel down and think about goodness has a settling effect on a child, but the whole bedtime routine shouldn't take more than 20 minutes or so. Parents have their rights, too.

He's then tucked in and left with a night light, a special stuffed animal to keep him company and the expectation that he will behave, because children respond to high expectations almost as much as to praise.

And if he still has the wanders -- and this is a great age for them -- his parents should deal with them as they deal with his afternoon outbreaks: No spankings, no raised voices -- and no nonsense.

This may sound heartless, but parents can be firm, without letting the child cry or be out of bed for more than 5-10 minutes. Instead they should go to him and give the same firm line: "I'm sorry, sweetie, I know you want to play, but not right now. Good night. I love you." This attention is so minimal -- and such a bore -- the child will usually behave at bedtime in a week or so.

He'll still get up early, however, because this is another habit of the 3-year-old. At this age he is easily awakened by early morning sights, like a sunrise, and such early sounds as chirping birds or the furnace clicking on.

His parents may try to persuade him to read books in his room, but it would be nice to ask him into their bed around 6 a.m., which may buy them all a short snooze. It also gives their son some extra loving, which will help him now that the new baby is at the cooing, gooing stage and more of a rival than ever.

An occasional gift for being good also will help your grandson, but it shouldn't be expected because that would be a bribe and the ante would soon go up. It will be even better if the present comes from some mythical being, like the sandman, so the parents can be as surprised as he is. When dealing with a 3-year-old, magic can be a great persuader.

So can a grandmother. If it's at all possible, invite the boy to visit you for a week so you can start him on his new routine. Every new mother could use that kind of break.

Questions may be sent to P.O. Box 15310, Washington, D.C. 20003.