The framework of professional noticing describes three components (attending, interpreting, and deciding) that allow teachers to better understand the thinking of their students. Via this method, teachers attend to their classroom by observing relevant cues from students, interpret these cues based on their knowledge of student development, and decide how best to proceed in their lesson. This study utilized an open‐response survey to collect data regarding the professional noticing skills, physics and mathematics content knowledge, and teaching experience of Science, Technology, Engineering, and Mathematics graduate students. Participants were given a physics and calculus problem to solve to assess their level of content knowledge and then watched a video‐based scenario of a teacher and student discussing the same problems. After, participants were prompted to answer questions corresponding with the attending, interpreting, and deciding components of professional noticing. We found significant results that suggest teaching experience alone is not enough to employ professional noticing skills when attending physics scenarios, and that possessing content knowledge has a positive impact on professional noticing ability, both overall and within the components.
This content will become publicly available on October 23, 2024
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 (
- NSF-PAR ID:
- 10483613
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- School Science and Mathematics
- Volume:
- 123
- Issue:
- 7
- ISSN:
- 0036-6803
- Format(s):
- Medium: X Size: p. 348-361
- Size(s):
- ["p. 348-361"]
- Sponsoring Org:
- National Science Foundation
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Abstract Background 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.
Results 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.Conclusion 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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null (Ed.)This workshop will focus on how to teach data collection and analysis to preschoolers. Our project aims to promote preschoolers’ engagement with, and learning of, mathematics and computational thinking (CT) with a set of classroom activities that engage preschoolers in a data collection and analysis (DCA) process. To do this, the project team is engaging in an iterative cycle of development and testing of hands-on, play-based, curricular investigations with feedback from teachers. A key component of the intervention is a teacher-facing digital app (for teachers to use with students on touch-screen tablets) to support the collaboration of preschool teachers and children in collecting data, creating simple graphs, and using the graphs to answer real-world questions. The curricular investigations offer an applied context for using mathematical knowledge (i.e., counting, sorting, classifying, comparing, contrasting) to engage with real-world investigations and lay the foundation for developing flexible problem-solving skills. Each investigation follows a series of instructional tasks that scaffold the problem-solving process and includes (a) nine hands-on and play-based problem-solving investigations where children answer real-world questions by collecting data, creating simple graphs, and interpreting the graphs and. (b) a teacher- facing digital app to support specific data collection and organization steps (i.e., collecting, recording, visualizing). This workshop will describe: (1) the rationale and prior research conducted in this domain, (2) describe an intervention in development focused on data collection and analysis content for preschoolers that develop mathematical (common core standards) and computational thinking skills (K-12 Computational Thinking Framework Standards), (3) demonstrates an app in development that guides teacher and preschoolers through the investigation process and generates graphs to answer questions (NGSS practice standards), (4) report on feedback from a pilot study conducted virtually in preschool classrooms; and (5) describe developmentally appropriate practices for engaging young children in investigations, data collection, and data analysis.more » « less
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In this article we describe secondary school practising teachers’ professional noticing expertise, which includes (a) attending to the details of students' written or verbal responses, (b) interpreting students' mathematical understandings, and (c) deciding how to respond to students based on their understandings, with a focus on algebraic-pattern generalisation. Quantitative results indicated that the majority of teachers in our study provided evidence that they could attend to the mathematical details of students' thinking. However, the practising secondary school teachers provided less evidence of interpreting students' understandings, and even less of deciding how to respond to students based on those understandings. We present qualitative trends to help mathematics professional developers prepare for the teachers they will support and discuss how these trends might influence work with secondary school practising teachers on noticing student thinking in pattern-generalisation tasks.more » « less
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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’.more » « less
