There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers simply because the content is inherently related. In this paper, we instead argue that there are connections between advanced mathematics and secondary mathematics that directly influence teaching. These are not discussions of the mathematical connections, per se, but rather discussions of specific ways in which knowing mathematical connections might influence secondary teachers' pedagogical choices in the classroom. With a focus on abstract algebra, we exemplify three categories of connections between advanced and secondary mathematics that influence teaching practice. Through exploring these examples, we aim to identify and situate more advanced mathematics knowledge within a practice-based lens of teacher knowledge.