As a teacher, I have learned that the best way to encourage youngsters is to make it into a game... that way, they are learning and doing the task without even realizing it. Once she begins to enjoy it (After a couple weeks or so) then enlighten her to the fact that the whole time she has actually been doing homework! (But refer to it as fun work from this point forward!) Her attitude toward the whole concept should change! (And NO - this is not ODD behavior. Children at this age have one track minds. All they want to do is play, not work!)
Also - you can call it something else too - Come up with some quirky name for whatever type of "homework" it might be. Like a title for the gamme you turn it into.
For example, the homework assignment is to draw a picture of her family pet. Read the instructrions from the teacher, then place everything in her backpack... and have her go put the backpack in her room. When she comes back to the family room, have some crayons and paper (or whatever supplies the teacher asked for her to use) and tell her that you want to have a family drawing contest! The winner gets and extra scoop of ice cream after dinner, or an extra cookie in their lunch the next day... or whatever! And yes, your child should always win! DO NOT say, HAHA, Mommies is better, I get the extra cookie! :) (Of course, you can ALWAYS have the extra cookie for yourself.. Afterall - you DESERVE it - You're a fabulous MOM!)
(The only potential problem with this plan is that the teacher might have a certain type of paper she sends home for the homework to be done on. IF you attempt to use this paper and your child feels she is being "tricked" into doing homework, she will be on guard forever! So I suggest using your own paper from home, then slip in a note to the teacher that this was what you needed to do to get her to do the homework. Surely they will understand! And in a couple weeks when you tell your daughter she was doing homework (funwork) the whole time, you can switch back to the teachers paper...)
You can turn nearly anything into a game... naptime, eating meals, picking up toys, manners, etc. the key is healthy competition and following through with the rewards.
Hope this helps!