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1. Noticing mathematics from multiple perspectives

   Kosko, K. W. ; Ferdig, R. E. ; Gandolfi, E. ( January 2022 , Psychology of Mathematics Education - North America)

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

   A key aspect of professional noticing includes attending to students’ mathematics (Jacobs et al., 2010). Initially, preservice teachers (PSTs) may attend to non-mathematics specific aspects of a classroom before attending to children’s procedures and then, eventually their conceptual reasoning (Barnhart & van Es, 2015). Use of 360 videos has been observed to increase the likelihood that PSTs will attend to more mathematics-specific student actions. This is due to an increased perceptual capacity, or the capacity of a representation to convey what is perceivable in a scenario (Kosko et al., in press). A 360 camera records a classroom omnidirectionally, allowing PSTs viewing the video to look in any direction. Moreover, several 360 cameras can be used in a single room to allow the viewer to move from one point in the recorded classroom to another; defined by Zolfaghari et al., 2020 as multi-perspective 360 video. Although multiperspective 360 has tremendous potential for immersion and presence (Gandolfi et al., 2021), we have not located empirical research clarifying whether or how this may affect PSTs’ professional noticing. Rather, most published research focuses on the use of a single camera. Given the dearth of research, we explored PSTs’ viewing of and teacher noticing related to a six-camera multiperspective 360 video. We examined 22 early childhood PSTs’ viewing of a 4th grade class using pattern blocks to find an equivalent fraction to 3/4. Towards the end of the video, one student suggested 8/12 as an equivalent fraction, but a peer claimed it was 9/12. The teacher prompts the peer to “prove it” and a brief discussion ensues before the video ends. After viewing the video, PSTs’ written noticings were solicited and coded. In our initial analysis, we examined whether PSTs attended to students’ fraction reasoning. Although many PSTs attended to whether 8/12 or 9/12 was the correct answer, only 7 of 22 attended to students’ part-whole reasoning of the fractions. Next, we examined the variance in how frequently PSTs switched their camera perspective using the unalikeability statistic. Unalikeability (U2) is a nonparametric measure of variance, ranging from 0 to 1, for nominal variables (Kader & Perry, 2007). Participants scores ranged from 0 to 0.80 (Median=0.47). We then compared participants’ U2 statistics for whether they attended (or not) to students mathematical reasoning in their written noticing. Findings revealed no statistically significant difference (U=38.5, p=0.316). On average, PSTs used 2-3 camera perspectives, and there was no observable benefit to using a higher number of cameras. These findings suggest that multiple perspectives may be useful for some, but not all PSTs’. 

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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)

   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. Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

   https://doi.org/10.1186/s40594-020-00263-y  

   Magiera, Marta T. ; Zambak, Vecihi S. ( February 2021 , International Journal of STEM Education)

   This paper contributes to current discussions about supporting prospective teachers (PSTs) in developing skills of noticing students’ mathematical thinking. We draw attention to PSTs’ initial noticing skills (prior to instruction focused on supporting noticing) as PSTs engage in analyzing written artifacts of student work and video-records. We examined and compared PSTs’ noticing skills as they analyzed how students reason about, generalize, and justify generalizations of figural patterns given student written work and video records. We identified aspects of student thinking about generalizations and justifications, which PSTs addressed and interpreted. We also examined how PSTs respond to students as they analyze student thinking given written artifacts of student work or video-records of small group discussions, and we identified the foci of PSTs’ responding practice.

   Our data revealed that PSTs’ initial noticing skills of student generalizations and justifications differed while accounting for ways in which student thinking was externalized (written work or video-records). PSTs’ attending-and-interpreting and their responding practices were focused on mathematically significant aspects of student thinking to a greater extent in the context of analyzing written artifacts compared to video records. While analyzing students’ written work, PSTs demonstrated greater attention to ways in which students analyzed patterns, students’ generalization strategies, and justifications linked to an understanding of the pattern structure, compared to analyzing student thinking captured via videos.

   Our results document that without providing any intentional support for PSTs’ noticing skills, PSTs are more deliberate to focus on mathematically significant aspects of student thinking while analyzing written artifacts of student work compared to video-records. We believe that the analysis of student written work might demand from PSTs to be more analytical. While examining written representations, PSTs have to reconstruct students’ reasoning. Unlike the videos where the students tell or use gestures to express their thinking, written work provides fewer clues about student thinking. Thus, written work demands a deeper level of engagement from PSTs as they strive to understand student reasoning. Our study extends research on PSTs’ noticing skills by documenting differences in PSTs’ noticing in relation to the nature of artifacts of student work that PSTs analyze. Our work also adds to prior research on PSTs’ noticing by characterizing specific aspects of students’ thinking about pattern generalizations and justifications that PSTs address as they analyze student thinking and respond to students.

    

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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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