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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’. 

A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although factorizations and divisibility in atomic domains have been systematically investigated for more than 30 years, the same aspects in the more general context of atomic semidomains have been considered just recently. Here we study subatomicity in the context of semidomains; that is, we study semidomains satisfying divisibility properties weaker than atomicity. We mostly focus on the Furstenberg property, which is due to P. Clark and motivated by the work of H. Furstenberg on the infinitude of primes, and the almost atomic and quasi-atomic properties, introduced by J. G. Boynton and J. Coykendall in the context of divisibility in integral domains. We investigate these three properties in the context of semidomains, paying special attention to whether they ascend from a semidomain to its polynomial and Laurent polynomial extensions. 

STEM integration holds significant promise for supporting students in making connections among ideas and ways of thinking that might otherwise remain “siloed.” Nevertheless, activities that integrate disciplines can present challenges to learners. In particular, they can require students to shift epistemological framing, demands that can be overlooked by designers and facilitators. We analyze how students in an 8th grade mathematics classroom reasoned about circles, across math and coding activities. One student showed evidence of shifting fluently between different frames as facilitators had expected. The dramatic change in his contributions gauge the demands of the activities, as do the contributions of other students, who appeared to work within different frames. Our findings have relevance for the design and facilitation of integrated STEM learning environments to support students in navigating such frame-shifts. 

We report the results of an investigation into the factors that affect students’ learning from calculus instructional videos. We designed 32 sets of videos and assessed students’ learning with pre- and post-video questions. We examined how students’ engagement and self-identified ways of interacting with the videos connected to their learning. Our results indicate that there is a complicated relationship between the student, curriculum, instructional practices, and the video content, and that the effectiveness of instructional videos may be contextualized by both instructional practices and the extent to which the understandings supported in the videos are compatible with the meanings promoted during instruction. 

Administrators, educators, and stakeholders have faced the dilemma of determining the most effective type of data for informing instruction for quite some time (Pella, 2015). While the type of standardized assessment a teacher gives during instruction is often set at the district or state level, teachers often have autonomy in the formative and summative assessments that serve as the day-to-day tools in assessing a student’s progress (Abrams et al., 2016). Choices about in-class assessment and instruction are building blocks towards a student’s success on standardized assessments. The purpose of this phenomenological qualitative study is to explore how 4th-8th grade math teachers’ preparation and instructional practices are influenced by the types of assessments administered to their students in one school. Research questions are as follows: (a) How do 4th-8th grade math teachers describe the math assessments they use? (b) How do 4th-8th grade math teachers adjust their instructional practices as a result of their students completing formative, summative, and standardized math assessments?