I think that demonstrated skill is independant of the number of dives in their log book.
Sure but it's also relative to the standards of the diving community. The diving community is not made up of DIR folks cave and wreck people, or even the recreational divers who attend these boards. It is made up of the hundreds of thousands of "go for one diving vacation in a lifetime" folks out there who never are going to get beyond the 10 dive mark, let alone go for AOW or Rescue or anything else.
But aren't they expected to have a grasp of the material that they are teaching?
No.
I have no expectation at all that a grade school teacher can explain to me the fundamental theorem of arithmetic, that every non-zero integer can be expressed as a signed product of primes in an essentially unique way. I have no expectation that if told that they could extrapolate the rules of addition.
I do expect them to be relatively capable of grasping it at a level appropriate for the teaching their doing. I don't expect a grade school teacher to explain to me the computational number theory behind the rules of algebra that allow them to say 2+2 =4. Indeed, I don't even expect them to know the associative, distributive and commutative properties of addition by heart. I expect them to be able to convey the information in the book to the students and answer basic questions about straight application correctly most of the time.
What I do expect them to do well is to be able to have the people skills to manage their students well, so that those who are interested in learning have a good time and have an opportunity to learn in a relatively safe environment. Which is pretty much what I expect DM's to do: manage people so that they hear and follow the rules as much as a bunch of yahoos on vacation can be expected to.
the teacher can multiply and devide, right?
Usually no more well than the best students in their class. Ask most grade school teachers to multiply 3 or 4 digit numbers in their heads and they'll fail, but most good 4th graders can do 2 digit numbers in their heads with a little coaching.
Maybe you've brought us to the root of the problem here. All things are relative and someone who can kneel well is probably a great diver compared to someone who hasn't quite mastered kneeling yet...so we have those who walk on the reef well and those who don't walk on the reef so well.
In some ways I think so. When the average diver has less than 10 dives, and a DM needs to have 60 to get the card, they have substantially more experience than the average diver.
Now, I agree their skills should be as good as someone with 60 dives can expect to be -- and that falls on the mentoring instructors as well as the DM's to achieve. But just as you have a range of teachers from the barely competent to the really fantastic, so too will you have a range of DM's.
The other side of this coin, from a purely economic perspective, is that DM's are pretty well abused and paid next to nothing. The work conditions and expectations of DM's probably selects out the more competent people, who either go on to instructor very quickly, or let their certs lapse due to a lack of interest in being abused.