, I wouldn't worry about certification as much as chemistry, ability,.....
This says it all for me. I took lessons from a guy who had all the credentials and music school qualifications and could play amazingly well but simply wasn't a great teacher. I think I realised on lesson 2 that the chemistry wasn't there and that, as the customer, I wasn't going to get what I wanted out of my lessons. Took a couple more lessons just to be sure and then we politely parted company before I looked elsewhere.
I have been seeing my current teacher for around 3 years now and couldn't be happier. I never asked to see a resume but new I was on to a winner from the first lesson. In addition to being able to play like an absolute beast across a range of styles, he's a fantastic guy and we have had great chemistry from lesson 2 or 3. Drums are a hard beast to learn (for me at least) and the more 'fun' lessons are, the better. My teacher has just the right balance of making things fun, praise, criticism and when necessary he will drop in the "Zero Let-Up Whiplash Approach". He's also incredibly patient!
Some of it is quite intangible but, looking back at it, the credentials I would seek if I were to move away and look for a new teacher would be as follows:
Ability - Either within a given style of playing or across various genres for more general lessons.
Resources - Books, Courses, Charts - These give structure to a lesson and mean I can take things away for practice or buy a new and inspiring book rather than a hastily scribbled chart that I cannot decode when I hit the kit at home. I may not want to follow a specific curriculum but if a teacher has experience of Rockschool, Trinity or Drumsense and getting students through exams then it all counts to their credentials for me. As a young(ish) father, I really don't have time to study for exams but we are always dipping into Trinity and Drumsense exercises. However, sometimes we will open up a Stanton Moore book and get funky with the chatter notes.
Attitude & Chemistry - At my stage in life, I play for fun. Am I looking to improve? Yes of course, but if lessons are a PITA that I don't look forward to because I know I am going to be beasted then it sucks the fun out of learning. A teacher needs to be a cool dude who understands (or is willing to understand) what I am looking to acheive, my limitations in terms of practice time and what makes me tick. This ultimately leads to the most important element which is
inspiration. I really define this as driving home from a lesson, walking through the front door and heading straight to the e-kit to further practice what I have just learned.
All of the above are more important to me than where a teacher graduated from, what letters they have after their name, who they have played with or what it says on their resume.