UC San Diego

Researchers have ample evidence of many positive benefits for students and teachers when teachers regularly elicit and use students’ ideas during instruction.  However, there are many challenges associated with this style of instruction.  In particular, an increase in student participation means teachers must be ready to quickly attend to important details of a student’s strategy, interpret the student’s mathematical understandings, and decide how to respond to the student in a way that respects and extends the student’s understandings, all in a moment’s notice.  This in-the-moment attention, interpretation, and decision-making is called professional noticing of students’ mathematical thinking (Jacobs, Lamb, & Philipp, 2010).  In this dissertation I share two related results. First, I share findings related to the development of this important expertise. In a cross-sectional analysis I compare and contrast the professional noticing expertise of three groups of secondary teachers (N = 72): prospective teachers, practicing teachers, and emerging teacher leaders.  Results provide characterizations of this expertise in secondary teachers at different points in their professional careers, and with varying amounts of experience with students’ mathematical thinking. Second, I share findings related to selection of artifacts of student thinking for teacher learning. By comparing teachers’ responses to 6 different artifacts of student thinking, I identify features of artifacts that increase the level of challenge associated with the artifact, and the amount of curiosity or excitement that an artifact can elicit.