Publications

This study explores how STEM teachers in crisis contexts understand and cultivate cognitive, emotional and social resilience in their classrooms. Twenty-seven Israeli STEM teachers participated in semi-structured interviews. Teachers embedded resilience in instruction through three strategies: (a) reorganizing content and problem-solving routines to maintain cognitive continuity, (b) modeling emotion-regulation techniques that normalize struggle and build confidence, and (c) nurturing peer and teacher-student networks that share resources and emotional labor. Framing resilience as an interactive classroom process rather than a fixed trait, the study offers transferable insights for professional development and policy to strengthen STEM education during crises.

This paper introduces a framework of two key shiftsepistemological and authorityto conceptualise the challenges mathematics teachers face when moving from classroom teaching to professional development (PD) facilitation. I argue that while teaching and facilitation may appear similar, critical differences in how knowledge is constructed and how authority operates in these environments can disrupt facilitation and limit opportunities for teacher learning. The framework is illustrated through narratives of novice facilitators in a video-based, process-oriented collaborative PD program. These shifts help explain how facilitation expertise emergesand why it can be difficult to developwithin the subject-specific context of mathematics.

The complexity of mathematics teaching is especially evident in lessons where teachers build on students genuine ideas, such as problem-based lessons. To enhance teachers capacity for rich discussions in problem-based instruction, we have developed a unique approximation of practice: digital asynchronous simulations where teachers make subject-specific decisions for a virtual teacher avatar. The simulations are based on materials and principles from a practice-based professional development (PD) program, implemented with small groups of teachers. The self-paced simulation model offers flexibility and scalability, allowing more teachers to participate on their own schedules, but it lacks key affordances of collaborative PD. To examine how to leverage the affordances of collaborative, practice-based PD, this paper uses a design-based research approach to explicate the mechanisms in which digital simulations can support mathematics teachers learning about problem-based lessons. We focus on two cycles of design, implementation, analysis, and revisions of the simulation model, drawing on data from focus groups with mathematics teacher educators, prospective teachers performance, and teachers reflective assignments. The analysis illustrates how two design principles Authenticity to the teachers work, and Nuanced feedback were transformed to better reflect aspects of practice-based teacher learning. We argue that self-paced, asynchronous simulations with indirect feedback can effectively emulate aspects of collaborative, practice-based PD in supporting teachers growth. The paper also contributes to the literature on mathematics teachers noticing and decision-making, examining how the two interact in simulated environments. We suggest implications for designing practice-based asynchronous digital simulations, drawing on emerging technologies.

Professional development (PD) facilitators are central to educational systems, yet their practices and professional growth have received limited attention. This paper examines positioning, identity, and agency among novice mathematics PD facilitators, focusing on how practicing teachers in these roles locate themselves in discussions in terms of sharing their professional stances. The context of facilitation is a video-based, process-oriented PD program-that is, a PD which prioritizes reflection and peer discussion over prespecified content. In such programs, facilitators guide discussions that extend beyond subject matter to tackle multifaceted, sensitive problems of practice, a context where stance-sharing dilemmas often emerge. Drawing on extensive data, we identify five positionings-Neutrality, Guided Discovery, Explicitness, Interweaving, and Protectiveness-and demonstrate how each relates to facilitators' evolving identities and sense of agency. Our framework offers new insights into STEM teacher leadership-including the work of coaches, teacher leaders, and mentors-by highlighting a unique problem of practice leaders face when navigating their participation in multiple professional communities.

Mathematics teachers' professional learning is moving away from prescriptive professional development (PD) toward collaborative, practice-based modelssuch as video-clubs and lesson co-designwhich provide teachers with space and time to discuss problems of practice among peers. Some models, which we term "process-oriented", exclusively focus on fostering teachers professional discourse and reflection rather than pushing for the implementation of specific classroom practices. Although research has documented the affordances of process-oriented teacher learning, less is known about the complexities involved. This multi-perspective qualitative study describes tensions surfaced by teachers and a facilitator in an online lesson-design programme in the United States. We identify two core tensions: valuing collaboration and relating to the programmes process-oriented aims, and we trace these tensions to participants prior PD and classroom experiences, showing how implicit expectations about PD processes and outcomes shape participants' engagement with innovative learning opportunities. These findings contribute to the field's understanding of collaborative and process-oriented teacher learning by highlighting the presence of a didactical contract within in-service teacher learning contexts, which resonates with the classroom didactical contract. We posit that recognising and addressing teachers' implicit expectations is essential for designing PD that is not only innovative in form but also responsive to practitioners.

