It depends. She can work independently, but she has to work at the kitchen table or in the living room to stay on task. If she works in her room, nothing gets done. So I don't "hover," but my presence is felt.
Depends on the child. My 8 yr old boy likes to get his work done and such... so most of the time, he can be fairly independent when needed.
My 11 yr old girl, however, is opposite. If you leave her to do ANYTHING... she will pick at her toes, fingers, draw imaginary circles on the table or wall with her fingers... she'll pick at a piece of tape or a sticker... etc. She has to be checked on frequently. It doesn't matter WHAT the incentive is... however we are starting to think about having her evaluated for being potentially on the spectrum or maybe ADD that comes out as inattentiveness mainly. She struggles with life in general.
My 5 yr old, though she hasn't started yet and is too young to be independent anyway really... she has signs of being like her sister only with some serious hyperactivity involved.
Marcus is 5yo and we do a combination of independent and joint tasks.
Math is largely together with a few independent tasks a week. Writing is almost always independent with sporadic supervision. Reading is entirely supervised
My duaghter (8) works independently for the most part. My son (4) does not lol. But its also not structured for him yet. I have a feeling when we do "officially" start with him, I'll have to keep a close eye on him...
This is our first year. DS is 5, doing 1st grade work. I'd say it's 50/50. Handwriting and most math is independent - but he's at the kitchen table and I'm putting dishes away, or folding laundry at the counter. So, I'm not sitting right there, but I am in the room. He has no set pattern though, some days he does better when I'm away from the table/kitchen and other days he wants me at the table with him.
The rest of what we do involves me reading or doing with him.
Just this year my dd started taking all her work to her room and getting it done completely on her own. She's 12. My 10 yr old ds is getting there, but I still have to swing through the room and remind him to focus. He's so easily distracted that just the cat walking through the room can stop everything in its tracks. We finally figured out that putting his favorite blanket over his head works really well to block out distractions LOL.