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Students' Mathematical Noticing

Joanne Lobato, Charles Hohensee, and Bohdan Rhodehamel

Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats noticing as a complex phenomenon that is distributed across individual cognition, social interactions, material resources, and normed practices. Specifically, this research demonstrates that different centers of focus emerged in two middle grades mathematics classes addressing the same content goals, which, in turn, were related conceptually to differences in student reasoning on subsequent interview tasks. Furthermore, differences in the discourse practices, features of the mathematical tasks, and the nature of the mathematical activity in the two classrooms were related to the different mathematical features that students appeared to notice.

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Eliciting and Analyzing Preservice Teachers' Mathematical Noticing

Julie M. Amador, Anne Estapa, Zandra de Araujo, Karl W. Kosko, and Tracy L. Weston

In an effort to elicit elementary preservice teachers' mathematical noticing, mathematics teacher educators at 6 universities designed and implemented a 3-step task that used video, writing, and animation. The intent of the task was to elicit preservice teachers' mathematical noticing–that is, noticing specific to mathematics content and how students reason about content. Preservice teachers communicated their noticing through both written accounts and selfcreated animations. Findings showed that the specific city of mathematical noticing differed with the medium used and that preservice teachers focused on different mathematical content across the methods sections, illuminating the importance for mathematics teacher educators understanding of the noticing practices of the preservice teachers with whom they work. This report includes implications for using the task in methods courses and modifying course instruction to develop noticing following task implementation.

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Mathematics Preservice Teachers Learning About English Language Learners Through Task-Based Interviews and Noticing

Anthony Fernandes

This article describes the 3rd cycle of an intervention in a mathematics content course that was designed to foster awareness among middle school mathematics preservice teachers (PSTs) of the challenges that English language learner (ELL) students face and the resources they draw on as they learn mathematics and communicate their thinking in English-only classrooms. Pairs of PSTs engaged 2 different ELL students in a videotaped task-based interview using 4 measurement tasks. Following each interview, the PSTs wrote a structured report guided by Mason's (2002) framework of noticing. The results of the intervention indicated that the PSTs went beyond awareness of ELLs' needs and challenges and also adopted strategies outlined in the literature that were aligned with best practices for teaching ELLs. The article also discusses the potential of the intervention and how it can be used by other mathematics educators.

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Noticing Children's Participation: Insights Into Teacher Positionality Toward Equitable Mathematics Pedagogy

Anita A. Wager

This article describes how teachers in a professional development course responded to what they noticed about children's participation in elementary mathematics classrooms and how what they noticed was connected to the teachers' positionality toward equitable mathematics pedagogy. Findings suggest that a lens of participation supported teachers as they considered how to provide more equitable mathematics instruction. Further, the depth to which teachers noticed children's participation was connected to their positionality as equitable mathematics educators.

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Noticing before Responding

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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Noticing Aloud: Uncovering Mathematics Teacher Noticing in the Moment

Jen Munson

Noticing student thinking is critical to crafting instructional responses ( Jacobs, Lamb, Philipp, & Schappelle, 2011 ). The details of student thinking teachers focus on and the sense they make of them shape the responses they consider, and

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Use of Video Analysis to Support Prospective K-8 Teachers' Noticing of Equitable Practices

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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Supporting Teacher Noticing of Students' Mathematical Strengths*

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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Noticing and Wondering to Guide Professional Conversations

Tracy E. Dobie and Eleanor R. Anderson

What do you notice? What do you wonder? In recent years, teachers have increasingly been using these questions in mathematics classrooms with students to encourage mathematical thinking and curiosity. We may show students an image, video, or

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Toward Professional Development for Multimodal Teacher Noticing

Janet Walkoe, Caroline (Caro) Williams-Pierce, Virginia J. Flood, and Margaret Walton

., 2009 ; and many others). In particular, professional development (PD) that supports teachers in noticing and interpreting student thinking is on the rise (e.g., Arbaugh et al., 2019 ; Kang & Anderson, 2015 ; Luna & Sherin, 2017 ; Walkoe, 2015