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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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Secondary practising teachers’ professional noticing of students’ thinking about pattern generalisation
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.
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- Award ID(s):
- 1240127
- PAR ID:
- 10123633
- Date Published:
- Journal Name:
- Mathematics teacher education and development
- Volume:
- 21
- Issue:
- 1
- ISSN:
- 1442-3901
- Page Range / eLocation ID:
- 4 - 27
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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This study examined potential bias with respect to perceived gender and race in pre-service teachers’ professional noticing of children’s mathematical thinking. The goal of the study was to explore emerging connections between professional noticing and equity concerns in mathematics education and discover the extent to which such noticing may be influenced by a student’s race and gender. A sample of 151 preservice teachers participated, and our findings suggest that bias tends to emerge in the interpreting phase of professional noticing; however, such emergence was not statistically significant when compared across the perceived race and gender of the students.more » « less
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Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC’s collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular noticing framework (attending, interpreting, and responding), we analyzed the meetings of a PLC with six teachers as they individually presented lessons to be redesigned with a focus on the group’s shared commitment. Findings indicate three ways ideas were introduced that led to expansive responses, which suggests this analytic approach could identify ways in which a PLC can work towards new curricular decisions.more » « less
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