In this article, we explore the influence of mathematics graduate students' experiences with the teaching assistantships and texts that they encounter in their programs on their development and identity as teachers. We look to von Foerster's notion of trivial and non-trivial machines to interpret the graduate students' experiences and explain how their identities begin to resemble their professors, and how their understandings of teaching point to the replication of the texts and practices they encounter. We then rely on Caputo's notion of the remainder to see how graduate students subtly "carve out an identity for themselves."