I thought I'd weigh in since it's going around the internet. Sweet Pea needs pretty close supervision for most of her school. It's not that she isn't capable of the work, it's that without being attended she gets distracted or dawdles, or doodles, or repeatedly falls out of her chair.
Some things she does well by herself- reading being high on that list. She now reads most of her history lessons to herself and does the corresponding activities for the lessons by herself. I check in with her later and she narrates the story back. She does most of her math solo as well, now that I think about it.
I do think teaching time management and independent work ethics are really important. We're just not there yet.