Last week I was at a USTA tennis trainning and started talking to another P.E. teacher about gymnastics. During our conversation she mentioned that teaching back handsprings in P.E. was difficult for her. Several years ago, I would have never taught back handsprings in P.E. My biggest fear was that I would drop a kid on their head. I tried to figure out how to safely spot by looking through online videos. However I never had the confidence to start having kids in my class do more advanced gymnastics.
A couple years ago I decided to spend my Saturday mornings at Central Vermont Gymnastics. It's amazing how quickly you become comfortable with spotting back handsprings when you spot hundreds of them during practice.
This video has a few drills that I use in my P.E. class. There are tons more drills that I use, and these are only a few examples. Good luck!