Publications

At AERA 2023, SIG-RME hosted a poster symposium (Garner et al., 2023) titledExpanding Coaching and Representations to Support Teacher Sense-Making Toward Disrupting Inequitable Mathematics Teaching Practices. The symposium discussed ways representations of instruction might support teacher learning with regard to equity and responsiveness. In this conceptual study, we continue and expand last years conversation, positioning the construct of representations of practice for teacher learning within the broader notion of pedagogical mediators. We provide categories to delineate their essential aspects and use these categories to compare and contrast four pedagogical mediators for mathematics teacher learning. Finally, we discuss implications for teacher learning with pedagogical mediators

Educational researchers widely acknowledge the promises and impediments of teachers collaborative sensemaking, illuminating the need to recognize additional resources that are salient for teachers within professional interactions. In line with this overarching goal, this study explores the role of mathematics teachers' previous professional experiences in their collaborative sensemaking. Theoretically, it is rooted in ecological theories of learning, highlighting that learning is always shaped by an interconnected set of environments. Empirically, it builds on data from a researchpractice partnership with a professional development (PD) organization, where we used classroom video to support secondary mathematics teachers' teams in improving their practice. The analysis first portrays two video-based conversations to illustrate the potential of inviting and building on teachers previous experiences and resources to support their collaborative reasoning. Then, it looks across nine video-based conversations of the same two teams and systematically describes experiences and resources that teachers spontaneously reference through six categories: PD workshops, conferences, PD organizations, online resources, research and policy, and curricula. These categories provide a framework for designers and facilitators who want to take seriously the practice of acknowledging that teacher learning happens through a complex web of learning experiences. The study brings forth the affordances of taking a learning ecology perspective on teacher collaborative sensemaking as professional development (CSPD) and provides guidance for designing, facilitating, and analyzing CSPD conversations in ways that center on teachers prior knowledge and experiences.

Students opportunities to persevere in making sense of mathematical ideas have long been considered significant to learning. Building on existing literature and a case study of video-based teacher collaborative sensemaking, we propose a conceptual framework for bridging perseverance and sensemaking. This framework synthesizes dispositional, metacognitive, and contextual-interactive theoretical perspectives on perseverance. Informed by these three research perspectives, the conceptual framework brings forth three interrelated mediators for bolstering perseverance practices and dispositions towards mathematical sensemaking: students positions as capable sensemakers, explicit problem-solving heuristics, and facilitation of student participation within their collective Zone of Proximal Development (ZPD). We argue that the three mediators, when brought together, provide a holistic and generative lens for teaching and teacher learning. To illustrate the framework and its utility, we build on a case study featuring a veteran middle-school mathematics teacher across his classroom facilitation of students engagement with a classical mathematical task, the Tower of Hanoi, and a subsequent video-based debrief about the lesson with his colleague and our research team. We first frame the analysis around classroom events, and then investigate teacher learning opportunities in the lesson debrief. By making explicit the complex work of directing perseverance towards sensemaking, this study provides a more nuanced understanding of perseverance for teaching and teacher learning. Moreover, developing clarity around notions of perseverance in mathematics classrooms helps mitigate the potential dangers of the term being taken up in ineffective or even harmful ways.

From a teachers perspective, teacher learning happens through a complex web of learning experiences. However, research on teacher professional development (PD) typically focuses on the direct influence of single activities or programs. PD researchers less often acknowledge the interactive impacts on teacher learning of the multiple experiences teachers have in different contexts. This conceptual paper works toward a more thoroughgoing ecological framing of teacher PD by bringing forth three dimensions of teacher learning that are often overlooked: scope, interconnectedness, and temporality. The essay centers on the type of design that is widely considered high-quality PDnamely, experiences that are collaborative and situated in teachers instructional contextand considers those experiences from the perspective of these three dimensions. I illustrate this framework and its affordances with data from a 4-year research project rooted in video-based mathematics teacher conversations. The focus on scope allows researchers to name and distinguish contexts that are salient to their different studies. The focus on interconnectedness uncovers the interactive relationship between the immediate and broader PD contexts. Finally, the focus on temporality affords the understanding of different phases in learning and extends linear conceptions of progress. Together, these dimensions provide a rich conceptualization to better inform the work of teacher educators.

In this chapter, we look at how our co-inquiry activity supported teachers' learning over longer time periods. Using the cases of Brad Miller and Julie Woodman, we show how teachers developed important practices and concepts about ambitious and equitable mathematics instruction through repeated experiences with the video formative feedback (VFF) process. For Brad, a moment of insight spurred by a VFF led him to pursue learning about supporting student groupwork systematically, making new modifications to his practice over two years. For Julie, her learning converged around a particular relationship in teaching the connections between instructional design and student engagement that gave her a new lens on how to make her classroom more inclusive. We describe their learning in relation to our model of teacher learning as the evolution of pedagogical judgment, highlighting how the VFF enabled them to reason about their pedagogical actions in light of their pedagogical responsibilities using the rich records of practice, bringing these in greater alignment.

