I am entering my senior year of undergraduate study in Computer Science at a small, primarily undergraduate institution. I plan to attend graduate school and pursue a PhD in Computer Science and Mathematics, my main goal to teach. The school I attend is quite small, and is all but unknown outside our geographic region. As such, I've attempted to add as many positive bullets to my CV as possible, mainly because I feel I will have to fight harder than my colleagues at larger universities to get into a great program.
One of the things I have attempted to add to my vita is teaching experience. I have had the opportunity to tutor in our Mathematics Tutoring Center for a couple years now, and have fallen in love. I have also had the pleasure of assisting a professor in her Freshmen CS labs. Last fall I spoke with her about increasing my duties to more than just fielding questions as the students type their programs. I wanted to start grading lab submissions, and perhaps even hold office hours. She was delighted that I wanted the increased responsibility, but sharply objected to calling it a "TA" position.
Is there a stigma of assigning the title TA to an undergraduate?