Critical elements of the expertise of mathematics teacher educators (MTE) can be identified in the artifacts they design for working with prospective teachers (PT), specifically for engaging PT in the double role of practitioners and students of practice. While MTE are increasingly utilizing designed multimodal representations of practice (such as storyboards), theoretical frameworks and methods for analyzing these pedagogical artifacts and the meanings they support are still in early development. We utilize a semiotic framework, expanding systemic functional linguistics to encompass non-linguistic elements, to identify aspects of what we call navigational expertisewhich supports PTs in engaging both as practitioners and students of the practice. We view this expertise as tacit knowledge-in-use, enacted through artifact production. The paper demonstrates MTEs navigational expertise by showing how MTE design storyboards of practice to engage PT as fellow teachers experiencing the lesson taught by a peer and as university students who consider the artifact (including the represented lesson) as an object of study. The framework allows us to identify how MTEs navigational expertise lies in seamlessly interweaving these two purposes and navigating between them, knowing when, how, and for what purposes to invoke each. Through analysis of storyboards from four MTE in diverse US settings, we uncover some of the nuanced tacit components of navigational expertise, highlighting linguistic and non-linguistic design choices and their potential meanings for transactions with PT.

Mathematically Responsive Teaching (MRT) is widely recognized as a cornerstone of high-quality instruction. However, its common definition is narrowly focused on specific teacher moves (e.g., eliciting student thinking). This theoretical paper redefines MRT to consider student experiences and needs alongside their mathematical ideas. Methodologically, it advocates moving beyond teaching moves to recognize a responsive stance toward students and emphasize authentic relationships with them, rooted in Buberian principles. The identification of an MRT stance is demonstrated through an analysis of a 10th-grade low-track statistics lesson.

We examine data from a simulation of teaching where teachers noticed similarities and differences among pieces of student work done in a problem-based lesson where they are selecting work to be discussed. In this methodological contribution, we illustrate the articulation of multidimensional scaling and Mantel correlations to examine the presence of considerations of normativity and serviceabilitycategories of perception that matter for a teachers management of problem-based instruction.

Rubel, L. H., Ehrenfeld, N., Schwarts, G., Dreyfus, T., & Sfard, A.

This group report focuses on two key aspects of research on teacher learning in TWG18:(1) what is being studied-the main topics of interest, that is, the subjects and objects of research; and (2) how these topics are investigated-particularly in relation to various theories of learning. Our goal is to map the contributions to CERME14 through these two lenses, offering both a descriptive overview of the current landscape and a critical perspective on our research community. Such a perspective is essential for identifying blind spots, questioning taken-for-granted assumptions, and pushing our collective work forward.

When novice facilitators start to lead teachers professional development (PD), they have been found to struggle to combine a strong participant focus (i.e., valuing and working with participating teachers needs and ideas) and goal focus (working toward the PD goals), whereas expert facilitators seem to be more able to integrate both focus. Empirical studies have identified these challenges across contexts and several situational demands, for example, when facilitators set goals, plan a PD activity, notice teachers ideas, and moderate video-based discussions. In this paper, we contribute to this line of research by investigating another situational demand in a longitudinal perspective: We studied how two novice facilitators moderated the discussion after the same PD activity several times. The qualitative comparative analysis of transcribed videos from PD sessions revealed that each facilitator used several practices with varying degrees of goal and participant focus. Over time, they learned to apply more practices that were, simultaneously, strongly goal and participant focused: By leveraging teachers ideas toward the PD content goals, they achieved integration of both focus, which have sometimes previously been experienced as conflicting. We discuss implications for facilitator preparation programs in terms of unpacking facilitation practices and explicitly working with the content elements for finer-grained goals.

Building on the critique of binary frameworks and the need for a nuanced understanding of instructional practices, we offer a methodological approach for gauging teachers professional growth through a simulation designed to support secondary mathematics teachers in facilitating problem-based lesson discussions. This paper explores data from a pilot online teaching simulation which, by design, avoids feedback reliant on binary labels for instructional practices. The study analyzes responses from ten prospective teachers in a simulation that supplements Milewski & Stricklands (2020) functional framework for responding with subject-generic and subject-specific categories. Our findings demonstrate the viability of this approach in revealing shifts in participants' awareness of the linguistic functions underlying their responding moves.

We illustrate how concepts from systemic functional linguistics are adapted for the analysis of multimodal representations of practice used in activities where teachers and teacher educators transact meanings about practice. We focus on the transactive register used to project practice meanings to the audience of these representations. We showcase the systems called visibility (how much of the classroom experience happening is made visible to the viewer), temporality (how sequence and duration of events are represented), and theme (how semiotic resources maintain and develop themes). We apply these systems to examine the differences between two storyboards of algebra lessons that were used in a professional development context and the different kinds of reactions teachers offered to the different story boards.

