I'm fortunate to be a PhD Candidate in a Department (NYU Steinhardt's Department of Applied Statistics, Social Science, and Humanities) that values teaching. I have a mentor who actively engages as both an adviser and acting program chair with all adjunct faculty and graduate students to strengthen teaching in whatever small ways she can. And even then it is difficult to find the space and time to focus on our teaching practice. I meet most Tuesdays with four other undergraduate TAs or Adjunct faculty to discuss issues in class, things we wish we could have done better and strategies for engaging students or working with an issue.
This, unfortunately, does not happen beyond our group. There is no commensurate process for graduate TAs or adjuncts.
One of my undergraduate students told me this semester that she loves taking courses in ASH because she thinks the professors actually care. When I asked her who she's had as professors in our department, she exclusively listed graduate students serving as adjunct faculty. When I asked her if she realized she only listed non-"Tenured" faculty, her response was "Of course! Those are the ones that actually care."
This issue goes beyond just making sure graduate students get the training they need - teaching is increasingly devalued across a university setting. Teaching itself rarely factors in to tenure packages. If you're a bad teacher, it likely won't effect your chances of employment. Ostensibly, universities are places where students should be taught, at a high caliber, and encouraged to think critically with texts and resources. How do we foster such learning if teaching is not a major component of a faculty's job? How can we increase our pedagogical practice as graduate students, when even faculty that we are supposed to help guide us through the process either devalue the profession or are not able to provide training because those above them discourage it?
I hope that conversations such as this one are important. Systemic change needs to happen so that teaching, not just for graduate students but for faculty as well, can improve.