I've done some hiring of math tutors for a small tutoring company I used to run and I was extremely diligent about reference checking. It made a big difference.

I've done some hiring of math tutors for a small tutoring company I used to run and I was extremely diligent about reference checking. It made a big difference. I never got a bad reference, but I got some where there were pauses on the other end of the line that made me curious. I was naive then and hired the people anyway. In one case it was worth it, but in both cases, it became clear early on what might give pause. Other than that it helped because a lot of people with cheerful demeanor and astonishing resumes simply disappeared when it became clear that I really did make calls and verify every degree they listed. That happened with a lot of people.