I'm a fourth year math student who's beginning to look into PhD schools. I worked at a math tutoring center for about three years, and I'm wondering whether it's a good idea to submit a letter of recommendation from my former employer along with those from my professors. I think that I can get one or two solid letters from my professors and one generic one, but I'm afraid that those won't be good enough.
Research experience in a Ph.D. application often shines more that teaching experience simply because no one often expects a Ph.D. student to teach that much (except TA responsibilities), but research capabilities are key elements to have a successful Ph.D. era. That being said, you may ask a recommendation letter from someone whose mindset about you is based on your teaching skills for the following (non-exhaustive) list of rationales:
1- A neutral letter (which does not sufficiently express you as a good or potentially successful researcher) from research perspective is definitely worse than a solid one in view of teaching skills. So, if you feel your current (professor) recommenders may not support your research skills solidly, their kind-of-neutral letters may even have detrimental effects on your application.
2- A recommendation letter may also include interpersonal and communication skills which are directly related to teaching experience of an applicant. So, following the guideline of the requirements associated with the application you are considering, you may ask your former employer to stress on such class of features of you.