Over the last two decades, researchers have portrayed quality professional development for mathematics teachers as collaborative and situated in teachers instructional realities. However, empirical findings also point out various impediments to transforming teacher conversations into consequential learning. These findings illuminate the need to acknowledge additional resourcesthat teachers bring to professional interactions and the need for ever more nuanced theories of teacher learning to inform teacher educators work. Inspired by ecological models of learning, in this conceptual paper I work towards understanding teachers collaborative sensemaking as part of broader teacher learning ecologies. I distinguish and name possible scopes and contextsfor the study of teacher learning in conversations about instruction, and then identify directions for future research towards stronger connections between immediate and broader contexts.

Research on mathematics teachers learning typically focuses on single activities or programs and does not acknowledge the interactive impacts of multiple experiences in different settings. In contrast, from a teacher perspective, teacher learning happens across time and settings, through a complex web of learning experiences. In this conceptual paper, I propose how we could extend interactionist approaches to include a systems-level lens, towards a theory of teacher learning ecologies.

Gender-based achievement and participation gaps in mathematics among Palestinian/Arab Israelis favor girls and women, in the face of various intersecting challenges. We follow the stories of Palestinian/Arab Israeli women students in mathematics education to better understand the context of their success in school mathematics and early career trajectories. Our analysis shows emergent related master-narratives: of Israel as a meritocracy; diligence as key to success in mathematics for girls and women; and mathematics achievement holding precious exchange-value. Guided by critical race feminism and Scott's notions of public/hidden transcripts, our intersectional analysis shows how the women's stories confirm, challenge, and inflect these narratives. We propose directions for further research and additional implications.

In this paper, we offer a framework for teacher monitoring routinesa consequential yet understudied aspect of instruction when teachers oversee students working together. Using a comparative case study design, we examine eight lessons of experienced secondary mathematics teachers, identifying common interactional routines that they take up with variation. We present a framework that illuminates the common moves teachers make while monitoring, including how they initiate conversations with students, their forms of conversational entry, the focus of their interactions, when and how they exit the interaction as well as the conversations overall participation pattern. We illustrate the framework through our focal cases, highlighting the instructional issues the different enactments engage. By breaking down the complex work of groupwork monitoring, this study informs both researchers and teachers in understanding the teachers role in supporting students collaborative mathematical sensemaking.

This session addresses two major problems that hold back research on teacher learning. First, research often tests efficacy of professional learning interventions without illuminating how teachers learn within the intervention. Second, as a field, we have not reached consensus on how to document teacher learning, making it hard to share results in robust ways. For instance, researchers rarely view and discuss video from each other's professional learning interventions, making it difficult to build shared ideas about concepts like \u201cnoticing student thinking\u201d or about specific experiences that build teacher learning. To address these issues, this session will present professional learning video from four research projects focused on teachers' learning to improve mathematics instruction. Video will be linked to a tentative conceptual framework of teacher learning that will be critiqued by the audience, discussant, and presenters, in order to expand it, identify gaps, and provide a shared framework for future research.

Our goal in this study is to explore students' mathematical participation in collaborative groupwork with relation to teachers' instruction. By doing so, we address two challenges for research of teaching and learning: (1) the under-conceptualization of the teacher role during students' groupwork; and (2) the need to explicate the connection between teaching and learning. We suggest that, to connect student learning to teacher monitoring practices, it is valuable to link two different scales of analysis: (1) between-groups teacher groupwork monitoring routines; and (2) within-groups interactions with and without the teacher. We argue that such methodology affords a generative discussion of teachers' instructional practices and their disruption or reproduction of exclusionary aspects of students' conversations. To illustrate our approach, we look at two teachers. First, we describe and compare their groupwork monitoring routines. Then, we look at students' conversations within those classrooms and discuss connections between these conversations and instruction.

Charles Goodwins legacy includes a multitude of analytical tools for examining meaning making in interaction. We focus on Goodwins substrate\u201cthe local, public configuration of action and semiotic resources\u201d available in interaction used to create shared meanings (Goodwin, 2018, p. 32), gathering early career scholars to explore how research designs adapt substrate as an analytical tool for education research in diverse settings. This structured poster session examines how substrate can be used to capture a complex web of learning phenomena and support important analytical shifts, including representing learning processes, privileging members phenomena to address issues of equity, and understanding shifting power relations through multi-layered and multi-scaled analyses.Teacher sensemaking with and about external conceptual resources

Mathematics teachers develop understandings about instruction across multiple settings, such as classrooms, workshops, and professional learning communities. When teacher teams collaborate, their prior teaching and learning experiences meaningfully inform their sensemaking. However, current research does not explicitly link teacher conversations and these multiple settings for learning. In this study, we seek to understand secondary mathematics teachers collaborativelearning in schools as part of broader teacher learning ecologies. Using discourse analysis and a comparative case study design, we examine how two teacher teams conversations recruit external conceptual resources to support the development of their collective pedagogical judgment. In particular, these external resources offered the teams rich representations of practice and productive framings of teaching problems.

