students, papers, and the question of organization

I've been struggling since the beginning of the year with the question of student organization. I have two quite hard-working classes, most of them are (slowly) improving their skills and trying quite hard to be "students" (something many of them had never considered before). Where do we still struggle? Organization. They shed paper; they loose books just by putting them on a desk; they never, ever, know where their reading study guides are.
Why is this? And what should I do?
I'm sure there are a myriad of reasons why students forget things. Number one, of course, is the hungry-backpack-hamsters that eat all paper put in and send out only overdue math homework. But I've also noticed a tendency of students to not have binders or to have binders but to have papers shoved into the side pockets and never use the three rings. Some of this tendency, of course, is about maturity--but I feel as if some of it is a basic hole in my students' educations. Somewhere along the way, they never learned that life is much, much easier when papers are in a binder (as opposed to piled in the bottom of a backpack).
What should I do?
My colleagues seem equally divided between to camps: Let them lose stuff--at some point they learn to organize and Do everything you can to make them organize as part of the class, don't allow disorganization because of your system, not theirs.
Right now, I feel I am somewhere in between. Because I cannot stand it when students don't have materials, each student keeps important papers in a folder beneath their chair. However, I do not chase, nag, or pressure for homework and due dates. I didn't start out there (I am a bit put-off by "organizing" for students--mainly because I am not naturally organized myself and find it difficult to design efficient ways to organize for each student!), but I've slowly found that if I can provide a place for organization, at least the student has a chance to achieve it.
I'm still struggling with this idea because I'm not sure they'll ever learn to organize themselves if it is my system they are following. I'm sure there will be more on this later.