This is a slightly different response as most people are assuming you are intending to teach at the university level. I respond only for informational purposes for those teaching not at the university level.
As an undergraduate, I took an "advanced" math course with a Ph.D graduate student as the teacher. After finishing his degree, he ended up seeking prep school and community college positions out of interest to teach small groups of students. Not only did these schools ask for "authoritative" recommendations, but a number also asked for multiple student recommendations.
Admittedly, I was asked to write one -- I do not think I really had the perspective then, nor now, to write something. But it seems these less than university positions desire that additional information.