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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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Using an Analytic Model to Gauge the Potential of Innovative Pedagogies of Approximation in Mathematics Teacher Education.
To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, “How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers’ knowledge and practices for teaching?” In this paper, we offer a model called the Dual Action Cycles of Approximations of Practice for identifying the pedagogical practices made available to pre-service teachers within various approximations of practice and describe its use to empirically investigate the potential of StoryCircles—a facilitated process of collaboratively representing a lesson using a multimedia storyboarding tool. We illustrate ways the model was used to make observations of pre-service teachers during StoryCircles. A key feature of the model is that it provides a bi-focal perspective on both the preactive and interactive phases of teaching, which help bring into focus the interdependent nature of these two phases. We close by suggesting that the development of new forms of approximation needs to be accompanied by research frameworks capable of investigating the potential of these various innovations.
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- Award ID(s):
- 2201087
- PAR ID:
- 10530548
- Publisher / Repository:
- Mathematics teacher education and development
- Date Published:
- Journal Name:
- Mathematics teacher education and development
- Volume:
- 24
- Issue:
- 2
- ISSN:
- 1442-3901
- Page Range / eLocation ID:
- 57 - 85
- Subject(s) / Keyword(s):
- mathematics teacher education practice-based٠pedagogies approximations methodological model StoryCircles preactive interactive postactive
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper examines the learning process of facilitators engaging in a practice-based professional development (PD) called StoryCircles facilitator training. We observed the language used by facilitators when engaging in a demonstration1) of practice in which another facilitator leads a group of secondary mathematics teachers engaged in StoryCircles PD to consensus. Subsequently, facilitators simulate the role of teachers in StoryCircles PD to anticipate challenges they, as facilitators, may face. By analyzing facilitators' collective dialogue across the different practice-based approaches within the StoryCircles facilitator training, we highlight the adoption of others' roles within the PD context and facilitators' understanding of their own roles as a result. Findings indicate that the demonstration of a facilitator's practice was a context in which facilitators developed an understanding of their own responsibilities. Meanwhile, simulating the participants' practices allowed facilitators to better understand the role of the facilitator from the demonstration of practice, as they navigated the potential tensions arising from teachers adopting practices that facilitators deemed less desirable. This paper highlights how such situated practice-based learning experiences may be associated with facilitators' perceptions of their roles within the StoryCircles framework, offering insights into the intricacies of PD facilitator training and practice.more » « less
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This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth.more » « less
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Many teacher education models involve reflecting on teaching practice for the sake of improving it. Such reflection must be carefully structured to help practitioners identify and act upon significant opportunities for improvement (SOIs). Learning from SOIs requires the cognitive activities of noticing students’ mathematical thinking and its connection to instructional practice, along with an affective disposition to view sub-optimal teaching practices as learning opportunities. We draw upon existing literature and theory related to the notion of developing positive error cultures to identify design principles for helping teachers learn from their own sub-optimal practices rather than becoming discouraged by them. The design principles include experience-based learning, low-stakes settings, collaboration, process reflection, and exploration of disagreements. We then describe a mathematics teacher education environment incorporating the design principles. Examples of pre-service teachers’ work within the environment are analysed for possible patterns of learning from SOIs within a positive error culture. Based on these examples, a four-quadrant model to characterise teachers’ learning from SOIs is proposed. The four quadrants describe various outcomes related to recognising and resolving SOIs.more » « less
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Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
