Examining Student Thinking Through Teacher Noticing: Commentary

Philipp, Randolph A.; Fredenberg, Mike; Hawthorne, Casey

doi:10.1007/978-3-319-46753-5_7

Cited by 5 publications

(5 citation statements)

References 5 publications

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“…These studies put much emphasis on teachers' sense-making of student mathematical thinking, but do not synthesize on the teachers' mathematical thinking or knowledge involved in this sense-making. In the words of Philipp et al (2017):…”

Section: Prior Research and Research Questionmentioning

confidence: 99%

Making sense of student mathematical thinking: the role of teacher mathematical thinking

et al. 2022

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In mathematical whole-class discussions, teachers can build on various student ideas and develop these ideas toward mathematical goals. This requires teachers to make sense of their students' mathematical thinking, which evidently involves mathematical thinking on the teacher's part. Teacher sense-making of student mathematical thinking has been studied and conceptualized as an aspect of teacher noticing and has also been conceptualized as a mathematical activity. We combine these perspectives to explore the role of teacher mathematical thinking in making sense of student mathematical thinking. In this study, we investigated that role using videobased teacher discussions in a teacher researcher collaboration in which five Dutch high school mathematics teachers and one researcher developed discourse based lessons in cycles of design, enactment, and evaluation. In video-based discussions, they collaboratively reflected on whole-class discussions from the teachers' own lessons. We analyzed these discussions to explore the mathematical thinking that teachers articulated during sense-making of students' mathematical thinking and how teachers' mathematical thinking affected their sense-making. We found five categories concerning the role of teacher mathematical thinking in their sense-making: flexibility, preoccupation, incomprehension, exemplification, and projection. These categories show how both the content and the process of teacher mathematical thinking can support or impede their sense-making. In addition, we found that the teachers often did not articulate explicit mathematical thinking. Our findings suggest that sense-making of students' mathematical thinking requires teachers to (re-)engage in reflective thinking with regard to the mathematical content as well as the process of their own mathematical thinking.

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Section: Prior Research and Research Questionmentioning

confidence: 99%

Making sense of student mathematical thinking: the role of teacher mathematical thinking

et al. 2022

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“…Researchers have proposed several frameworks for thinking about and operationalizing the practice of teacher noticing (e.g., Jacobs et al, 2010Jacobs et al, , 2011Llinares, 2013;Mason, 2002;Philipp, Fredenberg, & Hawthorn, 2017;Sherin & Han, 2004; van Es, 2011). Common across the various conceptualizations of teacher noticing is the notion of intentional noticing, that is, the ability to identify important classroom events, connect them to teaching situations, and broader concepts related to teaching and student learning.…”

Section: Conceptual Foundations and Review Of The Related Literaturementioning

confidence: 99%

“…Jacobs et al (2010) described Professional Noticing of Students' Mathematical Thinking in terms of three connected practices: (1) attending to mathematical details in students' thinking and strategies, (2) interpreting students' mathematical understanding and reasoning with a focus on details of the specific strategies, and (3) deciding how to respond to students in a way that builds on students' thinking, understanding, and strategies. Philipp et al (2017) described that these noticing practices are "highly interrelated and often occur seemingly simultaneously" (Philipp et al, 2017, p. 114). Bautista, Brizuela, Glennie, and Caddle (2014) noted that attending to and interpreting student thinking are often inseparable.…”

Section: Conceptual Foundations and Review Of The Related Literaturementioning

confidence: 99%

“…While these research-based trajectories provide useful guides for mathematics teacher educators and tools for assessing PSTs' noticing skills, they offer limited information about content-specific mathematical ideas PSTs notice. Philipp et al (2017) argued that helping PSTs develop the practice of noticing student mathematical thinking requires knowledge of mathematical ideas that PSTs notice while analyzing student thinking in well-defined content domains. In this paper, we focus on PSTs' noticing of student pattern generalization and justifications.…”

Section: Research On Psts' Noticing Skillsmentioning

confidence: 99%

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Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Magiera

Zambak

2021

IJ STEM Ed

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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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“…To achieve this, teachers should attend to what students understand and do not understand; students' affect related to a mathematical problem; students' misconceptions; and mathematical aspects of students' work, e.g. different solutions to a problem (Philipp, Fredenberg & Hawthorne, 2017). The teacher noticing perspective foregrounds the teacher as the observer, while students' mathematical activity is the phenomenon that is observed.…”

Section: Theoretical Perspectivementioning

confidence: 99%

Shifts in Primary School Students' Mathematical Noticing When Analyzing With Numerical Equality

Freiman¹

2019

Proceedings of the 2019 AERA Annual Meeting

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A fruit of international collaboration between researchers from Canada and from Norway, the study focuses on dialectic shifts in primary students' (Grade 6) mathematical noticing when analyzing numerical equalities. Using Zankov's developmental model, we found four patterns of changes in students noticing, as result of resolution of contradictions between teachers' focus and student's focus which lead to an intensive co-construction of knowledge. These changes are critical for development active and independent learners capable to deal with complex and challenging tasks.

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Examining Student Thinking Through Teacher Noticing: Commentary

Cited by 5 publications

References 5 publications

Making sense of student mathematical thinking: the role of teacher mathematical thinking

Making sense of student mathematical thinking: the role of teacher mathematical thinking

Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Shifts in Primary School Students' Mathematical Noticing When Analyzing With Numerical Equality

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