## ABSTRACT

Supporting student learning in mathematics requires a responsive stance on the part of teachers. Teachers must attend closely to what students say and do, make sense of their ideas, and respond in ways that move the lesson forward productively. Much remains to be understood, however, about the details of teachers’ in-the-moment noticing of student mathematical thinking. In particular, we know little about what precisely teachers notice when they notice student thinking. As B. Sherin and Star (2011) suggest, knowing the “sensory data” available to the teacher at a given time does not necessarily tell us to what that teacher is attending. Here we claim that an account of teacher noticing is incomplete unless we understand the significance that a teacher ascribes to a particular student comment or method. For example, in one middle school lesson, students were comparing a ratio of 3 cups of water to 2 cups of lemonade mix with a ratio of 4 cups of water to 3 cups of lemonade mix. When asked which lemonade is “more lemony” a student replied “Well, I think they’re the same ’cause it’s just one more.” The teacher might have noticed simply that the idea was incorrect. Alternatively, the teacher might have noticed that the student was using a different method to compare ratios than the other students at her table. Or the teacher might have noticed that the student was talking about “sameness” in a way that was novel to her. To us, these different approaches reflect important differences in teacher noticing.