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1. 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 (November 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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2. 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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3. Teacher noticing with 360 video

   Heisler, J.; Kosko, K. W. (January 2021, School science and mathematics)

   Herron, J. (Ed.)

   Teacher noticing is a crucial facet of math and science teacher education, with one goal being to shift preservice teachers’ (PSTs) noticing from teacher-centered to student-centered. In this study, we used 360 videos to examine PSTs’ choices of where to look in a classroom. We discuss differences in attending behavior of those PSTs who focused on the specific themes of teachers’ scaffolding and student engagement. 

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4. 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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5. The Value of Video Annotations: Noticing Different Modes and Aspects of Student Thinking

   https://doi.org/10.1111/ssm.70009  

   Walton, Margaret; Moon, Peter; Walkoe, Janet (January 2026, School Science and Mathematics)

   ABSTRACT The purpose of this study is to explore if and how different types of video annotations support pre‐service teachers (PSTs) in learning how to notice student multimodal, or verbal and non‐verbal, mathematical thinking. We implemented a video club intervention in a middle grades mathematics methods class. We asked PSTs to annotate classroom videos using two types of annotations. The first type was a pinning tool, which allowed the PSTs to mark video timestamps. The second type was a drawing tool, which allowed PSTs to draw directly on the video. We found that when PSTs used the pin tool, they largely attended to students' verbal thinking. In contrast, with the draw tool, PSTs began to attend to more of students' non‐verbal thinking. When PSTs attended to verbal student thinking, they mostly interpreted it in terms of students' disciplinary understanding. When PSTs attended to non‐verbal thinking, they reasoned about additional aspects of student thinking including affect, communication goals, and students' processes for learning the content. These findings have implications for PD design that supports teachers in expanding their multimodal noticing. 

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