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Olanoff, D. (Ed.)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 frameshifts.more » « less

Olanoff, D. (Ed.)This 5year mathematics professional development project involves 27 elementary teachers being prepared and supported as Elementary Mathematics Specialists (EMSs) through completion of a university’s K5 Mathematics and Teacher Supporting & Coaching Endorsement programs, as well as participation in Professional Learning Communities and individual mentoring. Across the project, data are gathered to examine changes in mathematical content knowledge, instructional and coaching practices, beliefs, and teacher leader skills of the EMSs. Described here are Year 1 data from the participants, who have been identified as successful, experienced teachers, focusing on specific aspects of teacher effectiveness. The findings illuminate their classroom instructional practices, including those that are learnercentered and equitable, along with their early histories as learners of mathematics.more » « less

Olanoff, D. (Ed.)This report documents how one undergraduate student used setbased reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in number theory and geometry). We document the progression of Theo’s emergent setbased model from a modelof the truth of statements to a modelfor logical relationships. This constitutes some of the first evidence for how such logical concepts can be abstracted in this way and provides evidence for the viability of the learning progression that guided the instructional design.more » « less

Olanoff, D. (Ed.)In this paper, we describe the theory guiding the development of microlearning modules connecting noticing and equity in mathematics. Gutiérrez’s (2009) four dimensions of equity framework is used to inform the modules. The professional noticing of children’s mathematical thinking (Jacobs, Lamb, & Philipp, 2010) is also woven into the module development. We analyze data from preservice elementary teachers’ ideas about equity and responses to a video to inform our project and discuss the importance of making equity explicit in mathematics methods courses. Results indicate that preservice elementary teachers’ ideas of equity primarily fall into the dominant axes of access and achievement, but also show evidence of the critical axes of identity and power in responses to the classroom video.more » « less

Olanoff, D. (Ed.)The perspectives in mathematics education and special education are in tension when it comes to productive struggle. This study describes how struggle surfaced for the students and teacher/researcher in teaching experiments using learning trajectories with three students with diverse cognitive profiles. The students’ activity helps to illustrate the relationships between struggle and mathematics learning. I share how students’ struggle led to my own challenge in navigating tensions between mathematics education and special education. I consider how my focus on productive struggle without attending to cognitive difference reflected ableist thinking. Finally, I suggest implications of these observations for reframing productive struggle.more » « less


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 nonmathematics 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 mathematicsspecific 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 multiperspective 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 sixcamera 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’ partwhole 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 23 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’.more » « less

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