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1. 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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2. A framework to support teacher noticing of students' mathematical thinking in technology‐mediated environments

   https://doi.org/10.1111/ssm.12601  

   McCulloch, Allison W.; Dick, Lara K.; Lovett, Jennifer N. (October 2023, School Science and Mathematics)

   Abstract The practice of teacher noticing students' mathematical thinking often includes three interrelated components: attending to students' strategies, interpreting students' understandings, and deciding how to respond on the basis of students' understanding. This practice gains complexity in technology‐mediated environments (i.e., using technology‐enhanced math tasks) because it requires attending to and interpreting students' engagement with technology. Current frameworks implicitly assume the practice includes noticing the ways students use tools (including technology tools) in their work, but do not explicitly highlight the role of the tool. While research has shown that using these frameworks supports preservice secondary mathematics teachers (PSTs) developing noticing practices, it has also shown that PSTs largely overlook students' technology engagement when they are working on technology‐enhanced tasks (Journal for Research in Mathematics Education, 2010; 41(2):169–202). In this article, we describe our adaptation of Jacobs et al.'s framework for teacher noticing student mathematical thinking to include a focus on making students' technology‐tool engagement explicit when noticing in technology‐mediated environments, the Noticing in Technology‐Mediated Environments (NITE) framework. We describe the theoretical foundations of the framework, provide a video case example, and then illustrate how the framework can be used by mathematics teacher educators to support PSTs' noticing when students are working in technology‐mediated environments. 

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3. Teacher noticing of students’ mathematics as student centered

   Zolfaghari, M.; Heisler, J.; Kosko, K. W. (January 2021, Psychology of Mathematics Education - North America)

   Olanoff, D.; Johnson, K.; Spitzer, S. (Ed.)

   Attending to students’ actions and mathematical thinking is an important aspect of professional teacher noticing. In this paper, we used 360 videos as a medium to examine the relationship between preservice teachers’(PSTs) observed attending behaviors and their written noticing. Findings suggest that PSTs focusing on students, instead of the teacher, during class discussions provide more specified descriptions of children’s mathematical thinking. 

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4. The self as noticer: Supporting preservice teachers’ developing awareness.

   Rubin, E. B.; van Es, E. A. (January 2022, Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   Gaining insight into how one’s noticing shapes decision-making can enable a teacher to reflect on how they frame, interpret, and respond to classroom activity and disrupt the influence of dominant ideologies. Working in the context of teacher education, we conjectured that systematically analyzing and reflecting on their own noticing can enable preservice teachers (PSTs) in mathematics to develop more equitable practices. Using data from summative assignments in a course on advancing equitable teaching, we investigate how PSTs use lenses of equitable teaching to make sense of their noticing and develop conceptions of equity. Analysis reveals that PSTs engaged in meaningful reflection and adopted terms from the course but avoided discussing the sociopolitical dimensions of instruction. These findings have implications for course design and facilitation in the context of developing PSTs’ noticing for equity. 

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5. Preservice Secondary Mathematics Teachers’ Reflective Noticing from 360-degree Video Recordings of Their Own Teaching.

   Buchbinder, O.; Brisard, S.; Butler, R.; McCrone, S. (January 2021, Journal of technology and teacher education)

   The benefits of using video in teacher education as a tool for reflection and for developing professional expertise have long been recognized. Recent introduction of 360 video technology holds promise to extend these benefits as it allows prospective teachers to reflect on their own performance by considering the classroom from multiple perspectives. This study examined nine prospective secondary teachers’ (PSTs) noticing and self-reflection on the 360 recordings of their own teaching. The PSTs, enrolled in a capstone course Mathematical Reasoning and Proving for Secondary Teachers, taught a proof-oriented lesson to small groups of students in local schools while capturing their teaching with 360 video cameras. We analyzed the PSTs’ written comments on their video and reflection reports to identify the categories of noticing afforded by the 360 technology as well as the instances of PSTs’ learning. The results point to the powerful potential of 360 videos for supporting PSTs’ self-reflection and professional growth. 

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