This study examined the spontaneous teacher-student interactions that occurred in three graduate student instructors' [GSIs] precalculus classrooms. We classified these interactions relative to these instructors' actions to make sense of and use student thinking to inform their in-the-moment interactions with students. Our characterizations of teacher-student interactions fell into five levels, ranging from no decentering, the instructor showing no interest in the student's thinking, to the instructor inquiring into and building a mental model of the student's thinking, then using that model productively when interacting with the student. Our descriptions of the instructors' mental actions and behaviors are summarized in our decentering framework. These descriptions may be useful for other researchers, curriculum developers, and professional developers working to study and advance teachers' ability to adapt their teaching based on student thinking.