I agree with Fuji. The "self employed or not" thingy has been around for years and is well rehearsed. A newcomer to "business" may well be unaware but it is easy enough to find out with a bit of research on the internet.
Simply working truly freelance for more than one school and using wholly one's own equipment should be pretty good.
Of course working for more than one school is not something the schools will approve of, which then sets up a trap for the school employed the SE instructor.