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Victoria R. Jacobs, Lisa L. C. Lamb and Randolph A. Philipp

The construct professional noticing of children's mathematical thinking is introduced as a way to begin to unpack the in-the-moment decision making that is foundational to the complex view of teaching endorsed in national reform documents. We define this expertise as a set of interrelated skills including (a) attending to children's strategies, (b) interpreting children's understandings, and (c) deciding how to respond on the basis of children's understandings. This construct was assessed in a cross-sectional study of 131 prospective and practicing teachers, differing in the amount of experience they had with children's mathematical thinking. The findings help to characterize what this expertise entails; provide snapshots of those with varied levels of expertise; and document that, given time, this expertise can be learned.

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Stephanie Casey and Joel Amidon

. Stacey knows professional noticing of students’ mathematical thinking—particularly building on student ideas in responding to them—is difficult. She saw that difficulty play out in the actions of the experienced classroom instructor, who did not build on

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Jonathan Thomas, Molly H. Fisher, Cindy Jong, Edna O. Schack, Lisa R. Krause and Sarah Kasten

What it means to be a good problem solver, what a good problem-solving activity looks like, and what teachers should keep in mind as they bring problem-solving activities to the classroom are explored in this month's practical research department.

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Jonathan N. Thomas, Sara Eisenhardt, Molly H. Fisher, Edna O. Schack, Janet Tassell and Margaret Yoder

Learn how to coordinate the use of CCSSM with this emerging framework to attend to children's actions, make interpretations, and respond with robust instruction.

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Julie M. Amador, David Glassmeyer and Aaron Brakoniecki

should be given to how teachers elicit student thinking, interpret this thinking, and ultimately make informed decisions to respond—a process referred to as professional noticing ( Jacobs, Lamb, and Philipp 2010 ; van Es and Sherin 2008 ). Professional

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Jennifer N. Lovett, Allison W. McCulloch, Lara K. Dick and Charity Cayton

, drawing on the extant literature related to TPACK, video case instruction, and professional noticing, we propose a set of design principles for the development of technology mediated and video-enhanced modules for preservice secondary mathematics teachers

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Edna O. Schack, Molly H. Fisher and Jonathan N. Thomas

“Noticing matters” (p. 223). Through these words in the concluding chapter, Alan Schoenfeld succinctly captures the theme of this seminal book, Mathematics Teacher Noticing: Seeing Through Teachers' Eyes. The book received the American Education Research Association 2013 Exemplary Research in Teaching and Teacher Education Award. It addresses a variety of meanings and interpretations of teacher noticing from Dewey's earlier work of inner and outer attention to more specific variations such as that of professional noticing, as defined by Jacobs, Lamb, and Philipp. Chapter contributors have provided the foundation and framing of teacher noticing as a construct for studying and improving teaching.

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Leslie Dietiker, Lorraine M. Males, Julie M. Amador and Darrell Earnest

Building on the work of Professional Noticing of Children's Mathematical Thinking, we introduce the Curricular Noticing Framework to describe how teachers recognize opportunities within curriculum materials, understand their affordances and limitations, and use strategies to act on them. This framework builds on Remillard's (2005) notion of participation with curriculum materials, connects with and broadens existing research on the relationship between teachers and written curriculum, and highlights new areas for research. We argue that once mathematics educators better understand the strategic curricular practices that support ambitious teaching, which we refer to as professional curricular noticing, such knowledge could lead to recommendations for how to support the curricular work of teachers and novice teachers in particular.

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Teruni Lamberg, Linda Gillette-Koyen and Diana Moss

( Dixon & Haigh, 2009 ). A challenge faced by mathematics teacher educators (MTEs) involves figuring out how to help teachers to formatively assess through professional noticing of student reasoning of mathematics, interpreting data, and using that

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Jen Munson

what teachers notice and the instructional decisions afforded by those noticings. To highlight the connection between noticing and instruction, I draw on Jacobs, Lamb, and Philipp’s (2010) conceptualization of the professional noticing of children