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1. Using gallery walks for compare and connect: Developing adaptive expertise of mathematics language routines

   Roberts, S A; Olarte, T R; Rodriguez, M (November 2024, Proceedings of the forty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Kosko, K W; Caniglia, J; Courtney, S A; Zolfaghari, M; Morris, G A (Ed.)

   We examined teachers’ development of adaptive expertise of mathematics language routines (MLRs) as they engaged in Studio Day professional learning focused on the MLR Compare and Connect. We collected video data from pre- and post-Studio Day meetings, as well as debriefs and their lesson enactments. We analyzed the data using three dimensions of adaptive expertise: flexibility, deeper level of understanding, and deliberate practice. We share a case study of a teacher exhibiting dimensions of adaptive expertise during the Studio Day Cycle through the use of a gallery walk. The teacher’s enactment of the MLR Compare and Connect provides an image of a teacher’s adaptive expertise of this MLR and helps us understand these MLRs and how teachers use and make sense of them in their instruction. 

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2. Studio as a Catalyst for Incremental and Ambitious Teacher Learning

   https://doi.org/10.3390/educsci14111160  

   Elliott, Rebekah; Roberts, Sarah A (November 2024, Education Sciences)

   This article explores how the practice-focused Studio professional learning (PL) model can provide incremental and ambitious teacher learning opportunities. We argue that when the model’s structures and practices are grounded in ambitious and equitable teaching, they catalyze incremental teacher learning. Studio, like lesson study, supports teachers in considering the entailments of lessons, focusing on the live shared enactment to strengthen teaching and learning through collaborative analysis and reflection. To build our argument, we drew from two Studio projects that had shared structures of cycles of learning and routines, as well as shared practices of using rich representations and collective interpretations of teaching. While both projects’ structures and practices take up ambitious and equitable teaching, they use different routines and attend to different features of equitable teaching. Building on a history of PL models, such as lesson study, which use similar structures and practices as powerful catalysts of teacher learning, we argue that Studio’s structures and practices can catalyze teachers’ incremental learning of ambitious and equitable teaching. We discuss the implications for future research based on this argument and for those leading PL. 

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3. A Sociocultural Perspective on Beginning Teachers Enacting Reasoning and Proving Practices

   Weingarden, M.; Buchbinder, O. (January 2022, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Higgins, A. (Ed.)

   The critical role of teachers in supporting student engagement with reasoning and proving has long been recognized (Nardi & Knuth, 2017; NCTM, 2014). While some studies examined how prospective secondary teachers (PSTs) develop dispositions and teaching practices that promote student engagement with reasoning and proving (e.g., Buchbinder & McCrone, 2020; Conner, 2007), very little is known about long-term development of proof-related practices of beginning teachers and what factors affect this development (Stylianides et al., 2017). During the supervised teaching experiences, interns often encounter tensions between balancing their commitments to the university and cooperating teacher, while also developing their own teaching styles (Bieda et al., 2015; Smagorinsky et al., 2004; Wang et al., 2008). Our study examines how sociocultural contexts of the teacher preparation program and of the internship school, supported or inhibited proof-related teaching practices of beginning secondary mathematics teachers. In particular, this study aims to understand the observed gap between proof-related teaching practices of one such teacher, Olive, in two settings: as a PST in a capstone course Mathematical Reasoning and Proving for Secondary Teachers (Buchbinder & McCrone, 2020) and as an intern in a high-school classroom. We utilize activity theory (Leont’ev, 1979) and Engeström’s (1987) model of an activity system to examine how the various components of the system: teacher (subject), teaching (object), the tasks (tools), the curriculum and the expected teaching style (rules), the cooperating teacher (community) and their involvement during the teaching (division of labor) interact with each other and affect the opportunities provided to students to engage with reasoning and proving (outcome). The analysis of four lessons from each setting, lesson plans, reflections and interviews, showed that as a PST, Olive engaged students with reasoning and proving through productive proof-related teaching practices and rich tasks that involved conjecturing, justifying, proving and evaluating arguments. In a sharp contrast, as an intern, Olive had to follow her school’s rigid curriculum and expectations, and to adhere to her cooperating teacher’s teaching style. As a result, in her lessons as an intern students received limited opportunities for reasoning and proving. Olive expressed dissatisfaction with this type of teaching and her desire to enact more proof-oriented practices. Our results show that the sociocultural components of the activity system (rules, community and division of labor), which were backgrounded in Olive’s teaching experience as a PST but prominent in her internship experience, influenced the outcome of engaging students with reasoning and proving. We discuss the importance of these sociocultural aspects as we examine how Olive navigated the tensions between the proof-related teaching practices she adopted in the capstone course and her teaching style during the internship. We highlight the importance of teacher educators considering the sociocultural aspects of teaching in supporting beginning teachers developing proof-related teaching practices. 

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4. Designing approximations of practice: The case of teacher noticing

   Bailey, Nina G; McCulloch, Allison W; Dick, Lara K; Lovett, Jennifer N; Yalman_Özen, D; Cayton, C (August 2024, Journal of Educational Research in Mathematics)

   As a core practice, teacher noticing of students' mathematical thinking is foundational to other teaching practices. Yet, this practice is difficult for preservice teachers (PSTs), particularly the component of interpreting students' thinking (e.g., Teuscher et al., 2017). We report on a study of our design of a specific approximation of teacher noticing task with the overarching goal of conceptualizing how to design approximations of practice that support PSTs' learning to notice student thinking in technology-mediated environments with a specific focus on interpreting students' mathematical thinking. Drawing on Grossman et al.'s (2009) Framework for Teaching Practice (i.e., pedagogies of practice), we provided decomposed opportunities for PSTs to engage with the practice of teacher noticing. We analyzed how our design choices led to different evidence of the PSTs' interpretations through professional development design study methods. Findings indicate that the PSTs frequently interpret what students understood. Yet, they were more challenged by interpreting what students did not yet understand. Furthermore, we found that providing lesson goals and asking the PSTs to respond to a prompt of deciding how to respond had the potential to elicit PSTs' interpretations of what the students did not yet understand. The study highlights the interplay between task design, prompt wording, and PSTs' interpretations, which emphasizes the complexity of developing teacher noticing 

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5. Developing adaptive expertise: Examining opportunities for reflective practices during a studio day cycle

   Olarte, T R; Greany, D; Hunter, U; Nemandoust, P; Rodriguez, M; Roberts, S A (November 2024, Proceedings of the forty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Kosko, K W; Caniglia, J; Courtney, S A; Zolfaghari, M; Morris, G A (Ed.)

   Engaging teachers in reflective practices is recognized as a crucial component of their adaptive expertise development. Drawing on this perspective of adaptive expertise development, we qualitatively examined how the design and structure of a Studio Day professional learning cycle afforded opportunities for reflective practice for secondary in-service mathematics teachers. We found that small group reflections, immediate reflections-on-action, and the use of videos afforded notable instances of reflective practices throughout the Studio Day Cycle that supported teachers’ development of adaptive expertise of equity-based, language-responsive teaching. We suggest that Studio Day Cycles are one avenue to better support in-service teachers’ development of adaptive expertise of mathematics language routines and multilingual learner core practices. 

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