Q.I have an 8-year-old daughter in third grade who is bright, industrious, very sociable and normally very easy to get along with. However, I have run across a problem this year that I don't quite know how to handle.

Every evening she and I battle to get her to do her homework. She can have a half-hour's worth of work, but take 2 1/2 hours to complete it. She will do anything rather than get started and finish her work. She'll have to sharpen her pencil every two words, or go to the bathroom or she'll erase every other word and rewrite it 2-3 times. Then the crying starts because the assignment is too long, or her hand is tired of writing or she doesn't understand (when she and I both know that she does) -- anything not to do her homework. She just rebels.

I've spoken with her teacher on several occasions and find she's also having a problem completing her work in school. She won't get started without the teacher speaking to her and then she sulks and pouts and acts very immature. The school work she does complete is correct, but she won't finish things and her grades suffer. Going through the crying and fighting is ruining both our evenings. I dread homework time myself now. I've tried patience, encouragement, praise, sternness, spanking, even changing the time she does the homework (thinking a nap beforehand might help). I've even tried rewards. All to no avail; the cycle continues.

What can I do to break this cycle? She is very much an approval-seeking child and I've noticed she is very possessive of my attention and spends a lot of time looking for reinforcement of my love for her, which I try to give. Why does she rebel so in this area?

Recently her father and I divorced and I know that has been hard for her. She has reverted to more babyish behavior and I know that she needs more attention and reassurance now. I try to give her more love and patience but my patience is wearing very thin.

As a matter of information, she does have an older sister, 11, who is doing well in school. The relationship between the two seems pretty normal to me. A.

A. Your little girl needs help, A. but not with her homework. A family can't go through the rigors of divorce without each member reacting to it in some way and most of those ways won't be joyous. The death of a parents' marriage can cause as much grief to their children as the death of a parent. At first they can't believe a new and stronger family can emerge.

Even though they may be relieved that the arguing has stopped, the children are bound to be a little less confident and more tentative for a while. They may become terribly good, hoping somehow that this will make their parents patch up again, or they may get openly hostile, now or later. One child may withdraw from friends and immerse himself in books or television, or get quite anxious about the health or the safety of the parent still at home. If anything happens, who'll take care of him? Another child (especially the money-anxious 8-year-old) may worry about food, shelter and clothing. Or she may start doing rotten work in school.

Since your daughter has made homework -- and schoolwork -- the focus of her anxiety, you have to deal with the situation as well as the cause. And that means you and the teacher have to quit playing her game, both for her sake and her big sister. If you spend so much time with one child, even in anger, the other will resent it.

Although your little girl should get the extra attention and approval she needs, you want to give it for the things she does well and on her own initiative: for taking good care of her clothes; for helping you clear the dinner dishes; for painting such a terrific picture. You'll find you need to give much less.

And let the homework be. Either she does it without being begged or she doesn't do it at all and takes the consequences in class. And at school, the teacher, it is hoped, will follow the same policy, giving praise, when deserved, before your child begs for it.

Even so, she may have trouble in school, for she probably has missed quite a bit. Any trauma, such as divorce, is so stressful it can rob a child of her ability to concentrate, and she will need tutoring by someone new, who can bring a fresh approach.

She may even get such poor marks she has to repeat the grade, but if she hasn't learned the subject, this isn't such a bad idea. It's never kind to overplace a child, whether she's too young for the work or upset by her life.

What she needs most, however, is some counseling with other children of divorce. Misery not only loves company but the company of other people with the same problem, so it seems more manageable. Such a group, led by a psychologist or a clinical social worker, is usually made up of children of varying ages whose parents have been separated for varying lengths of time so the children can see where they've been and where they're going.

This help may seem unnecessary, but studies show that children take about five years to get over the effects of divorce -- and that's with counselling.

Nor do husbands and wives fare any better. You'll find Crazy Time by Abigail Traford, a classic tell-it-like-it-really-is book on divorce (Bantam; $3.95), charts the patterns of husbands and wives as if the author read their diaries. This should speed your own healing and help your child too. Sorrow is mirrored in a family -- and so is joy.