What do you have students do after they finish their independent work? Do you let them turn it in as soon as they're done or all at the same time?
I have a "Finished Work" basket and the students know to always turn their work in there so I can keep it all together. They turn it in as soon as they are finished so they can start working on something else.
When I student taught I had it go into the corresponding basket. They went back to their desks and either read silently, worked on work from the morning, or did packets.
I have two red "folder" pocket charts. Their morning folder work goes in there. At a quick glance, I am able to see who has not turned in their work. (Each pocket is labeled) It's also easy for them to turn in other work if I don't want to take it up at the time.
I also have a finished work basket and they turn it in whenever they are done, with the exception of tests. I tell them to flip it over then I collect all at once, just so that the room remains quiet while others are working.