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1. Understanding Preservice Teachers’ Noticing of Online Teaching.

   Liu, J. ; Buchbinder, O. ; Weingarden, M. ( January 2022 , 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.)

   The rapid move to online teaching brought about by the global pandemic highlighted the need for the educational research community to develop new conceptual tools for characterizing these environments. In this paper, we propose a conceptual framework Instructional Technology Triangle (ITT) which extends the instructional triangle of teachers, students, and content to include technology as a mediating mechanism. We use the ITT framework to analyze noticing patterns in the written reflection of a prospective secondary teacher, Nancy, who, over the course of one semester taught online four lessons integrating reasoning and proof . The fluctuations in Nancy’s noticing patterns, in particular, with respect to technology, shed light on her trajectory of learning to teach online and the role of reflective noticing in this process. We discuss implications for teacher preparation and professional development. 

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2. 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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3. 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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4. Preservice Teachers’ Professional Noticing When Viewing Standard and 360 Video

   https://doi.org/10.1177/0022487120939544  

   Kosko, Karl W. ; Ferdig, Richard E. ; Zolfaghari, Maryam ( May 2021 , Journal of Teacher Education)

   Use of video as a representation of practice in teacher education is commonplace. The current study explored the use of a new format (360 video) in the context of preservice teachers’ professional noticing. Findings suggest that preservice teachers viewing 360 videos attended to more student actions than their peers viewing standard video. In addition, using a virtual reality headset to view the 360 videos led to different patterns in where preservice teachers looked in the recorded classroom, and to increased specificity of mathematics content from the scenario. Thus, findings and results support the use of 360 video in teacher education to facilitate teacher noticing. However, future research is needed to further explore this novel technology.

    

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5. 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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