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Jen Munson

, ultimately, the decisions teachers make. A growing body of research has explored what teachers notice and how professional development might support teachers in learning to notice in increasingly nuanced ways (cf., Jacobs & Empson, 2016 ; Jilk, 2016 ; van

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Madhuvanti Anantharajan

of teacher noticing ( Jacobs et al., 2010 ; Sherin et al., 2011 ), the present study applies the framework to examine the mathematical ideas that participants perceived when observing their students’ counting activities and representations

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Rachael Eriksen Brown and Kimberly Masloski

This article shares the authors' use of written teaching replays as part of a professional development experience for beginning secondary mathematics teachers. This form of narrative writing is inspired by Horn's (2010) descriptions of teachers sharing their practice in professional learning communities. In this study, written teaching replays are used to gain insights about what beginning teachers noticed about their teaching practice and whether these noticings highlighted dilemmas or successes in their teaching practice. The analysis of teaching replays indicated that, despite being in their _ rst years of teaching, these beginning teachers' narrative writings focused least on management issues. Instead, the writings had a strong focus on mathematics or teaching mathematics as well as on social issues within their classrooms. These _ ndings counter the research literature that suggests beginning teachers are overwhelmingly concerned with classroom management. The authors conclude with their re_ ections on the potential of this form of narrative writing for beginning teachers and how it could be used by other mathematics educators.

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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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Stephanie Casey and Joel Amidon

PSTs’ professional noticing skills, which can be used to inform future learning opportunities. However, challenges with such assessments include collecting meaningful artifacts of preservice teachersnoticing ( Nickerson, Lamb, & LaRochelle, 2017 ) and

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Lisa M. Jilk

Video cases and video clubs have become popular tools for supporting teacher learning. One concern is that many of the video projects discussed in the research literature may unintentionally continue to perpetuate deficit perspectives about students by focusing more on their gaps in understanding than on the strengths they bring to their learning. This article describes a video club that is part of a multidimensional professional development network that aims to re-culture mathematics classrooms so that all students have challenging and empowering learning experiences. I discuss shifts in teachers' ways of seeing and talking about students' mathematical activity that the video club has made possible, as well as features of the video club that have supported these shifts.

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Amy Roth McDuffie, Mary Q. Foote, Corey Drake, Erin Turner, Julia Aguirre, Tonya Gau Bartell and Catherine Bolson

Mathematics teacher educators (MTEs) designed and studied a video analysis activity intended to support prospective teachers (PSTs) in learning to notice equitable instructional practices. PSTs from 4 sites (N = 73) engaged in the activity 4 to 5 times during the semester, using a set of 4 “lenses” to analyze teaching and learning as shown in videos. In an earlier analysis of this activity, we found that PSTs increased their depth and expanded their foci in noticing equitable instructional practices (Roth McDuf_ e et al., 2013). In this analysis, we shift the focus to our work as MTEs: We examine our decisions and moves in facilitating the video analysis activity with a focus on equity, and we discuss implications for other MTEs.

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Higinio Dominguez and Melissa Adams

Complement teacher noticing with student noticing to enhance the teaching and learning of estimation.

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Sarah A. Roller

Teachers and mathematics teacher education scholars have identified field experiences and quality mentoring as influential components of math teacher preparation and development. Yet, quality mentoring is a complex and demanding practice. Providing educative feedback to novices, particularly that which encourages reflection versus evaluation, can be challenging work for mentors. To study the potential of an intervention for providing professional development for mentors, I worked with pairs of mentors and prospective teachers (PSTs) offering Smith's (2009) noticing and wondering language as a way of structuring mentoring conversations that maintain both descriptive and interpretive analytic stances. Analysis of before and after conversations provided evidence of how mentor-PST pairs adopted noticing and wondering language, and in particular illuminated the ways in which the language structure might support interpretive mentoring conversations for studying teaching. The results suggest that mathematics teacher educators may want to consider what makes wondering challenging work and how to best support wondering in educative mentoring conversations.

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Melissa Soto and Bethany Schwappach

Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorporate into his or her classroom repertoire with little effort and maximum impact. Screencasts allow students to share their thinking and strategies and help teachers notice how a child solved a problem, beyond just examining the student's finished work. The authors share novel ways to use screencasting in mathematics classrooms.