This paper examines the mechanisms by which students cultural background plays an active role in the study of mathematics. It does so with the aid of two main constructs: hybrid discourse and intellective identities. At the center of the article is an analysis of a classroom episode from a preparatory program in which adult ultra-orthodox Jews study high school mathematics for the first time. We show how different cultural resources, among them students cultural preference for disagreement, are being used to create a new hybrid discourse of mathematics and the Talmud while discussing the veracity of a mathematical proof. The hybridity can be seen in four characteristics of discourse: routines for endorsement of narratives, interactional routines, authority structure, and purpose of learning. We elaborate on the process by which this hybridity is constructed through students positioning actions and the ways in which these positions are supported by students intellective identities.

In this paper we conceptualize teacher monitoring routines a consequential yet understudied phase of instruction during students collaborative work. We examine 5 lessons of experienced and equity-oriented secondary math teachers using a comparative case study design and analysis of their interactional routines. Our goal is to understand how teachers monitor group work and how they decide (intentionally or not) when, where, and how to intervene in student talk. We identified various patterns that make clearer the micro-judgments monitoring routines entail for teachers (a) ways of moving among students and conversational initiation, (b) conversational entry; (c) focus of the interaction; (d) when and how to exit the interaction; and (e) conversation participation pattern; with an eye toward teachers goals and instructional contexts. We end by considering implications for research on teaching and professional education in support of collaborative learning.

Students opportunities to struggle with mathematical ideas have long been considered paramount to learning. However, theres little research on how teachers (1) draw on and make sense of the discourses of perseverance, (2) enact it in classroom, and (3) develop an expansive view of perseverance. To contribute to these lines of research, we build on a case study featuring a veteran mathematics middle-school teacher across two settings: his classroom where hefacilitates students engagement with a classical mathematical task, the Tower of Hanoi, and in a subsequent video-based debrief with his colleague and our research team. We propose a conceptualization of perseverance as upholding three dimensions of (a) persistence (b) sensemaking and (c) problem solving heuristics. We argue for its potential as a conceptual resource for operationalizing perseverance more comprehensively.

This case study explored the educational benefits that can be gained from experiencing and sharing pedagogical failure. It examined the potential of an instructional failure to open up opportunities for teachers collaborative learning and the development of their adaptive expertise. Applying linguistic ethnographic methods and frame analysis, we focused on an audio-recorded team meeting of mathematics teachers discussing a videotaped ninth-grade geometry lesson. The videotaped teacher shared the lesson with her colleagues to explore her failure to teach her students how to write a two-column proof. We show how the team's discussion of their colleague's failure opened up an opportunity to critically reflect on a standard practice and advance their pedagogical sensitivity, interpretation, and repertoire. However, this opportunity was not fully realized because of the team's failure to productively frame the failure. The findings highlight the role of socio-emotional obstacles, such as face-work and coping with uncertainty, in framing failure and in turning an individual instructional failure into a collaborative opportunity for teachers to learn. The study expands our understanding of how failure experiences can be beneficial in educational contexts by underscoring the centrality of framing processes in managing socio-emotional obstacles. It suggests that educating teachers about productive framing of failure and ways to support it is imperative for failure experiences to promote learning.

This study examines \u201critual\u201d and \u201cexplorative\u201d participation in math classroom. We use the case of adult ultra-Orthodox studying algebra for the first time, to present a rare example of ritual teaching which is responded to by explorative participation. We explain it by addressing students \u201cintellective identities\u201d as they stem from students experience in Talmud studies, a main practice of the ultra-Orthodox culture. We conclude by discussing the potential relevancy of the case to mathematics education.

במחקר זה אנו מנתחים את השיח המתמטי בכתה של חרדים מבוגרים שלומדים מתמטיקה תיכונית לראשונה.התלמידים מגיעים לכתה כמעט ללא רקע מתמטי, אך עם ניסיון רב בלימודי תלמוד בישיבה. במאמר ננתח שיעורבנושא הוכחת נוסחת השורשים ונדגים כיצד התלמידים משתמשים במקורותיהם התרבותיים ליצירת שיח היברידימתמטי-תלמודי. לסיכום נדגים כיצד השיח ההיברידי פותח וסוגר בפניהם אפשרויות ללמידה.

This paper examines the case of adult ultra-orthodox Jews studying algebra for thefirst time, in a pre-college course. First, the social context and Talmudic backgroundof the students is presented. Then, we analyse how cultural resources from both theTalmudic studies, the main practice of ultra-orthodox culture, and the mathematicsclassroom culture, were used by students to construct a new hybrid discourse. Weconclude by discussing how our analysis demonstrates some productive possibilitiesand potential problems for the students' mathematical learning.