We are in Moodle 2.7. Is there any way for a non-editing teacher to move students in and out of groups or is that only an administrative level function?
It's a permission that by default is available to the Teacher and Manager roles only.
The permission is course:managegroups
You should be able to give this permission to the non-editing teacher role on a course-by-course basis, but apparently not on a site-wide basis. (I'm looking at this on my Moodle v2.6 site. It may be different on later versions.)
Administration (block) > Course administration > Users > Permissions
As always when adjusting permissions, try it out in a test environment first and test-test-test with accounts with various roles before applying to a live environment.
Thanks Donna. I'll take a look at those settings and try it out.