Virtual simulations are a promising tool for mathematics teachers preparation and professional development. This paper focuses on a set of simulations of a problem-based lesson, illustrating how their design informed prospective teachers changes in decision-making during simulations. Using a design-based approach and conjecture mapping, we trace the processes that could be attributed to the observed changes in teachers' decisions. The analysis shows that after completing the set of simulations, teachers increased their selection of student work that relates to the lesson goal, regardless of its correctness. The paper contributes to the understanding of virtual simulations as a sustainable tool for teacher preparation and professional learning.

A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the analysis of the resulting artifacts, especially when these are multimodal? This paper lays the groundwork for answering such questions by drawing on empirical data from a lesson-centered PD program for secondary geometry teachers. We show how semiotic choices were made to convey that the teacher would need to support students when geometry instruction moves from a construction task to a proof, by (1) addressing students confusion; and (2) creating a shared language to discuss diagrams.We relate these findings to teachers professional growth and the conference theme.

Facilitators of professional development (PD) for mathematics teachers currently gain increasing attention, as their practices are crucial for the success of spreading mathematics educational ideas and innovations into schools and strengthening the professional expertise of teachers. So far, mainly two components of facilitation have been empirically researched: facilitators knowledge resources and facilitation moves. In this paper, we propose to develop a more comprehensive conceptual framework in order to explain facilitators practices and underlying decisions. For this purpose, we lift Schoenfelds ROG framework for teachers' decision-making (comprising resources, orientations, and goals) to the facilitator level, and add identity as a fourth component to obtain what we call the ROGI framework. We draw on data collected simultaneously in two PD projects for mathematics teachers in Germany and in Israel. Through three cases of facilitation, we illustrate how the adapted ROGI framework helps to understand processes of decision-making made by facilitators during mathematics professional development sessions.

Professional development (PD) courses are the main context for mathematics teachers' lifelong learning. Leaders with expertise are needed to facilitate these courses; thus, there is a growing interest in understanding the nature of this profession, its core practices, and the challenges it entails. This paper focuses on a specific group of facilitators: experienced mathematics teachers who have just begun facilitating PD courses in addition to their classroom teaching. To better understand these novice facilitators' practices, a commognitive approach was implemented to examine how they draw on their mathematics teaching experience when leading PD courses. In commognitive terms, these practitioners draw on multiple professional discourses, but mostly on the discourses of teaching and facilitation. The analysis of the challenges and affordances associated with participating in these two professional discourses showed that novice facilitators bring into play their teaching practices in four distinct ways: enacting a familiar practice, negating a familiar practice, questioning the relevance of a familiar practice, and generating a new practice based on their teaching experience. We claim that novice facilitators' well-established identity as teachers is both a challenge and an asset in grounding successful facilitation practices. Overall, facilitators modify their teaching experience through the adoption, adaptation, and retraction of their teaching practices. Implications for the preparation and support of facilitators, within processes of upscaling PD programs, are discussed.

How can mathematics teachers (MTs) be supported in teaching mathematics for climate justice (TMfCJ) if mathematics teacher educators (MTEs) lack climate-related expertise? In this paper, we challenge the assumption that such expertise is essential, and consider ways in which MTEs can use their existing expertise to support MTs in TMfCJ. The context of this study is a professional development programme for MTs in England where we examine how one MTE relates to ways of knowing about mathematics, pedagogy, climate justice and their intersections. Results suggest that the MTEs existing expertise in relation to how MTs learn, together with her lack of climate-related expertise, enable an authentic co-inquiry where expertise relating to the intersection of mathematics teaching and climate justice can be co-created.

Building on student work (SW) in mathematics classroom discussion requires complex decision-making from mathematics teachers. Previous literature on problem-based lessons recommends selecting and sequencing pieces of SW in a way that creates a mathematical storyline, but there is rarely any empirical evidence on how mathematics teachers can master such practices. We use the case of StoryCircles, a lesson-based professional development program, to show how iterative processes in which teachers were engaging with SW assisted them in developing heuristics for a careful selection and sequencing of SW. The results show that these processes involved 1) the teachers emerging awareness of features of SW; and 2) an evolving capacity to relate these features to the lesson goal. We discuss design features that fostered these changes.

In this paper we examine how facilitators' prior experiences as mathematics teachers frame their work when facilitating a practice-based professional development (PD) for the first time. We focus on the experiences of a novice facilitator of StoryCircles, a professional learning process in which teachers collectively script and visualize a problem-based lesson, arguing about theirrationales for different decisions connected to discussions of students work. We situate the challenges the facilitator encountered by identifying the expectations that were not met while she was facilitating and offer possible connections to the PD design. We close by suggesting a perspective to account for facilitation challenges

The enactment of norms is a key challenge for professional development (PD) facilitators, particularly in video-based programs where teachers tend to be judgmental. This study follows seven novice facilitators of a video-based PD program that aims to promote reflection on practice while downplaying criticism on the filmed teachers' actions. We describe how the novice facilitators enacted norms and responded to teachers' judgmental comments, in order to unpack this challenge. The findings show that although the facilitators underwent the same preparation, considerable variations were found in their decision-making concerning this issue. We describe possible reasons for the different decisions, and suggest implications.

