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<p>You’re not mistaken; that’s absolutely right. TAs are typically grad students pursuing their Ph.D.s. In most fields, Ph.D. candidates are seeking that degree with the hope that they’ll land academic positions (though perhaps this is less true in engineering and some sciences than in the social sciences and humanities). But many colleges and universities won’t hire people into tenure-track faculty positions unless they have some prior teaching experience. That puts the graduate schools in the position of needing to give their grad students some kind of teaching experience so they can be competitive on the academic job market, and that means putting them in front of undergraduates. That’s why, back in the day when I was a grad student at a leading Ivy with a reputation for being strongly undergrad-oriented, every grad student in my department worked as a TA, doing exactly the same kind of work—leading “recitation” sessions, grading assignments and papers, etc—that they would have done at a Michigan or a Berkeley.</p>
<p>Now I won’t say it’s just the same everywhere. Some cash-strapped universities DO rely more heavily on TAs to do more of the undergrad teaching as lecturers in entry-level and sometimes even intermediate-level courses. In those schools undergrads do have less contact with actual faculty members. But generally the fault line isn’t public v. private or large school v. small school. It’s better-resourced schools v. more thinly-resourced schools. And by and large the top graduate programs are going to be at schools on the better-resourced side of that line, including a mix of top publics and top privates.</p>