This one is for instructors/ school owners.
If you have students who show up early or stay late to do extra things around the school: clean up, sweep or mop floors, etc., and they do it all the time not to be a “kiss up” but because they feel they want to.
I have a few - but most of my students are between 10 and 13, and are at their parents' mercy for rides, so for many of them, it's not possible. The adults generally do, because they can come early, and understand that it makes the class better. The kids do what they can - but mostly their parents deliver them about 5 minutes before class starts, so they do things like hanging the US flag (I teach at a Y, and I quit leaving it up after someone borrowed it and forgot to put it back... and by the time I found it, I'd bought another one).
Do you reward them in any way. Perhaps show them a form you have not done in a long time, or something else? At what point if you give them something for their efforts do you give it to them? After a month of their efforts, a year, never?
Yes, but probably not the way you mean. The students who are most likely to volunteer are the ones most likely to come early or stay late, and I am always available to help anyone who is there before or after class... so it just sort of happens. Sometimes it takes a week, sometimes a month, sometimes a year... it depends on the circumstances. Those are also the students most likely to accept invitations to other associated classes in the area, and they get a lot of extra that way too.
Do you think students should volunteer to do these extra things.
If it is a requirement, then it's not volunteering. However, I was taught that it is a student's responsibility to help out around the dojang, to help improve everyone's experience, and that's what I teach my students. Someone almost always sweeps the room - there's a cleaning service, but they come in after we leave, and the classes before us wear shoes, so the floor is usually pretty bad.
Do you demand they do because then they are not doing it because they want to but because you expect them to.
No. It should be voluntary. Good students realize that it helps the class, and that's why they do it. I expect nothing, and always appreciate anything anyone chooses to do.
What things have students done for you that you did not expect
Hmmm... A 10 year-old learned to open a combination lock so he could get the flag out and hang it before class. Another student (adult) gave me a tanbo. A third student gave me a hand-knitted hat his mother made after testing (that one really surprised me - it's been a long time since I got a testing gift, and I can't remember the last one that was handmade). Several students have held extra help sessions for other students in the class to help them prep for tournaments and/or tests, or volunteered to come help at self-defense seminars I was teaching. My students never cease to amaze and humble me.