Hi Connor,
Welcome to the forum.
I hope i can be of help having been a teacher now for 10 years.
As you know, every student is different and has different needs - the job of a teacher is to really understand each students bad points and know right away the correct exercises to work through to put him or her on the right path.
Knowledge of pretty much all styles, although i hate thrash metal, is needed so if a student gets a phone call to do a Latin, Jazz, Funk, etc gig they can go and do it.
I have my second book out, 808 exercises (progressional) which a lot of teachers are using, this covers many things - this is a link which has much more information.
Paperback Book - Drum Kit Lessons - Online Drum Tutorials - Dan's Drum Lessons
If you have any further question, please get in touch on here or via my email
dan@dansdrumlessons.com
Keep up the good work also
Dan