With the proliferation of video-based professional development (PD) courses for mathematics teachers, understanding the role of the facilitators of these courses has become an emerging field of theoretical and empirical study. The purpose of this article is to address some of the challenges and opportunities that facilitation of discussions between mathematics teachers poses, by analysing catalytic episodes in which we were involved as facilitators. We offer a new construct, discussions sense, to capture the complex decision-making done by facilitators.

Novice facilitators of professional development (PD) programs for mathematics teachers often face challenges in leading productive discussions and achieving the goals of these programs. Although research in this area is gradually accumulating, not much is known about how novice facilitators address these challenges and change their practices accordingly. This paper presents case studies of two novice facilitators of PD programs in two different countries. The analyses look at their work over one year, to illustrate the changes in their practices while managing discussions. The results show that although the facilitators operated in different contexts, their practices and their processes of change resembled, suggesting that these processes are not idiosyncratic. We argue that novice facilitators changes in practices correspond to changes in their resources, orientations, goals, and identities and that PD program teams can support these changes.

Many professional development environments (e.g., courses, teacher communities) center on discussions about pedagogical and mathematical practices. These discussions usually go beyond \u201crights and wrongs\u201d towards the formation of reflective arguments through interactions and dialogues. Thus, the productiveness of these discussions largely depends on facilitation skills, which only recently have become the object of thorough scrutiny. This study focuses on one aspect of facilitation of discussions: do the facilitators envision their role as a neutral \u201cguide on the side\u201d or rather as a participating colleague, or somewhere in between? The consideration of this question raises important theoretical and practical implications for the professional development of facilitators.

This paper reports on a study conducted within VIDEO-LM (Viewing, Investigating and Discussing Environments of Learning Mathematics), a video-based professional development project for secondary mathematics teachers that aims to enhance reflection on practice. The study explored VIDEO-LM sessions where Israeli teachers watched an 8th grade geometry lesson from Japan. We analyzed teachers discussions around this lesson and characterized main themes and reflection types. Findings suggest that watching the Japanese lesson, using the VIDEO-LM framework, led to productive discussions among teachers. The fact that the videotaped lesson was culturally \u201cfar\u201d from the teachers reality provoked them to re-see everyday aspects of their practice, revealing some dissonances which promoted reflective thoughts and actions.

Collaborative professional development initiatives require skillful facilitation. The purpose of this paper is to characterize challenges in leading a collaborative video-based professional development for the first time, and highlight the importance of the programs support team in addressing them. A case-study approach was used to illustrate one novice facilitator's professionalization process over one year. It was found that although the facilitator did not perceive herself as a leader at the beginning of the year, towards its end she fostered collaborative video-based discussions, in parallel with the consolidation of her facilitator identity. This study provides insight into how novice facilitators practices and identities evolve, as well as what is required to support this process

The purpose of the study reported herein was to closely observe the reflective process of one teacher who participated in a video-based professional development course for secondary school mathematics teachers. This process was initiated in a session where a group of teachers watched and analysed a Japanese TIMSS lesson, and continued with the teachers decision to teach this lesson in her class. We analyse the teachers reflective process in terms of Ricks (2011) "process reflection" framework, and explore the factors that affected it. The results demonstrate the impact that facilitated peer discussion around a videotaped foreign lesson may have on teachers' reflection.

במסגרת פרויקט עדש"ה )עמיתים דנים בשיעורי המתמטיקה( במחלקה להוראת המדעים במכון ויצמן, מתנהלות מזה שלוש שנים השתלמויות המשתמשות בוידאו ככלי ללמידה של מורים למתמטיקה ברמה העל-יסודית. המורים המשתתפים בהשתלמויות צופים בשיעורי מתמטיקה מהארץ ומהעולם ומנתחים אותם באמצעות מסגרת ניתוח ייחודית לפרויקט. אחד השיעורים בהם צופים המורים הוא שיעור יפני שנסקר ונותח במקומות שונים בעולם, ואשר מקובל לראות בו סרט המייצג את שיעורי המתמטיקה ביפן. בהרצאה זו אציג מחקר אמפירי המנתח דיונים של מורים סביב השיעור היפני וסוגיות עמוקות העולות מדיונים אלו. ממצאים ראשוניים מראים כי, בין השאר, הסרט הציף בקרב המורים סוגיות של זמן לעומת עומק בבניית השיעור. כמו כן, מורים רבים אימצו לכיתתם מאפיינים מהשיעור בו צפו.