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Description
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 sets of findings. 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, experienced teachers, and emerging teacher leaders. Results indicated that experienced secondary teachers were fairly similar to prospective secondary teachers in the attending and interpreting component-skills, and were only marginally better than prospective secondary teachers in deciding how to respond. In contrast, secondary emerging teacher leaders provided much more evidence of attending to the students’ strategies, interpreting the students’ understandings, and deciding how to respond based on the students’ understandings. This implies a need for sustained professional development, as teaching experience alone does not appear to provide sufficient support for teachers to develop this important teaching practice. 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. In particular, scalar strategies and strategies with non-integer ratios were more interesting than the alternatives, perhaps due to teachers’ unfamiliarity with scalar strategies and the added complexities afforded by non-integer ratios. In addition, scalar strategies were more challenging for teachers to comprehend than unit-rate strategies.
